Development and testing of two simple metaphor-free optimization algorithms for solving real-life nonconvex constrained and unconstrained engineering problems

Development and testing of two simple metaphor-free optimization algorithms for solving real-life nonconvex constrained and unconstrained engineering problems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Development and testing of two simple metaphor-free optimization algorithms for solving real-life nonconvex constrained and unconstrained engineering problems RAVIPUDI VENKATA RAO, RAVIKUMAR SHAH This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4970235/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Two simple yet powerful optimization algorithms, named the Best-Mean-Random (BMR) and Best-Worst-Random (BWR) algorithms, are developed and presented in this paper to handle both constrained and unconstrained optimization problems. These algorithms are free of metaphors and algorithm-specific parameters. The BMR algorithm is based on the best, mean, and random solutions of the population generated for solving a given problem, and the BWR algorithm is based on the best, worst, and random solutions. The performances of the proposed two algorithms are investigated by implementing them on 26 real-life nonconvex constrained optimization problems given in the Congress on Evolutionary Computation (CEC) 2020 competition, and comparisons are made with those of the other prominent optimization algorithms. The performances on 12 constrained engineering problems are also investigated, and the results are compared with those of very recent algorithms (in some cases, compared with more than 30 algorithms). Furthermore, computational experiments are conducted on 30 unconstrained standard benchmark optimization problems, including 5 recently developed benchmark problems with distinct characteristics. The results demonstrated the superior competitiveness and superiority of the proposed simple algorithms. The optimization research community may gain an advantage by adapting these algorithms to solve various constrained and unconstrained real-life optimization problems across various scientific and engineering disciplines. Operations Research Artificial Intelligence and Machine Learning Mechanical Engineering Optimization BMR algorithm BWR algorithm CEC 2020 Real-life nonconvex constrained problems Constrained engineering problems Unconstrained problems New benchmarks Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Population-based metaheuristic algorithms are adaptable and are used to solve complex optimization problems in a variety of domains. They are especially helpful when traditional optimization techniques—such as deterministic techniques or gradient-based methods—prove inappropriate because of certain factors such as large search spaces, nonlinearity, multimodality, or complex problem domains. Through a series of iterative procedures, the metaheuristic algorithms methodically investigate the solution space, improving the initial solution or solution population over time. Metaheuristics offer several advantages, such as versatility, gradient independence, global search capability, multiobjective problem-solving capability, exploration and exploitation capability, configurability, practical applicability. On the other hand, there are certain limitations of metaheuristics, such as the absence of a global optimum guarantee, difficulty in achieving convergence in the case of high-dimensional or complex solution spaces, the requirement of tuning common control parameters, and the algorithm-specific parameters, black-box nature, etc. Nearly all algorithms that rely on population information are probabilistic in nature and necessitate common parameters such as the number of generations and the size of the population. With a few exceptions (e.g., the Jaya algorithm, and Rao algorithms), each algorithm needs its own set of control parameters apart from common parameters. Inadequate adjustment of algorithm-specific parameters results in a locally optimal solution or escalates the computing effort. The body of literature on metaheuristics has expanded significantly in recent years. Recent review papers on metaheuristics give a clear idea to readers about various metaheuristics and their working principles, applications, limitations, future directions, etc. To date, more than 600 metaheuristic algorithms have been developed, with more than 400 of them being developed during the past ten years. Many new optimization algorithms based on metaphors are released each month, with the authors claiming that their algorithms are “novel” and are better than those of the other algorithms. A profusion of "novel" population-based metaheuristic algorithms, inspired by metaphors based on diverse natural phenomena, including floods, disasters, animals (animals on earth as well as in the ocean), birds, insects, reptiles, fishes, viruses, matings, humans, human activities, societies, cultures, planets, heavenly bodies, plants, trees, swamps, deserts, musical instruments, sports, household items, physics, chemistry, mathematics, etc. has emerged in the last 15 years. The developers of these algorithms make an analogy of the equations proposed by them with any of the metaphors related to the phenomena mentioned above and try to justify the analogy. Ironically, in almost all such algorithms, there is no real relation between the phenomena and the equations they use. This kind of research may be considered risky and detrimental to the development of the optimization field. Several researchers have questioned the contentious subject of the exponential increase in new algorithms. Regretfully, a sizeable portion of the scientific community resorted to believing that the development of so-called “novel” optimization algorithms based on ever more bizarre analogies (in the name of metaphors) can advance science. Arguably, the most dubious features of these techniques can be found in the literature, such as meaningless and unfair metaphors, poor experimental validation and comparison, and lack of novelty. Regretfully, over the past 10 years, we have seen the emergence of a new trend in which hundreds of metaphor-based metaheuristics have been proposed. These metaheuristics incorporate the greatest variety of natural, man-made, social, and sometimes even paranormal occurrences and actions, and their authors have not provided a clear rationale for their proposals other than the desire to publish their papers. Sörensen [1] opined that the current research trajectory in metaheuristics threatens to deviate from a rigorous scientific approach, and it appears that no concept is too ridiculous to serve as motivation to launch yet another metaheuristic algorithm. Sörensen et al. [2] described the development of metaheuristics over the course of five separate eras, beginning well before the name was coined and concluding far into the future. They commented that a sizable portion of the research community has fooled itself into believing that the development of so-called "novel" approaches that rely on ever-more bizarre analogies may advance science. By the time these metaphor-based ideas are suppressed, they expect that the scientific community will suffer great injury, even though science will ultimately win out. Campelo and Aranha [3] compiled a long list of "novel" algorithms and showed that developing a metaheuristic that approximates a real-world process is a fruitless exercise and should not be added to the corpus of scientific literature. Moreover, when metaheuristics are used, the mathematical models obtained from metaphors are often modified or omitted since they result in subpar implementations. Aranha et al. [4] opined that the emergence of publications that suggest metaphor-based algorithms that are influenced by often absurd processes that are not optimized at all show poor scientific housekeeping and reflect poorly on the metaheuristic research community. A large number of metaphor-based metaheuristics include three (nearly wholly) distinct entities: the metaphor, the mathematical model "derived" from the metaphor, and the algorithm itself [5,6]. Rao [7] expressed concern that the flood of metaphor-based metaheuristics might threaten the optimization field's scientific viability and suggested that rather than concentrating on creating metaphor-based algorithms, researchers should concentrate on creating simple optimization strategies that can solve complex optimization problems. The primary metaheuristic techniques and their diversification mechanisms were explained by Sarhani et al. [8]. They suggested a new classification for the current initialization techniques after reviewing and analyzing them. Rajwar et al. [9] reviewed approximately 540 metaheuristics and provided statistical information. The authors raised an important question: If the search properties of an optimization algorithm are altered or almost identical to those of current methods, can it still be considered "novel"? The authors categorized metaheuristics based on the number of control parameters, which is a new taxonomy in the field. Salgotra et al. [10] classified metaheuristics as physics-based, human-based, swarm-based, or evolutionary-based. A large number of metaphor-based algorithms, including some bizarre metaphors, were mentioned in the classification. Different benchmark test functions related to existing metaheuristics were reviewed. It can be observed from the metaheuristics listed under each category of classification that the researchers have touched on almost all the “nature inspirations” and are trying to make analogies irrespective of whether that metaphor has anything to do with the equations shown by them. Sharma and Raju [11] presented a comprehensive overview of metaheuristic optimization algorithms and the classification of benchmark test functions Velasco et al. [12] examined 111 recent articles that proposed "new, hybrid, or improved optimization algorithms". A significant observation that was mostly ignored by the academics developing new algorithms was that only 43% of the reviewed articles referenced the no free lunch (NFL) theorem. The black widow optimization and coral reef optimization metaheuristics were examined to show how algorithms with little innovation can mistakenly be regarded as novel frameworks. These algorithms were found to be nothing more than inadequate combinations of various evolutionary operators. Benaissa et al. [13] explained the core ideas and elements of metaheuristics, focusing on the utilization of search references and the careful balancing of exploration and exploitation. Although intuitively appealing, metaphor-based optimization algorithms have generated controversy because of possible oversimplification and inflated expectations, and the names of the algorithms do not always correspond to the guiding ideas or methods they use. Sometimes, researchers use fashionable or catchynames, but these names cannot accurately represent the algorithm's originality or uniqueness. Developing straightforward optimization approaches that can solve complex optimization problems more effectively would be a better course of action for researchers than trying to develop metaphor-based algorithms. In light of this, the objectives of the work presented in this paper are listed below. To prove that there is no need to depend on metaphors to develop optimization algorithms. To develop two simple basic metaphor-free and algorithm-specific parameter-free optimization algorithms. To demonstrate the convergence efficiency of the proposed algorithms and the results for real-life nonconvex constrained optimization problems (e.g., CEC 2020 problems). To test the performance of the proposed algorithms on 12 constrained engineering problems that have been recently tested by many of the latest algorithms (in some cases, more than 30 algorithms). To demonstrate how well the proposed algorithms perform on a range of standard unconstrained optimization problems, including the most recent benchmark functions, each with unique characteristics. The next section explains the proposed optimization algorithms. 2. Proposed best-mean-random (BMR) and best-worst-random (BWR) algorithms 2.1 BMR algorithm Let f(x ), the objective function, be the function to be minimized or maximized. Assume that there are ' m ' design variables and ' n ' candidate solutions (i.e., population size, k = 1,2, ..., n ) for every iteration i . The candidate with the best overall performance receives the best value of f ( x ) (i.e., f ( x ) best ), while the candidate with the poorest overall performance obtains the worst value of f ( x ) (i.e., f ( x ) worst ) in all candidate solutions. Let r 1 , r 2 , r 3 , and r 4 be four random numbers. Each can take any value randomly from 0 to 1, and U j and L j are the upper and lower values of the j th variable, respectively. Additionally, let V j,k,i represent the j th variable's value for the k th candidate in the i th iteration, and T is a factor that randomly takes either 1 or 2 during an iteration. r 1 , r 2 , r 3 , r 4 ∼ Uniform(0, 1) T ∼ Choice({1, 2}) If r 4 > 0.5, the value of V j,k,i changes according to Eq. (1). V' j,k,i = V j,k,i + r 1,j,i ( V j,best,i - T * V j.mean,i ) + r 2,j,i ( V j,best,i - V j,random,i ) (1) Otherwise, V' j,k,i = R = U j – (U j - L j )r 3 (2) The modified value of V j,k,i is V' j,k,i . The best value of f ( x ) during the i th iteration is V j,best,i for the j th variable. The mean value of the j th variable is V j.mean,i during the i th iteration. The randomly picked up value, during the i th iteration, for the j th variable is V j,random,i . The exploitation and exploration capabilities of the BMR algorithm are explained in Eqs. (1) and (2). 2.2 BWR algorithm With the same description of the terms given in subsection 2.1 , the BWR algorithm is described below. r 1 , r 2 , r 3 , r 4 ∼ Uniform(0, 1) T ∼ Choice({1, 2}) If r 4 > 0.5, the value of V j,k,I changes according to Eq. (3). V' j,k,i = V j,k,i + r 1,j,i ( V j,best,i - T * V j,random,i ) - r 2,j,i ( V j,worst,i - V j,random,i ) (3) otherwise, V' j,k,i = R = U j – (U j - L j )r 3 (4) The modified value of V j,k,i is V' j,k,i . The best value of f ( x ) during the i th iteration is V j,best,i for the j th variable. The worst value of f ( x ) during the i th iteration for the j th variable is V j,worst,i . The randomly picked up value of j th variable during the i th iteration is V j,random,i . The exploitation and exploration capabilities of the BWR algorithm are explained in Eqs. (3) and (4). It can be noted that both the BMR and BWR algorithms are not based on any metaphors. Figure 1 shows the flow diagram of the proposed BMR and BWR optimization algorithms. 3. Illustration of the functionality of the proposed algorithms 3.1. Illustration of the functionality of the BMR algorithm To illustrate the functionality of the BMR algorithm, we explore an unconstrained standard benchmark function, Sphere. The objective function is to determine the values of x i that minimize the sphere function. Minimize, This benchmark function's known solution is 0 for all x i values of 0. To illustrate the BMR algorithm, let us use the following: two design variables, x 1 and x 2 ; an iteration serving as the termination criterion; and a population size of five (i.e., five solutions). Table 1 shows the values of the objective function corresponding to the initial population, which is created at random within the bounds of the variables. Since f(x) is a minimization function, the best solution is defined as having the lowest value, and the worst solution is defined as having the greatest value. Table 1 Randomly generated initial solutions. Solution x 1 x 2 f ( x ) Status 1 -5 18 349 2 14 33 1285 worst 3 30 -6 936 4 7 -12 193 best 5 -18 8 388 Mean of x 1 = 5.6 Mean of x 2 = 8.2 Table 1 clearly shows that solution 4 offers the best solution, while solution 2 offers the worst solution. Eq. (1) is used to determine the new values of the variables for x 1 and x 2 and are included in Table 2 , considering random numbers r 1 = 0.30 and r 2 = 0.10 for x 1 and r 1 = 0.60 and r 2 = 0.30 for x 2 . Assuming T = 1 and random interaction with solution 5, the new values of x 1 and x 2 for solution 1 are computed as follows during the first iteration. V' 1,1,1 = V 1,1,1 + r 1,1,1 ( V 1,4,1 − 1*Mean of x 1 ) + r 2,1,1 ( V 1,4,1 - V 1,5,1 ) = -5 + 0.30 (7 − 1*5.6) + 0.10 (7- (-18)) = -2.08 V' 2,1,1 = V 2,1,1 + r 1,2,1 ( V 2,4,1 – 1*Mean of x 2 ) + r 2,2,1 ( V 2,4,1 - V 2,5,1 ) = 18 + 0.60 (-12- 1*8.2) + 0.30 (-12-8) = -0.12 The new values of x 1 and x 2 for the remaining solutions are determined similarly. The new values of x 1 and x 2 , along with the corresponding values of the objective function, are displayed in Table 2 . For illustration purposes, solutions 2, 3, 4, and 5 are taken into consideration for their random interactions with 4, 2, 1, and 3, respectively. Table 2 New values of x 1 , x 2 and f(x) during the first iteration of the BMR algorithm. Solution x 1 x 2 f ( x ) 1 -2.08 -0.12 4.3408 2 14.42 20.88 643.9108 3 29.72 -31.62 1883.103 4 8.62 -33.12 1171.239 5 -19.88 -5.92 430.2608 After the values of f(x) are compared in Tables 1 and 2 , Table 3 is prepared which contains the updated values of f(x) based on the fitness comparison. The first iteration of the BMR algorithm is complete. Table 3 Updated values of x 1 and x 2 , and f(x) after the first iteration of the BMR algorithm. Solution x 1 x 2 f ( x ) Status 1 -2.08 -0.12 4.3408 best 2 14.42 20.88 643.9108 3 30 -6 936 worst 4 7 -12 193 5 -18 8 388 Table 3 illustrates that solution 1 is the best, while solution 3 is the worst. Additionally, it is evident that in just one iteration, the objective function's value drops from 193 to 4.3408. If the number of iterations is increased, the known value of the objective function, or 0, can be obtained in a few iterations. It is important to keep in mind that in cases of maximization problems, the highest value of the objective function is referred to as the best value, and calculations must be performed accordingly. This means that problems involving either minimization or maximization can be handled using the proposed BMR algorithm. 3.2. Illustration of the functionality of the BWR algorithm The same sphere function is considered to illustrate the functioning of the BWR algorithm. For a fair comparison, the same random number, the same T , and the same random interactions are considered. The values are calculated accordingly. Assuming T = 1 and random interaction with solution 5, the new values of x 1 and x 2 for solution 1 are computed as follows during the first iteration. V' 1,1,1 = V 1,1,1 + r 1,1,1 ( V 1,4,1 − 1* V 1,5,1 ) - r 2,1,1 ( V 1,2,1 - V 1,5,1 ) = -5 + 0.30 (7 − 1*(-18)) − 0.10 (14- (-18)) = -0.70 V' 2,1,1 = V 2,1,1 + r 1,2,1 ( V 2,4,1 – 1* V 2,5,1 ) + r 2,2,1 ( V 2,4,1 - V 2,5,1 ) = 18 + 0.60 (-12- 1*8) -0.30 (33 − 8) = -1.50 The new values of x 1 and x 2 for the remaining solutions are determined similarly. The new values of x 1 and x 2 , along with the corresponding values of the objective function, are displayed in Table 4 . Table 4 New values of x 1 and x 2 , and f(x) during the first iteration of the BWR algorithm. Solution x 1 x 2 f ( x ) 1 -0.7 -1.5 2.74 2 13.3 19.5 557.14 3 27.9 -33 1867.41 4 8.7 -34.5 1265.94 5 -23.3 -7.3 596.18 After comparing the values of (x) in Tables 1 and 4 , Table 5 is prepared, and it contains the updated values of f(x) based on fitness comparison. The first iteration of the BWR algorithm is complete. Table 5 Updated values of x 1 and x 2 , and f(x) after the first iteration of the BWR algorithm. Solution x 1 x 2 f ( x ) Status 1 -0.7 -1.5 2.74 best 2 13.3 19.5 557.14 3 30 -6 936 worst 4 7 -12 193 5 -18 8 388 Table 5 illustrates that solution 1 is the best solution, while solution 3 is the worst. Additionally, it is evident that in just one iteration, the objective function's value drops from 193 to 2.74. The known value of the objective function, or 0, can be reached in a few iterations if the number of iterations is increased. Problems involving either minimization or maximization can be handled by the BWR. This illustration pertains to an unconstrained optimization problem. Nonetheless, the same procedures can be employed when dealing with constrained optimization problems. The primary distinction is that in the constrained optimization problem, each violation of a constraint is handled by a penalty function that is applied to the objective function. The experimentation of the proposed algorithms on 26 real-life nonconvex constrained benchmark problems given in CEC 2020 [ 14 ] is explained in the following section. 4. Experiments on real-life nonconvex constrained benchmark problems of CEC 2020 To demonstrate and prove the effectiveness of the BMR and BWR algorithms, 26 real-life constrained optimization problems (COPs) from the CEC 2020 competition [ 14 ] are considered. A detailed description of the 26 COPs is available in [ 14 ] and hence is not provided here for space reasons. Table 6 presents the COPs, the number of decision variables, the number of equality constraints, and the number of inequality constraints. Table 6 Details of 26 nonconvex COPs and the associated numbers of decision variables and constraints. COP designation No. of decision variables No. of equality constraints No. of inequality constraints Process synthesis and design problems RC08 2 0 2 RC09 3 1 1 RC10 3 0 3 RC11 7 4 4 RC12 7 0 9 RC13 5 0 3 RC14 10 0 10 Mechanical engineering problems RC15 7 0 11 RC16 14 0 15 RC17 3 0 3 RC18 4 0 4 RC19 4 0 5 RC20 2 0 3 RC21 5 0 7 RC22 9 1 10 RC23 5 3 8 RC24 7 0 7 RC25 4 0 7 RC26 22 0 86 RC27 10 0 3 RC28 10 0 9 RC29 4 0 1 RC30 3 0 8 RC31 4 1 1 RC32 5 0 6 RC33 30 0 30 The decision variables, objective functions, and constraints of the 26 considered nonconvex COPs are available in [ 14 ]. Kumar et al. [ 14 ] presented 57 COPs belonging to different domains, such as industrial chemical processes (RC01-RC07), process synthesis and design problems (RC08-RC14), mechanical engineering problems (RC15-RC33), power system problems (RC34-RC44), power electronics problems (RC45-RC50), and livestock feed ratio problems (RC51-RC57), and presented the results of the application of the improved unified differential evolution algorithm (IUDE) [ 15 ], matrix adaptation evolution strategy (εMAgES) [ 16 ], and LSHADE44 with an improved 𝜖 constraint-handling method (iLSHADE ε ) [ 17 ]. Gurrola-Ramos [ 18 ] used the COLSHADE algorithm, and Sallam et al. [ 19 ] used the multi-operator differential evolution (EnMODE) algorithm to solve the same COPs. Rao and Pawar [ 20 ] applied an improved Rao (I-Rao) algorithm for solving mechanical engineering problems (RC15-RC33) and compared their results with those given in [ 14 ], [ 18 ], and [ 19 ] and reported good performance of the I-Rao algorithm. In the present work, to demonstrate and prove the effectiveness of the BMR and BWR algorithms, the COPs numbered RC08-RC33 are attempted because of the familiarity of the authors with these problems . These problems have decision variables ranging from 2 to 30, with inequality constraints ranging from 1 to 30 and equality constraints ranging from 0 to 4. All algorithms (i.e., IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, I-Rao, BMR, and BWR) use the same termination criterion based on the number of decision variables to end the optimization process. A set number of function evaluations are permitted throughout the optimization process. When the maximum number of function evaluations is reached, the algorithm’s optimization process concludes, and the optimal solution is returned. For every COP, the maximum function evaluations are determined using the following criteria [ 14 ]. Maximum function evaluations = 1 x 10 5 if D ≤ 10 = 2 x 10 5 if 10 < D ≤ 30 In the present work, MATLAB r2024a was used to implement the BMR and BWR algorithms to evaluate the COPs. A laptop with a Microsoft Windows 10 operating system with AMD Ryzen 7- CPU and 24 GB RAM was used for the computational experiments. Table 7 presents the results of the application of the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, BMR, and BWR algorithms to the process synthesis and design problems after 25 runs of each algorithm. A static penalty method is used to address constraint violations. For example, in the case of the minimization of a COP designated RC08, which has two constraints g 1 (x) and g 2 (x) , the penalized value of f(x) is calculated as, penalized f(x) = f(x) + 10* g 1 (x) 2 + 10*g 2 (x) 2 . In the case of maximization of a COP designated as RC26, which has 9 constraints from g 1 (x) to g 9 (x) , the penalized value of f(x) is calculated as, Penalized f(x) = f(x) -10* g 1 (x) 2 - 10*g 2 (x) 2 - 10*g 3 (x) 2 -……….- 10*g 8 (x) 2 - 10*g 9 (x) 2 . A similar approach is followed in the case of equality constraints. For example, in the case of minimization of RC09, which has an inequality constraint g 1 (x) and an equality constraint h 1 (x) , the penalized value of f(x) is calculated as, penalized f(x) = f(x) + 10* g 1 (x) 2 + 10*h 1 (x) 2 . If there is no constraint violation, then there will not be any penalty, and the penalized f(x) = f(x) . It may be noted here that the user can decide which type of penalty can be imposed for constraint violation. The statistical results are expressed in terms of “best” “median,” “mean,” “worst,” “standard deviation,” “feasibility rate (FR),” “mean constraint violation (MV),” and “success rate (SR)” in Table 7 . The FR is defined as the ratio of total runs to the number of runs in which at least one workable solution is found within the maximum function evaluations. The SR represents the ratio between the total number of runs and the number of viable solutions (x) that an algorithm was able to obtain, meeting f(x) − f (x∗) ≤ 10 − 8 within the maximum function evaluations. The equation for computing the MV is available in [ 14 ]. Including all the results of the IUDE, εMAgES, iLSHADE ε , COLSHADE, and EnMODE algorithms in Table 7 for the RC08-RC14 problems will, unfortunately, increase the similarity content of this paper (even though such inclusion will provide much clarity). Hence, for illustration, the results of all the algorithms are shown for the RC08 and RC09 problems only. For the remaining problems (i.e., RC10-RC14), only the results of the BMR and BWR algorithms are shown. The bold values in Table 7 indicate better values compared to the corresponding values given by the other algorithms. Table 7 Statistical results of the application of different algorithms for the RC08-RC14 problems. Problem Algorithm Best Median Mean Worst Std. Dev. FR MV SR RC08 IUDE 2.00E + 00 2.00E + 00 2.00E + 00 2.00E + 00 6.41E-17 100 0 100 εMAgES 2.00E + 00 2.00E + 00 1.99E + 00 1.29E + 00 1.52E-01 96 4.58E-03 64 iLSHADE ε 2.00E + 00 2.00E + 00 2.00E + 00 2.00E + 00 0 100 0 100 COLSHADE 2.00E + 00 2.00E + 00 2.00E + 00 2.00E + 00 0 100 --- --- EnMODE 2.00E + 00 2.00E + 00 2.00E + 00 2.00E + 00 0 100 --- --- BMR 1.625E + 00 1.625E + 00 1.625E + 00 1.625E + 00 0 100 0 100 BWR 1.625E + 00 1.625E + 00 1.625E + 00 1.625E + 00 0 100 0 100 RC09 IUDE 2.56E + 00 2.56E + 00 2.56E + 00 2.56E + 00 1.36E-15 100 0 100 εMAgES 2.56E + 00 2.56E + 00 2.55E + 00 1.93E + 00 2.70E-01 92 1.15E-02 92 iLSHADE ε 2.56E + 00 2.56E + 00 2.56E + 00 2.56E + 00 1.46E-07 100 0 100 COLSHADE 2.557655 2.557655 2.557655 2.557655 0 100 --- --- EnMODE 2.5577E + 00 2.5577E + 00 2.5577E + 00 2.5577E + 00 1.3597E-15 100 --- --- BMR 2.489216E + 00 2.489216E + 00 2.489216E + 00 2.489216E + 00 9.0649E-16 100 0 100 BWR 2.489216E + 00 2.489216E + 00 2.489216E + 00 2.489216E + 00 0 100 0 100 RC10 BMR 8.826130E-01 8.826130E-01 8.826130E-01 8.826130E-01 1.1331E-16 100 0 100 BWR 8.826130E-01 8.826130E-01 8.826130E-01 8.826130E-01 0 100 0 100 RC11 BMR 9.804858E + 01 9.804858E + 01 9.804858E + 01 9.804858E + 01 2.9724E-14 100 0 100 BWR 9.804858E + 01 9.804858E + 01 9.804858E + 01 9.804858E + 01 0 100 0 100 RC12 BMR 2.900126E + 00 2.900126E + 00 2.900126E + 00 2.900126E + 00 4.0539E-16 100 0 100 BWR 2.900126E + 00 2.900126E + 00 2.900126E + 00 2.900126E + 00 0 100 0 100 RC13 BMR 22586.82857 22586.82857 22586.82857 22586.82857 3.713E-12 100 0 100 BWR 22586.82857 22586.82857 22586.82857 22586.82857 3.713E-12 100 0 100 RC14 BMR 28336.49265 28336.49265 28336.49265 28336.49265 1.1647E-11 100 0 100 BWR 28336.49265 28336.49265 28336.49265 28336.49265 1.2755E-11 100 0 100 The results of IUDE, εMAgES, and iLSHADEε are taken from [14]; COLSHADE results from [18]; and EnMODE results from [19]; −−−: not available; The bold numbers denote better values in comparison to the similar values provided by the other algorithms . Figure 2 displays the convergence behavior of the BMR and BWR algorithms for the RC08–RC14 functions. The 0e + 00 shown at the origin of the graphs indicates the iteration during which the population is randomly generated. Complete convergence until the end is not clearly visible in the graphs in certain cases (because of the scale step size taken on the x- and y-axes); however, the readers may understand that the convergence occurred at the mean function values shown in Table 7 . To further test the proposed BMR and BWR algorithms, 19 nonconvex COPs are tested for the mechanical engineering of RC15-RC33. Computational experiments are carried out to evaluate the performances of the BMR and BWR algorithms, and the performances are compared with those of the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, and I-Rao algorithms. A common platform is offered by maintaining the same function evaluations for all the algorithms for comparison. As a result, the consistency of the comparison is maintained while comparing the performances of the BMR and BWR algorithms with those of the other optimization algorithms Table 8 shows the results, and these results include the results of the I-Rao algorithm [ 20 ] for comparison in addition to the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, BMR, and BWR algorithms. However, including all the results of the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, and I-Rao algorithms in Table 8 for the RC15-RC33 problems will, unfortunately, increase the plagiarism content of this paper (even though such inclusion will provide much clarity). Hence, for illustration, the results of all the algorithms are shown for the RC15 problem only. For the remaining problems (i.e., RC16-RC33), only the results of the BMR and BWR algorithms are shown. Table 8 Statistical results of the application of different algorithms for the RC15-RC33 problems. Problem Algorithm Best Median Mean Worst Std. Dev. FR MV SR RC15 IUDE 2.99E + 03 2.99E + 03 2.99E + 03 2.99E + 03 4.64E-13 100 0 100 ε MAgES 2.99E + 03 2.99E + 03 2.99E + 03 2.99E + 03 4.64E-13 100 0 100 iLSHADE ε 2.99E + 03 2.99E + 03 2.99E + 03 2.99E + 03 4.64E-13 100 0 100 COLSHADE 2994.4245 2994.4245 2994.4245 2994.4245 4.5475E-13 100 --- --- EnMODE 2.9944E + 03 2.9944E + 03 2.9944E + 03 2.9944E + 03 4.6412E-13 100 --- --- I-Rao 2.9944E + 03 2.9944E + 03 2.9944E + 03 2.9944E + 03 4.6412E − 13 100 0 100 BMR 2.835522E + 03 2.835522E + 03 2.835522E + 03 2.835522E + 03 9.51172E-13 100 0 100 BWR 2.835522E + 03 2.835522E + 03 2.835522E + 03 2.835522E + 03 9.28249E-13 100 0 100 RC16 BMR 3.2107853E-02 3.2107853E-02 3.2107853E-02 3.2107853E-02 8.13657E-18 100 0 100 BWR 3.2107853E-02 3.2107853E-02 3.2107853E-02 3.2107853E-02 1.4164E-18 100 0 100 RC17 BMR 1.2647549E-02 1.2647549E-02 1.2647549E-02 1.2647549E-02 9.36858E-19 100 0 100 BWR 1.2647549E-02 1.2647549E-02 1.2647549E-02 1.2647549E-02 1.00154E-18 100 0 100 RC18 BMR 4.840545E + 02 4.840545E + 02 4.840545E + 02 4.840545E + 02 1.14277E-13 100 0 100 BWR 4.840545E + 02 4.840545E + 02 4.840545E + 02 4.840545E + 02 1.16031E-13 100 0 100 RC19 BMR 1.655108E + 00 1.655108E + 00 1.655108E + 00 1.655108E + 00 1.01349E-16 100 0 100 BWR 1.655108E + 00 1.655108E + 00 1.655108E + 00 1.655108E + 00 2.26623E-16 100 0 100 RC20 BMR 1.742761E + 02 1.742761E + 02 1.742761E + 02 1.742761E + 02 2.90078E-14 100 0 100 BWR 1.742761E + 02 1.742761E + 02 1.742761E + 02 1.742761E + 02 2.90078E-14 100 0 100 RC21 BMR 2.3523981E-01 2.3523981E-01 2.3523981E-01 2.3523981E-01 1.13312E-16 100 0 100 BWR 2.3523981E-01 2.3523981E-01 2.3523981E-01 2.3523981E-01 0 100 0 100 RC22 BMR 5.25768707E-01 5.25768707E-01 5.25768707E-01 5.25768707E-01 2.26623E-16 100 0 100 BWR 5.25768707E-01 5.25768707E-01 5.25768707E-01 5.25768707E-01 0 100 0 100 RC23 BMR 8.324755E + 00 8.324755E + 00 8.324755E + 00 8.324755E + 00 5.20221E-06 100 0 100 BWR 8.324755E + 00 8.324755E + 00 8.324755E + 00 8.324755E + 00 0 100 0 100 RC24 BMR 2.543785555 2.543785555 2.543785555 2.543785555 1.75778E-14 100 0 100 BWR 2.543785555 2.543785555 2.543785555 2.543785555 1.75778E-14 100 0 100 RC25 BMR 1.35696115E + 02 1.652756328E + 02 1.621518179E + 02 1.8018240591E + 02 1.347590917E + 01 100 0 100 BWR 1.244136094E + 02 1.244136094E + 02 1.244136094E + 02 1.244136094E + 02 1.35006E-11 100 1.320932E-03 100 RC26 BMR 6.97503E + 01 7.77871E + 01 7.809039E + 01 8.66574E + 01 0.5346E + 01 0 0 0 BWR 3.625240118E + 01 3.625240118E + 01 3.625240118E + 01 3.625240118E + 01 2.7030667E-02 68 1.3694574E-02 0 RC27 BMR 1.296992551E + 02 1.296992551E + 02 1.296992551E + 02 1.296992551E + 02 1.80034E-10 100 0 100 BWR 1.296992551E + 02 1.296992551E + 02 1.296992551E + 02 1.296992551E + 02 6.46034E-14 100 0 100 RC28 BMR 1.46E + 04 1.46E + 04 1.46E + 04 1.46E + 04 2.8002E-12 100 0 100 BWR 1.46E + 04 1.46E + 04 1.46E + 04 1.46E + 04 1.4002E-18 100 0 100 RC29 BMR 1.010989E + 06 1.010989E + 06 1.010989E + 06 1.010989E + 06 1.18816E-10 100 0 100 BWR 1.010989116E + 06 1.010989116E + 06 1.010989116E + 06 1.010989116E + 06 0 100 0 100 RC30 BMR 2.562333478E + 00 2.562333478E + 00 2.562333478E + 00 2.562333478E + 00 9.06493E-16 100 0 100 BWR 2.562333478E + 00 2.562333478E + 00 2.562333478E + 00 2.562333478E + 00 9.06493E-16 100 0 100 RC31 BMR 0 0 0 0 0 100 0 100 BWR 0 0 0 0 0 100 0 100 RC32 BMR -3.21641E + 04 -3.21641E + 04 -3.21641E + 04 -3.21641E + 04 7.42599E-12 100 0 100 BWR -3.21641E + 04 -3.21641E + 04 -3.21641E + 04 -3.21641E + 04 7.42599E-12 100 0 100 RC33 BMR 2.639346497E + 00 2.639346497E + 00 2.639346497E + 00 2.639346497E + 00 0 100 0 100 BWR 2.639346497E + 00 2.639346497E + 00 2.639346497E + 00 2.639346497E + 00 0 100 0 100 The results of IUDE, εMAgES, and iLSHADEε are taken from [14]; COLSHADE results from [18]; EnMODE results from [19]; and I−Rao results from [20]; −−−: not available; The bold values indicate better values compared to the corresponding values given by the other algorithms . The graphs showing the convergence behavior of the BMR and BWR algorithms corresponding to the RC15-RC33 functions are shown in Fig. 3 . Table 9 summarizes the performances of the BMR and BWR algorithms compared to those of the other algorithms, namely, IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, and I-Rao. The comparison summary shows how many times the BMR and BWR algorithms performed “better”, “similar or equal” or “inferior” to the other algorithms. The “success %” is calculated as follows: Success % = (summation of the no. of times a particular algorithm performed “better”, “similar or equal”)/total no. of optimization problems. Table 9 Summary of the performances of the BMR and BWR algorithms for 26 problems (i.e., RC08-RC33). Algorithms Best Median Mean FR MV SR BMR and BWR Vs. IUDE Better 20 (21) 21(22) 21(22) 3(4) 4(3) 8 Similar or equal 5 4 4 22 22 17 Inferior 1(0) 1(0) 1(0) 1(0) 0(1) 1 Success % 96.15(100) 96.15(100) 96.15(100) 96.15(100) 100(96.15) 96.15 BMR and BWR Vs. εMAgES Better 21 20 19 6 7 15 Similar or equal 5 5 5 19 18 11 Inferior 0 1 2 1 1 0 Success % 100 96.15 92.31 96.15 96.15 100 BMR and BWR Vs. iLSHADE ε Better 20 20(21) 20(21) 3 2 10 Similar or equal 5 5 5 21 23(22) 15 Inferior 1 1(0) 1(0) 2 1(2) 1 Success % 96.15 96.15(100) 96.15(100) 92.31 96.15(92.31) 96.15 BMR and BWR Vs. COLSHADE Better 20 20 20(21) 1 --- --- Similar or equal 5 5 5 24 --- --- Inferior 1 1 1(0) 1 --- --- Success % 96.15 96.15 96.15(100) 96.15 --- --- BMR and BWR Vs. EnMODE Better 20 20 20 0 --- --- Similar or equal 5 5 5 26 --- --- Inferior 1 1 1 0 --- --- Success % 96.15 96.15 96.15 100 --- --- BMR and BWR Vs. I-Rao* Better 12 12(14) 13(14) 2 1 9 Similar or equal 5 5 5 17 18 10 Inferior 2 2(0) 1(0) 0 0 0 Success % 89.47 89.47(100) 94.73(100) 100 100 100 *Results of I−Rao [20] are available for 19 RC problems only (i.e., RC15−RC33). The tabulated summary is applicable for both the BMR and BWR algorithms. However, wherever the values are shown in brackets, those values are exclusively applicable to BWR . 5. Experiments on 12 constrained engineering optimization problems Very recently, Ghasemi et al. [ 21 ] proposed a metaphor-based algorithm named “flood algorithm (FLA)” and compared its performance with that of many optimization algorithms (in some problems, more than 30 algorithms) for solving certain CEC functions along with 12 constrained engineering problems. The decision variables, objective functions, constraints, and bounds of the decision variables are available in Ghasemi et al. [ 21 ] and hence are not reproduced here for space reasons and to avoid similarity issues. Now, the proposed BMR and BWR algorithms are applied to the same 12 constrained engineering problems under the same conditions as those used by FLA and other optimization algorithms. Table 10 presents the many optimization algorithms with which the FLA was compared by Ghasemi et al. [ 21 ]. Table 10 List of the optimization algorithms* previously applied to 12 constrained engineering problems. Problem numbers and the optimization algorithms used 1 2 3 4 5 6 7 8 9 10 11 12 CPO SCHO BLPSO mGWO SCHO YDSE WOA YDSE AD-IFA PSO AEFA-C MPDO IAS PSA MBWO BES PSA VCO SSA SRS LS-LF-FA DE FPSA MGO SCHO AMO CCEO GOA KOA BP-εMAg-ES MBA CPA LF-FA GA AD-IFA RAO-3 LSO DSA IAS EBS DSA COLSHA GWO SOS FA HPSO LS-LF-FA PSA KOA ESOA MPDO UPSO EEFO DE − QL ER-WCA DO HPSO-Q LF-FA WOA SWO iLSHADEε PSA VCO VMCH ALO KOA SNS FA SSA GSO RL-BA EEFO GGO UPSO LFD DBB-BC MBA DSA AD-IFA AD-IFA ESOA G-QPSO ACVO WCA VCO LS-LF-FA LS-LF-FA WO CPSO EChOA ER-WCA SAO LF-FA LF-FA DE − QL mGWO I-GWO ALO OA FA FA VMCH RFO HFPSO MFO MMLA SFO GCHHO EnMODE EO HEAA T-CSS AD-IFA mGWO GOA QS CDE SHO CSS LS-LF-FA PSO-HBF MFO GCHHO DHOA SETO FACSS LF-FA WOA SMA-AGDE LFD FA SMA COOT SELO WCA m-SCA SDO AHA SFO CPSO AO EPSO mGWO MBWO FSA PFA CCEO CPSO G-QPSO MPDO TEO WCA SCHO CDE DDAO GAO UPSO CDE YDSE PFA (l + λ)-ES LEA HGS HPSO CSA EO EO SCA GWO INFO MVO IPSO NRBO MFO HMS IMSCSO RSA POA LSO hHHO-SCA CPO EBS AOA HGA TDO UPSO CSA SCA MVO MFO * The abbreviations of the optimization algorithms are available in Ghasemi et al. [21] . Table 11 presents the results of the BMR and BWR algorithms along with the results of FLA. The results of so many other algorithms are not included in Table 11 , as FLA has already claimed its supremacy over those algorithms, and it is felt that comparison with FLA is sufficient to check the performance of the BMR and BWR algorithms. Table 11 Statistical results obtained by the BMR and BWR algorithms and FLA for 12 constrained engineering problems. No. Name of the problem Algorithm Best Mean Worst Std. dev. 1 Welded beam optimization BMR 1.6981 1.7010 1.7032 1.5674 E − 03 BWR 1 . 6979 1 . 6979 1 . 6979 2.7043 E − 10 FLA [21] 1.7248523 1.7248527 1.7248536 3.08E-06 2 Three-bar truss optimization BMR 1 . 085211 E + 02 1 . 085211 E + 02 1 . 085211 E + 02 1.4504 E − 14 BWR 1 . 085211 E + 02 1 . 085211 E + 02 1 . 085211 E + 02 1.8346 E − 14 FLA [21] 263.89584 263.89586 263.89665 7.10E-05 3 Cantilever beam optimization BMR 1 . 3351 1 . 3351 1 . 3351 1.9342 E − 11 BWR 1 . 3351 1 . 3351 1 . 3351 1.5367 E − 14 FLA [21] 1.339956 1.339958 1.339963 6.48E-07 4 Optimal design of gear train BMR 4.287642E − 22 3.4497E − 18 3.4131E − 17 8.21E − 18 BWR 7.3856E − 25 7.1755E − 21 4.3061E − 20 1.121E − 20 FLA [21] 2.700857E-12 8.7526E-10 1.4069E-09 2.76E-09 5 Tension/compression spring optimization BMR 0.012648 0.012648 0.012648 8.0429E − 14 BWR 0.012648 0.012648 0.012648 0.012648 FLA [21] 0.0126652 0.012666 0.012667 6.29E-07 6 Pressure vessel optimization BMR 4.840545E + 02 4.840545E + 02 4.840545E + 02 1.6409E − 13 BWR 4.840545E + 02 4.840545E + 02 4.840545E + 02 1.6409E − 13 FLA [21] 6.059714E + 03 6.06021E + 03 6.09052E + 03 3.86 7 Speed reducer optimization BMR 2.35748E + 03 2.357481E + 03 2.35748E + 03 9.2825E − 13 BWR 2.35748E + 03 2.35748E + 03 2.35748E + 03 9.2825E − 13 FLA [21] 2.99447E + 03 2.994471E + 03 2.994473E + 03 2.09E-04 8 I-beam vertical deflection BMR 0.0016369 0.0016369 0.0016369 6.6394E − 19 BWR 0.0016369 0.0016369 0.0016369 6.6394E − 19 FLA [21] 0.013074 0.01307445 0.01307579 6.91E-06 9 Tubular column optimal design BMR 1.03168E + 01 1.03168E + 01 1.03168E + 01 9.2825E − 13 BWR 1.03168E + 01 1.03168E + 01 1.03168E + 01 9.2825E − 13 FLA [21] 2.64995E + 01 2.64995E + 01 2.651003E + 01 1.41E-04 10 Piston lever optimal design BMR 7.585 7.585 7.5851 2.4052E − 05 BWR 7.585 7.585 7.585 2.054E-14 FLA [21] 8.412698 23.821251 167.232196 47.2 11 Corrugated bulkhead optimal design BMR 6.5795 6.5795 6.5795 2.7195E − 15 BWR 6.5795 6.5795 6.5795 2.7195E − 15 FLA [21] 6.842958 6.8429676 6.8432916 1.25E-05 12 Car side impact optimization BMR 2.22857E + 01 2.22857E + 01 2.22857E + 01 1.0534E − 14 BWR 2.22857E + 01 2.22857E + 01 2.22857E + 01 1.0534E − 14 FLA [21] 2.284297E + 01 2.288914E + 01 2.317638E + 01 7.38E-03 The bold numbers denote better values in comparison to the similar values provided by the FLA [21] . The BMR and BWR algorithms outperformed the very recently published FLA [ 21 ]. Interestingly, the FLA was shown by Ghasemi et al. [ 21 ] to be superior to 32 other algorithms for problem 1; 14 other algorithms for problem 2; 17 other algorithms for problem 3; 5 other algorithms for problem 4; 39 other algorithms for problem 5; 14 other algorithms for problem 6; 32 other algorithms for problem 7; 4 other algorithms for problem 8; 7 other algorithms for problem 9; 6 other algorithms for problem 10; 6 other algorithms for problem 11; and 14 other algorithms for problem 12. The proposed BMR and BWR algorithms have shown better performance in outperforming the FLA algorithm on all 12 engineering problems, which was recently published in June 2024. The convergence behavior behaviors of the BMR and BWR algorithms are shown in Fig. 4 . It may be noted that the 0e + 00 shown at the origin of the graphs indicates the iteration during which the population is randomly generated. Complete convergence until the end is not clearly visible in the graphs in certain cases (because of the scale step size taken on the x- and y-axes); however, the readers may understand that the convergence occurred at the mean function values shown in Table 11 . In a preprint [ 22 ], the results of the application of the BMR and BWR algorithms on 26 real-life nonconvex constrained optimization problems of CEC 2020 were presented. In another preprint [ 23 ], the results of the application of the BMR and BWR algorithms on 12 engineering problems were presented. 6. Experiments on 30 unconstrained optimization problems 6.1 Experiments on 25 unconstrained standard benchmark functions To test the performance of the BMR and BWR algorithms on unconstrained optimization problems, 25 standard benchmark functions frequently used by researchers are considered. These benchmark functions are separable, nonseparable, multimodal, and unimodal. The algorithms are coded in Python 3.11.5. Thirty separate runs of each function and a maximum of 500000 function evaluations were used in the computational studies. Table 12 displays the "best", "mean", "worst", "standard deviation (std. dev.)", and "mean function evaluations (MFE)" results for the BMR and BWR algorithms. Table 12 Statistical results obtained by the BMR and BWR algorithms for 25 unconstrained standard benchmark problems. No. Unconstrained function Optimum Algorithm Best Mean Worst Std. dev. MFE F 1 Sphere 0 BMR 0 0 0 0 125018 BWR 0 0 0 0 68256 F 2 SumSquares 0 BMR 0 0 0 0 124709 BWR 0 0 0 0 62936 F 3 Beale 0 BMR 0 0 0 0 10317 BWR 0 0 0 0 4535 F 4 Easom -1 BMR 0 0 0 0 5174 BWR 0 0 0 0 2891 F 5 Matyas 0 BMR 0 0 0 0 13610 BWR 0 0 0 0 23663 F 6 Colville 0 BMR 0 0 0 0 23195 BWR 0 0 0 0 14469 F 7 Trid 6 -50 BMR -50 -50 -50 0 18496 BWR -50 -50 -50 0 13793 F 8 Trid 10 -210 BMR -210 -210 -210 0 55635 BWR -210 -210 -210 0 52834 F 9 Zakharov 0 BMR 0 0 0 0 128387 BWR 0 0 0 0 79267 F 10 Schwefel 1.2 0 BMR 0 0 0 0 129580 BWR 0 0 0 0 80000 F 11 Rosenbrock 0 BMR 0 4.62E-29 1.09E-29 1.44E-29 434010 BWR 0 0 0 0 167089 F 12 Dixon-Price 0 BMR 0.24906 0.24906 0.24906 0 19000 BWR 0.24906 0.24906 0.24906 0 14300 F 13 Branin 0.397887 BMR 0.397887 0.397887 0.397887 0 22330 BWR 0.397887 0.397887 0.397887 0 11080 F 14 Bohachevsky 1 0 BMR 0 0 0 0 2746 BWR 0 0 0 0 1788 F 15 Bohachevsky 2 0 BMR 0 0 0 0 2738 BWR 0 0 0 0 1761 F 16 Bohachevsky 3 0 BMR 0 0 0 0 2757 BWR 0 0 0 0 1749 F 17 Booth 0 BMR 0 0 0 0 7862 BWR 0 0 0 0 3910 F 18 Michalewicz 2 -1.8013 BMR -1.8013 -1.8013 -1.8013 0 1819 BWR -1.8013 -1.8013 -1.8013 0 1157 F 19 Michalewicz 5 -4.6877 BMR -4.6877 -4.6877 -4.6877 5.76E-07 180120 BWR -4.6877 -4.6877 -4.6877 1.38E-15 23600 F 20 GoldStein-Price 3 BMR 3 3 3 1.94E-14 12517 BWR 3 3 3 1.87E-14 4317 F 21 Perm 0 BMR 0 0 0 0 55635 BWR 0 0 0 0 38393 F 22 Ackley 0 BMR 4.44E-16 4.44E-16 4.44E-16 0 11350 BWR 4.44E-16 4.44E-16 4.44E-16 0 2300 F 23 Foxholes 0.998004 BMR 0.998004 0.998004 0.998004 0 741 BWR 0.998004 0.998004 0.998004 0 600 F 24 Hartmann 3 -3.86278 BMR -3.86278 -3.86278 -3.86278 0 1784 BWR -3.86278 -3.86278 -3.86278 0 780 F 25 Penalized 2 0 BMR 1.50E-33 1.50E-33 1.50E-33 0 402120 BWR 1.50E-33 1.50E-33 1.50E-33 0 150000 Recently, Rao and Pawar [ 20 ] used the I-Rao algorithm for solving the above 25 unconstrained functions and proved that I-Rao performed better than the three Rao algorithms reported by Rao [ 7 ]. Hence, the results of the BMR and BWR algorithms are now compared with those of the I-Rao. Table 13 summarizes the performances of the BMR and BWR algorithms compared to that of the I-Rao algorithm. The comparison summary shows how many times the BMR and BWR algorithms performed “better”, “similar or equal” or “inferior” to the I-Rao algorithm. The “success %” was calculated similarly to what was explained in section 4 . Table 13 Summary of the performances of the BMR and BWR algorithms for 25 unconstrained problems. Criterion Best Mean Worst MFE BMR vs. I-Rao* Better 3 5 5 17 Similar or equal 21 20 20 0 Inferior 1 0 0 8 Success % 96 100 100 68 BWR vs. I-Rao* Better 3 5 5 22 Similar or equal 21 20 20 0 Inferior 1 0 0 3 Success % 96 100 100 88 BWR vs. BMR Better 0 1 1 24 Similar or equal 25 24 24 0 Inferior 0 0 0 1 Success % 100 96 96 96 *Results of I−Rao are taken from [20] . The convergence behavior of the BMR and BWR algorithms for 4 selected unconstrained functions are shown in Fig. 5 . These graphs give an idea about the convergence behavior. The convergence graphs for the remaining 21 unconstrained problems are not shown for space reasons. 6.2 Experiments on 5 new unconstrained standard benchmark functions To further demonstrate the potential of the proposed BMR and BWR algorithms for unconstrained optimization problems, 5 out of the 10 latest benchmark functions recently proposed by Yang [ 24 ] are considered. Thirty separate runs of each function and a maximum of 500000 function evaluations were used in the computational studies. The “best”, “mean”, “worst” “standard deviation (std. dev.)”, and “mean function evaluations (MFE)” values corresponding to the BMR and BWR algorithms are shown in Table 14 . Table 14 Statistical results of the BMR and BWR algorithms for the latest benchmark functions of Yang [ 24 ]. S. No. New benchmark function Optimum Algorithm Best Mean Worst Std. dev. MFE 1 Complex Noisy Function -1 BMR -1 -1 -1 0 2787 BWR -1 -1 -1 0 2772 2 Non-differentiable function 0 BMR 3.21228E-06 3.21228E-06 3.21228E-06 0 250380 BWR 1.8488E-07 1.8488E-07 1.8488E-07 0 221840 3 Hyperboloid Function 1 BMR 1 1 1 0 471400 BWR 1 1 1 0 222030 4 Non-Smooth Multi-Layered Function (D = 1) 0 BMR 0 0 0 0 155 BWR 0 0 0 0 232 5 Shortest-Path Problem 1 BMR 1 1 1 0 400 BWR 1 1 1 0 209 To understand the convergence behavior, the convergence graph for the “nonsmooth multilayered function” is shown in Fig. 6 . 7. Discussion on the results obtained for nonconvex COPs (RC08-RC33) and unconstrained problems 7.1 Nonconvex constrained optimization problems In the case of constrained problems of process synthesis and design (i.e., RC08-RC14), Table 7 clearly shows that compared to the IUDE, εMAgES, iLSHADE ε , COLSHADE, and EnMODE algorithms, the BMR and BWR algorithms performed better in terms of "Best," "Median," "Mean," "FR," "MV," and "SR". Both the BMR and BWR algorithms performed equally well on these 7 problems. The convergence graphs shown in Fig. 2 (drawn between the mean fitness value on the y-axis and the number of generations on the x-axis) indicate the better convergence behavior of the BMR and BWR algorithms. These algorithms converge much faster in the cases of RC08-RC10 and RC13. In the case of constrained problems of mechanical engineering (i.e., RC14-RC33), once again, Table 8 shows that the proposed BMR and BWR algorithms mostly outperformed the remaining algorithms (i.e., the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, and I-Rao) in terms of “Best”, “Median”, “Mean”, “FR”, “MV”, and “SR”, respectively. In the case of RC21 and RC24, Kumar [ 14 ] provided the results of IUDE, εMAgES, and iLSHADE ε only up to two digits after the decimal point (e.g., 2.35E-01 in the case of RC21, and 2.54E + 00 in the case of RC24). However, the values provided by the BMR and BWR algorithms are precisely 2.352398E-01 and 2.54378555, respectively, for RC24. In these two RCs, the performances of the IUDE, εMAgES, and iLSHADE ε algorithms are considered similar or equal to those of the BMR and BWR algorithms. The convergence graphs shown in Fig. 3 (drawn between the mean fitness value on the y-axis and the number of generations on the x-axis) indicate the better convergence behavior of the BMR and BWR algorithms for RC15-RC33 problems. These algorithms converge much faster in the cases of the RC18, RC20-RC25, RC27, RC29, and RC31-RC33 functions. In the case of other RC problems, the convergence behavior is appreciable. Table 9 shows a summary of the performances of the BMR and BWR algorithms for 26 problems (i.e., RC08-RC33) compared to those of the IUDE, εMAgES, iLSHADE ε , COLSHADE, EnMODE, and I-Rao algorithms. The comparison summary shows how many times the BMR and BWR algorithms performed “better”, “similar or equal” or “inferior” to the other algorithms. It is clear from Table 9 that the success percentages of the BMR and BWR algorithms are very high, at more than 90% (i.e., 100%, 96.15%, 94.73%, and 92.31%). Furthermore, both the BMR and BWR algorithms performed well on these RC08-RC33 problems. However, the performance of BWR may be slightly better than that of the BMR algorithm. 7.2 Constrained engineering problems In the case of 12 constrained engineering problems, Table 11 clearly shows that, compared to FLA [ 21 ] and many other algorithms in which FLA outperformed the other algorithms, the BMR and BWR algorithms performed much better in terms of "best," "mean," and "worst". Both the BMR and BWR algorithms performed equally well on these 12 problems. The convergence graphs shown in Fig. 4 indicate the better convergence behavior of the BMR and BWR algorithms. 7.3 Unconstrained optimization problems 7.3.1 Standard unconstrained optimization problems In the case of 25 standard unconstrained optimization problems, the selected convergence graphs shown in Fig. 5 for Beale, Easom, Bohachevsky 2, and Bohachevsky 2 indicate the better convergence behavior of the BMR and BWR algorithms. In the case of other unconstrained problems, the convergence behavior is also appreciable (however, those graphs are not shown in this paper for space reasons). Table 13 shows summary of the performances of the BMR and BWR algorithms for 25 problems compared to the recently published I-Rao algorithm of Rao and Pawar [ 20 ]. The comparison summary shows how many times the BMR and BWR algorithms performed “better”, “similar or equal”, or “inferior” to the other algorithms. It is clear from Table 13 that the success percentages of the BMR and BWR algorithms are very high, at more than 90% (i.e., 100% and 96%). In the case of MFE, compared to those of the I-Rao algorithm, the success percentages of the BMR and BWR algorithms are 68 and 88, respectively. Furthermore, both the BMR and BWR algorithms performed well on these 25 unconstrained problems. However, the performance of BWR may be somewhat better than that of the BMR algorithm. 7.3.2 New unconstrained optimization problems proposed by Yang [ 24 ] The statistical results of the BMR and BWR algorithms for the 5 latest benchmark functions of Yang [ 22 ] presented in Table 14 show that the proposed BMR and BWR algorithms produced the optimum results. The MFE required by the BWR algorithm is less than that required by the BMR algorithm. The convergence behavior is also found to be good. Normally, statistical tests such as the Friedman test, and the Home-Sidak test, etc. are used to determine the significance of the algorithms and to rank the competing optimization algorithms. However, these tests are not necessary here, as for the constrained and unconstrained problems presented in this paper, the BMR and BWR algorithms have established their competitiveness by providing better Best, Median, Mean, FR, MV, SR, and MFE values (with the performance of the BWR algorithm being slightly better than that of the BMR algorithm in some problems). 8. Conclusions The proposed BMR algorithm is based on “best”, “mean”, and “random” values in the population of a given iteration, and the proposed BWR algorithm is based on “best”, “worst”, and “random”. These two algorithms are developed in the present work without using any metaphors (as explained in section 1 ), and it was proven that there is no need to depend on metaphors to develop new optimization algorithms. The metaphor-free and algorithm-specific parameter-free BMR and BWR algorithms are simple to understand and easy to implement. The efficiency of the proposed algorithms is demonstrated in terms of convergence and results on real-life nonconvex constrained optimization problems (such as CEC 2020 problems), 12 constrained engineering problems, and a range of standard unconstrained optimization problems, including the most recent benchmark functions, each with unique characteristics. Thus, the objectives mentioned in section 1 are met. It is important to understand that the proposed BMR and BWR algorithms are not claimed as the "best" optimization algorithms available from all of the algorithms published in the optimization literature. An "optimal" algorithm may not exist for every type of optimization problem! However, the BMR and BWR algorithms demonstrate great potential for tackling optimization problems that are both constrained and unconstrained. Currently, we can say that the BMR and BWR algorithms produce the best results in a comparatively small number of function evaluations, are simple to comprehend and apply, and have no algorithm-specific parameters. The preliminary investigations serve as the foundation for the proposed algorithm outcomes, which are given in this work. In-depth investigations are planned to be conducted in the upcoming days on more real-life constrained and new unconstrained benchmark problems. Testing the effectiveness of the proposed algorithms on a range of intricate and computationally demanding benchmark functions involving high dimensions as well as real-life engineering optimization problems will be part of these investigations. The results are compared with those of other well-known and well-established optimization algorithms, and statistical analyses are also carried out. The application of the BMR and BWR algorithms for fine-tuning and training deep neural networks in machine learning will also be investigated. The objective of this paper is NOT to insult researchers who have developed (and who are developing) metaphor-based optimization algorithms. The objective is to prove that there is no need to depend on metaphors to develop new optimization algorithms. The preliminary investigations serve as the foundation for the proposed algorithm outcomes, which are given in this work. In-depth investigations of more real-life constrained and unconstrained engineering problems are planned to be conducted in the upcoming days. Testing the effectiveness of the proposed algorithms on a range of intricate and computationally demanding problems involving high dimensions, as well as investigating the convergence behavior, will be part of these investigations. The results are compared with those of other well-known and well-established optimization algorithms, and statistical analyses are also carried out. The application of the BMR and BWR algorithms for fine-tuning and training deep neural networks in machine learning will also be investigated. The optimization community researchers may attempt to enhance these two algorithms to increase their potency. We hope that researchers from various technical and scientific fields—including the physical, biological, and social sciences—will find the BMR and BWR algorithms to be effective instruments for optimizing systems and processes. If certain flaws in these algorithms are found, researchers may offer suggestions to address the drawbacks. The codes of the BMR and BWR algorithms are available at https://sites.google.com/view/bmr-bwr-optimization-algorithm/home?authuser=0 . Declarations Acknowledgments The research is supported by the Department of Science and Technology (DST) of the Government of India under the Mathematical Research Impact Centric Scheme (MATRICS) with the project number MTR/2023/000071. References K. Sörensen, “Metaheuristics – the metaphor exposed”, International Transactional in Operational Research , vol. 22, pp. 3-18, 2015. K. Sörensen, M. Sevaux and F. Glover, “A history of metaheuristics. In: Martí R, Pardalos P, Resende M (eds), Handbook of heuristics , Springer, pp. 791-808, 2018. F. Campelo and C. Aranha, “Evolutionary computation bestiary”, https://github. Com// fcamp elo// ECBestiary , 2021, Version visited last on 8 July 2024. C. L. C. Aranha, F. Villalón, M. Dorigo, R. Ruiz, M. Sevaux, K. Sörensen, and T. Stützle, “Metaphor-based metaheuristics, a call for action: the elephant in the room”, Swarm Intelligence, Vol. 16, pp. 1-6, 2021. C. L. C. Villalón, T. Stützle, and M. Dorigo, “Grey wolf, firefly and bat algorithms: Three widespread algorithms that do not contain any novelty”, In: International Conference on Swarm Intelligence , Springer, pp. 121-133, 2020. C. L. C. Villalón, T. Stützle, and M. Dorigo, “Cuckoo search ≡ (µ+λ)–evolution strategy — A rigorous analysis of an algorithm that has been misleading the research community for more than 10 years and nobody seems to have noticed”, Technical Report TR/IRIDIA/2021-006 , IRIDIA, Université Libre de Bruxelles, Belgium, 2021. R. V. Rao, “Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems”, International Journal of Industrial Engineering Computations , vol. 11, pp. 107-130, 2020. M. Sarhani, S. Voß, and R. Jovanovic, “Initialization of metaheuristics: comprehensive review, critical analysis, and research directions”, International Transactions in Operational Research , vol. 30, pp. 3361-3397, 2023. Rajwar, K. Deep, and S. Das, “An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges”, Artificial Intelligence Review , vol. 56, pp. 13187-13257, 2023. R. Salgotra, P. Sharma, S. Raju, and A. H. Gandomi, “A contemporary systematic review on meta-heuristic optimization algorithms with their MATLAB and Python code reference”, Archives of Computational Methods in Engineering , vol. 31, pp. 1749-1822, 2024. P. Sharma, and S. Raju, “Metaheuristic optimization algorithms: a comprehensive overview and classification of benchmark test functions”, Soft Computing, vol. 28, pp. 3123-3186, 2024. L. Velasco, H. Guerrero, and A. Hospitaler, “A literature review and critical analysis of metaheuristics recently developed”, Archives of Computational Methods in Engineering , vol. 31, pp. 125-146, 2024. B. Benaissa, M. Kobayashi, M. A. Ali, T. Khatir, and M. E. A. E. Elmeliani, “Metaheuristic optimization algorithms: An overview”, HCMCOUJS-Advances in Computational Structures , vol. 14, pp. 34-62, 2024. A. Kumar, G. Wu, M. Z. Ali, R. Mallipeddi, P. N. Suganthan, and S. Das, “A test-suite of non-convex constrained optimization problems from the real-world and some baseline results”, Swarm and Evolutionary Computation , vol. 56, 100693, 2020. A. Trivedi, D. Srinivasan, and N. Biswas, “An improved unified differential evolution algorithm for constrained optimization problems”, in: 2018 IEEE Congress on Evolutionary Computation (CEC) , IEEE, pp. 1–10, 2018. M. Hellwig, and H.-G. Beyer, “A matrix adaptation evolution strategy for constrained real-parameter optimization”, in: 2018 IEEE Congress on Evolutionary Computation (CEC) , IEEE , pp. 1–8, 2018. Z. Fan, Y. Fang, W. Li, Y. Yuan, Z. Wang, X. Bian, “LSHADE44 with an improved 𝜖 constraint-handling method for solving constrained single-objective optimization problems, in: 2018 IEEE Congress on Evolutionary Computation (CEC), IEEE , pp. 1–8, 2018. J. Gurrola-Ramos, A. Hern´andez-Aguirre, and O. Dalmau-Cede˜no, “COLSHADE for real-world single-objective constrained optimization problems”, In: 2020 IEEE Congress on Evolutionary Computation (CEC) , IEEE , pp.1-8, 2020. K. M. Sallam, S. M. Elsayed, R. K. Chakrabortty, and M. J. Ryan, “Multioperator differential evolution algorithm for solving real-world constrained optimization problems. In: 2020 IEEE Congress on Evolutionary Computation (CEC), IEEE , pp. 1-8, 2020. R. V. Rao and R. B. Pawar, “Improved Rao algorithm: A simple and effective algorithm for constrained mechanical design optimization problems”, Soft Computing , vol. 27, 3847-3868, 2022. M. Ghasemi, K. Golalipour, M. Zare, S. Mirjalili, P. Trojovsky, L. Abbuligah, and R. Hemmati, Flood algorithm (FLA): an efficient inspired meta‐heuristic for engineering optimization”, Journal of Supercomputing , doi: https://doi.org/10.1007/s11227-024-06291-7, 2024. R. V. Rao and R. Shah. http://arxiv.org/abs/2407.11149, 2024. Arxiv. R. V. Rao and R. Shah. https://doi.org/10.32388/6EGLFW, Qeios. X-S. Yang, “Ten new benchmarks for optimization”, in: Benchmarks and Hybrid Algorithms in Optimization and Applications (Ed. X-S Yang), Springer Tracts in Nature-Inspired Computing , pp. 19 – 32, 2023 (arXiv:2309.00644v1). Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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V. NATIONAL INSTITUTE OF TECHNOLOGY","correspondingAuthor":true,"prefix":"","firstName":"RAVIPUDI","middleName":"VENKATA","lastName":"RAO","suffix":""},{"id":344625557,"identity":"1baad0be-f761-4857-9fdf-9a095d0e70b8","order_by":1,"name":"RAVIKUMAR SHAH","email":"","orcid":"","institution":"S. V. NATIONAL INSTITUTE OF TECHNOLOGY","correspondingAuthor":false,"prefix":"","firstName":"RAVIKUMAR","middleName":"","lastName":"SHAH","suffix":""}],"badges":[],"createdAt":"2024-08-24 17:54:28","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4970235/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4970235/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63366068,"identity":"2d97690c-1989-4f98-82ae-110d10e80008","added_by":"auto","created_at":"2024-08-27 11:18:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":108313,"visible":true,"origin":"","legend":"\u003cp\u003eFlow diagram of the BMR and BWR algorithms.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/203b529a4f0cc2eb847ff432.png"},{"id":63365362,"identity":"09df46fa-c2e8-484f-ad6f-a3ea568bd06c","added_by":"auto","created_at":"2024-08-27 11:10:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":387270,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence behavior of BMR and BWR algorithms for the RC08-RC14 functions.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/a5db9b2c22f43843341f1ad0.png"},{"id":63366961,"identity":"d23efeed-b186-4bab-befc-8df7c2bb6de6","added_by":"auto","created_at":"2024-08-27 11:26:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1158184,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence graphs of the BMR and BWR algorithms for the RC15-RC33 functions.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/030f61bc79b5d0673cbb5f27.png"},{"id":63365363,"identity":"170f2410-9482-484e-a2e2-e5e901a06f2b","added_by":"auto","created_at":"2024-08-27 11:10:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":801930,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence graphs of the BMR and BWR algorithms for 12 engineering problems.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/01a28b7425808f5251811ad3.png"},{"id":63365365,"identity":"22ba559e-c022-407d-9062-a0d95c2a624b","added_by":"auto","created_at":"2024-08-27 11:10:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":260995,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence graphs of the BMR and BWR algorithms for 4 sample unconstrained functions.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/71cd291aa42996a903af1928.png"},{"id":63365360,"identity":"7d3b9b72-29fe-4ba9-8f10-b75513d9edd7","added_by":"auto","created_at":"2024-08-27 11:10:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":62989,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence graph for the nonsmooth multilayered function function.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/644fdd666d41240f18d65d10.png"},{"id":63367798,"identity":"ededf15f-c537-43e6-ae0b-dc7e2764c077","added_by":"auto","created_at":"2024-08-27 11:34:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5843605,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4970235/v1/e4624e8f-d52d-4f10-8d97-5f4251cfdbd6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eDevelopment and testing of two simple metaphor-free optimization algorithms for solving real-life nonconvex constrained and unconstrained engineering problems\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003ePopulation-based metaheuristic algorithms are adaptable and are used to solve complex optimization problems in a variety of domains. They are especially helpful when traditional optimization techniques—such as deterministic techniques or gradient-based methods—prove inappropriate because of certain factors such as large search spaces, nonlinearity, multimodality, or complex problem domains. Through a series of iterative procedures, the metaheuristic algorithms methodically investigate the solution space, improving the initial solution or solution population over time. Metaheuristics offer several advantages, such as versatility, gradient independence, global search capability, multiobjective problem-solving capability, exploration and exploitation capability, configurability, practical applicability. On the other hand, there are certain limitations of metaheuristics, such as the absence of a global optimum guarantee, difficulty in achieving convergence in the case of high-dimensional or complex solution spaces, the requirement of tuning common control parameters, and the algorithm-specific parameters, black-box nature, etc.\u003c/p\u003e\n\u003cp\u003eNearly all algorithms that rely on population information are probabilistic in nature and necessitate common parameters such as the number of generations and the size of the population. With a few exceptions (e.g., the Jaya algorithm, and Rao algorithms), each algorithm needs its own set of control parameters apart from common parameters. Inadequate adjustment of algorithm-specific parameters results in a locally optimal solution or escalates the computing effort.\u003c/p\u003e\n\u003cp\u003eThe body of literature on metaheuristics has expanded significantly in recent years. Recent review papers on metaheuristics give a clear idea to readers about various metaheuristics and their working principles, applications, limitations, future directions, etc. To date, more than 600 metaheuristic algorithms have been developed, with more than 400 of them being developed during the past ten years.\u0026nbsp;Many new optimization algorithms based on metaphors are released each month, with the authors claiming that their algorithms are “novel” and are better than those of the other algorithms.\u003c/p\u003e\n\u003cp\u003eA profusion of \"novel\" population-based metaheuristic algorithms, inspired by metaphors based on diverse natural phenomena, including floods, disasters, animals (animals on earth as well as in the ocean), birds, insects, reptiles, fishes, viruses, matings, humans, human activities, societies, cultures, planets, heavenly bodies, plants, trees, swamps, deserts, musical instruments, sports, household items, physics, chemistry, mathematics, etc. has emerged in the last 15 years. The developers of these algorithms make an analogy of the equations proposed by them with any of the metaphors related to the phenomena mentioned above and try to justify the analogy. Ironically, in almost all such algorithms, there is no real relation between the phenomena and the equations they use. This kind of research may be considered risky and detrimental to the development of the optimization field. Several researchers have questioned the contentious subject of the exponential increase in new algorithms. Regretfully, a sizeable portion of the scientific community resorted to believing that the development of so-called “novel” optimization algorithms based on ever more bizarre analogies (in the name of metaphors) can advance science. Arguably, the most dubious features of these techniques can be found in the literature, such as meaningless and unfair metaphors, poor experimental validation and comparison, and lack of novelty.\u003c/p\u003e\n\u003cp\u003eRegretfully, over the past 10 years, we have seen the emergence of a new trend in which hundreds of metaphor-based metaheuristics have been proposed. These metaheuristics incorporate the greatest variety of natural, man-made, social, and sometimes even paranormal occurrences and actions, and their authors have not provided a clear rationale for their proposals other than the desire to publish their papers.\u0026nbsp;Sörensen\u0026nbsp;[1]\u0026nbsp;opined that\u0026nbsp;the current research trajectory in metaheuristics threatens to deviate from a rigorous scientific approach, and it appears that no concept is too ridiculous to serve as motivation to launch yet another metaheuristic algorithm.\u0026nbsp;Sörensen\u0026nbsp;et al. [2] described the development of metaheuristics over the course of five separate eras, beginning well before the name was coined and concluding far into the future. They commented that a sizable portion of the research community has fooled itself into believing that the development of so-called \"novel\" approaches that rely on ever-more bizarre analogies may advance science. By the time these metaphor-based ideas are suppressed, they expect that the scientific community will suffer great injury, even though science will ultimately win out.\u003c/p\u003e\n\u003cp\u003eCampelo and Aranha [3] compiled a long list of \"novel\" algorithms and showed that developing a metaheuristic that approximates a real-world process is a fruitless exercise and should not be added to the corpus of scientific literature. Moreover, when metaheuristics are used, the mathematical models obtained from metaphors are often modified or omitted since they result in subpar implementations. Aranha et al. [4] opined that the emergence of publications that suggest metaphor-based algorithms that are influenced by often absurd processes that are not optimized at all show poor scientific housekeeping and reflect poorly on the metaheuristic research community.\u003c/p\u003e\n\u003cp\u003eA large number of metaphor-based metaheuristics include three (nearly wholly) distinct entities: the metaphor, the mathematical model \"derived\" from the metaphor, and the algorithm itself [5,6]. Rao [7] expressed concern that the flood of metaphor-based metaheuristics might threaten the optimization field's scientific viability and suggested that rather than concentrating on creating metaphor-based algorithms, researchers should concentrate on creating simple optimization strategies that can solve complex optimization problems.\u003c/p\u003e\n\u003cp\u003eThe primary metaheuristic techniques and their diversification mechanisms were explained by Sarhani et al. [8]. They suggested a new classification for the current initialization techniques after reviewing and analyzing them.\u0026nbsp;Rajwar et al. [9] reviewed approximately 540 metaheuristics and provided statistical information. The authors raised an important question:\u0026nbsp;If the search properties of an optimization algorithm are altered or almost identical to those of current methods, can it still be considered \"novel\"? The authors categorized metaheuristics based on the number of control parameters, which is a new taxonomy in the field.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSalgotra et al. [10] classified\u0026nbsp;metaheuristics as physics-based, human-based, swarm-based, or evolutionary-based. A large number of metaphor-based algorithms, including some bizarre metaphors, were mentioned in the classification. Different benchmark test functions related to existing metaheuristics were reviewed. It can be observed from the metaheuristics listed under each category of classification that the researchers have touched on almost all the “nature inspirations” and are trying to make analogies irrespective of whether that metaphor has anything to do with the equations shown by them. Sharma and Raju [11] presented a comprehensive overview of metaheuristic optimization algorithms and the classification of benchmark test functions\u003c/p\u003e\n\u003cp\u003eVelasco et al. [12] examined 111 recent articles that proposed \"new, hybrid, or improved optimization algorithms\". A significant observation that was mostly ignored by the academics developing new algorithms was that only 43% of the reviewed articles referenced the no free lunch (NFL) theorem. The black widow optimization and coral reef optimization metaheuristics were examined to show how algorithms with little innovation can mistakenly be regarded as novel frameworks. These algorithms were found to be nothing more than inadequate combinations of various evolutionary operators.\u003c/p\u003e\n\u003cp\u003eBenaissa et al. [13] explained the core ideas and elements of metaheuristics, focusing on the utilization of search references and the careful balancing of exploration and exploitation. Although intuitively appealing, metaphor-based optimization algorithms have generated controversy because of possible oversimplification and inflated expectations, and\u0026nbsp;the names of the algorithms do not\u0026nbsp;always correspond to the guiding ideas or methods they use. Sometimes, researchers use fashionable or catchynames, but these names cannot accurately represent the algorithm's originality or uniqueness.\u003c/p\u003e\n\u003cp\u003eDeveloping straightforward optimization approaches that can solve complex optimization problems more effectively would be a better course of action for researchers than trying to develop metaphor-based algorithms. In light of this, the objectives of the work presented in this paper are listed below.\u003c/p\u003e\n\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eTo prove that there is no need to depend on metaphors to develop optimization algorithms.\u003c/li\u003e\n \u003cli\u003eTo develop two simple basic metaphor-free and algorithm-specific parameter-free optimization algorithms.\u003c/li\u003e\n\u003c/ol\u003e\n\u003col\u003e\n \u003cli\u003eTo demonstrate the convergence efficiency of the proposed algorithms and the results for real-life nonconvex constrained optimization problems (e.g., CEC 2020 problems).\u003c/li\u003e\n \u003cli\u003eTo test the performance of the proposed algorithms on 12 constrained engineering problems that have been recently tested by \u003cem\u003emany of the\u0026nbsp;\u003c/em\u003elatest algorithms (in some cases, more than 30 algorithms).\u003c/li\u003e\n \u003cli\u003eTo demonstrate how well the proposed algorithms perform on a range of standard unconstrained optimization problems, including the most recent benchmark functions, each with unique characteristics.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe next section explains the proposed optimization algorithms.\u003c/p\u003e"},{"header":"2. Proposed best-mean-random (BMR) and best-worst-random (BWR) algorithms","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 BMR algorithm\u003c/h2\u003e \u003cp\u003eLet \u003cem\u003ef(x\u003c/em\u003e), the objective function, be the function to be minimized or maximized. Assume that there are '\u003cem\u003em\u003c/em\u003e' design variables and '\u003cem\u003en\u003c/em\u003e' candidate solutions (i.e., population size, \u003cem\u003ek\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1,2, ...,\u003cem\u003en\u003c/em\u003e) for every iteration \u003cem\u003ei\u003c/em\u003e. The candidate with the best overall performance receives the best value of \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) (i.e., \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003csub\u003ebest\u003c/sub\u003e), while the candidate with the poorest overall performance obtains the worst value of \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) (i.e., \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003csub\u003eworst\u003c/sub\u003e) in all candidate solutions. Let \u003cem\u003er\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e, and \u003cem\u003er\u003c/em\u003e\u003csub\u003e4\u003c/sub\u003e be four random numbers. Each can take any value randomly from 0 to 1, and \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e are the upper and lower values of the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable, respectively. Additionally, let \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e represent the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable's value for the \u003cem\u003ek\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e candidate in the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration, and \u003cem\u003eT\u003c/em\u003e is a factor that randomly takes either 1 or 2 during an iteration.\u003c/p\u003e \u003cp\u003e \u003cem\u003er\u003c/em\u003e \u003csub\u003e1\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e4\u003c/sub\u003e \u0026sim; Uniform(0, 1)\u003c/p\u003e \u003cp\u003e \u003cem\u003eT\u003c/em\u003e \u0026sim; Choice({1, 2})\u003c/p\u003e \u003cp\u003eIf \u003cem\u003er\u003c/em\u003e\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u003cem\u003e\u0026gt;\u003c/em\u003e\u0026thinsp;0.5, the value of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e changes according to Eq.\u0026nbsp;(1).\u003c/p\u003e \u003cp\u003e \u003cem\u003eV'\u003c/em\u003e \u003csub\u003e \u003cem\u003ej,k,i\u003c/em\u003e \u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,j,i\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,best,i\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eT\u003c/em\u003e*\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej.mean,i\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,j,i\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,best,i\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,random,i\u003c/em\u003e\u003c/sub\u003e) (1)\u003c/p\u003e \u003cp\u003eOtherwise, \u003cem\u003eV'\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e = R = \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026ndash; (U\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- L\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)r\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e (2)\u003c/p\u003e \u003cp\u003eThe modified value of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e is \u003cem\u003eV'\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e. The best value of \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,best,i\u003c/em\u003e\u003c/sub\u003e for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable. The mean value of the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej.mean,i\u003c/em\u003e\u003c/sub\u003e during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration. The randomly picked up value, during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration, for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,random,i\u003c/em\u003e\u003c/sub\u003e. The exploitation and exploration capabilities of the BMR algorithm are explained in Eqs.\u0026nbsp;(1) and (2).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 BWR algorithm\u003c/h2\u003e \u003cp\u003eWith the same description of the terms given in subsection \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e, the BWR algorithm is described below.\u003c/p\u003e \u003cp\u003e \u003cem\u003er\u003c/em\u003e \u003csub\u003e1\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003e4\u003c/sub\u003e \u0026sim; Uniform(0, 1)\u003c/p\u003e \u003cp\u003e \u003cem\u003eT\u003c/em\u003e \u0026sim; Choice({1, 2})\u003c/p\u003e \u003cp\u003eIf \u003cem\u003er\u003c/em\u003e\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u003cem\u003e\u0026gt;\u003c/em\u003e\u0026thinsp;0.5, the value of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,I\u003c/em\u003e\u003c/sub\u003e changes according to Eq.\u0026nbsp;(3).\u003c/p\u003e \u003cp\u003e \u003cem\u003eV'\u003c/em\u003e \u003csub\u003e \u003cem\u003ej,k,i\u003c/em\u003e \u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,j,i\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,best,i\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eT\u003c/em\u003e* \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,random,i\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,j,i\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,worst,i\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,random,i\u003c/em\u003e\u003c/sub\u003e) (3)\u003c/p\u003e \u003cp\u003eotherwise, \u003cem\u003eV'\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e = R = \u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026ndash; (U\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- L\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)r\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e (4)\u003c/p\u003e \u003cp\u003eThe modified value of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e is \u003cem\u003eV'\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,k,i\u003c/em\u003e\u003c/sub\u003e. The best value of \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,best,i\u003c/em\u003e\u003c/sub\u003e for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable. The worst value of \u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration for the \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,worst,i\u003c/em\u003e\u003c/sub\u003e. The randomly picked up value of \u003cem\u003ej\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e variable during the \u003cem\u003ei\u003c/em\u003e\u003csup\u003eth\u003c/sup\u003e iteration is \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ej,random,i\u003c/em\u003e\u003c/sub\u003e. The exploitation and exploration capabilities of the BWR algorithm are explained in Eqs.\u0026nbsp;(3) and (4). It can be noted that both the BMR and BWR algorithms are not based on any metaphors. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the flow diagram of the proposed BMR and BWR optimization algorithms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Illustration of the functionality of the proposed algorithms","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Illustration of the functionality of the BMR algorithm\u003c/h2\u003e\n \u003cp\u003eTo illustrate the functionality of the BMR algorithm, we explore an unconstrained standard benchmark function, Sphere. The objective function is to determine the values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e that minimize the sphere function.\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003c/span\u003eMinimize,\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n \u003cp\u003eThis benchmark function\u0026apos;s known solution is 0 for all \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e values of 0. To illustrate the BMR algorithm, let us use the following: two design variables, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e; an iteration serving as the termination criterion; and a population size of five (i.e., five solutions). Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the values of the objective function corresponding to the initial population, which is created at random within the bounds of the variables. Since \u003cem\u003ef(x)\u003c/em\u003e is a minimization function, the best solution is defined as having the lowest value, and the worst solution is defined as having the greatest value.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eRandomly generated initial solutions.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSolution\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStatus\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e349\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1285\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eworst\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e936\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ebest\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e388\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e clearly shows that solution 4 offers the best solution, while solution 2 offers the worst solution. Eq. (1) is used to determine the new values of the variables for \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and are included in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, considering random numbers \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.30 and \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.10 for \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.60 and \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.30 for \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e. Assuming T\u0026thinsp;=\u0026thinsp;1 and random interaction with solution 5, the new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e for solution 1 are computed as follows during the first iteration.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eV\u0026apos;\u003c/em\u003e \u003csub\u003e\u0026nbsp;\u003cem\u003e1,1,1\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,1,1\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,1,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,4,1\u003c/em\u003e\u003c/sub\u003e \u0026minus;\u0026thinsp;1*Mean of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,1,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,4,1\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,5,1\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e\n \u003cp\u003e= -5\u0026thinsp;+\u0026thinsp;0.30 (7\u0026thinsp;\u0026minus;\u0026thinsp;1*5.6)\u0026thinsp;+\u0026thinsp;0.10 (7- (-18)) = -2.08\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eV\u0026apos;\u003c/em\u003e \u003csub\u003e\u0026nbsp;\u003cem\u003e2,1,1\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,1,1\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,2,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,4,1\u003c/em\u003e\u003c/sub\u003e \u0026ndash; 1*Mean of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,2,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,4,1\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,5,1\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e\n \u003cp\u003e=\u0026thinsp;18\u0026thinsp;+\u0026thinsp;0.60 (-12- 1*8.2)\u0026thinsp;+\u0026thinsp;0.30 (-12-8) = -0.12\u003c/p\u003e\n \u003cp\u003eThe new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e for the remaining solutions are determined similarly. The new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, along with the corresponding values of the objective function, are displayed in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. For illustration purposes, solutions 2, 3, 4, and 5 are taken into consideration for their random interactions with 4, 2, 1, and 3, respectively.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNew values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e,\u003c/sub\u003e \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ef(x)\u003c/em\u003e during the first iteration of the BMR algorithm.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSolution\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-2.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.3408\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e643.9108\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-31.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1883.103\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-33.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1171.239\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-19.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-5.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e430.2608\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAfter the values of \u003cem\u003ef(x)\u003c/em\u003e are compared in Tables \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e is prepared which contains the updated values of \u003cem\u003ef(x)\u003c/em\u003e based on the fitness comparison. The first iteration of the BMR algorithm is complete.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eUpdated values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003ef(x)\u003c/em\u003e after the first iteration of the BMR algorithm.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSolution\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStatus\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-2.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.3408\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ebest\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e643.9108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e936\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eworst\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e388\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates that solution 1 is the best, while solution 3 is the worst. Additionally, it is evident that in just one iteration, the objective function\u0026apos;s value drops from 193 to 4.3408. If the number of iterations is increased, the known value of the objective function, or 0, can be obtained in a few iterations. It is important to keep in mind that in cases of maximization problems, the highest value of the objective function is referred to as the best value, and calculations must be performed accordingly. This means that problems involving either minimization or maximization can be handled using the proposed BMR algorithm.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Illustration of the functionality of the BWR algorithm\u003c/h2\u003e\n \u003cp\u003eThe same sphere function is considered to illustrate the functioning of the BWR algorithm. For a fair comparison, the same random number, the same \u003cem\u003eT\u003c/em\u003e, and the same random interactions are considered. The values are calculated accordingly. Assuming T\u0026thinsp;=\u0026thinsp;1 and random interaction with solution 5, the new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e for solution 1 are computed as follows during the first iteration.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eV\u0026apos;\u003c/em\u003e \u003csub\u003e\u0026nbsp;\u003cem\u003e1,1,1\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,1,1\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,1,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,4,1\u003c/em\u003e\u003c/sub\u003e \u0026minus;\u0026thinsp;1* \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,5,1\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,1,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,2,1\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,5,1\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e\n \u003cp\u003e= -5\u0026thinsp;+\u0026thinsp;0.30 (7\u0026thinsp;\u0026minus;\u0026thinsp;1*(-18)) \u0026minus;\u0026thinsp;0.10 (14- (-18)) = -0.70\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eV\u0026apos;\u003c/em\u003e \u003csub\u003e\u0026nbsp;\u003cem\u003e2,1,1\u003c/em\u003e\u0026nbsp;\u003c/sub\u003e = \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,1,1\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e1,2,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,4,1\u003c/em\u003e\u003c/sub\u003e \u0026ndash; 1* \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,5,1\u003c/em\u003e\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,2,1\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,4,1\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2,5,1\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e\n \u003cp\u003e=\u0026thinsp;18\u0026thinsp;+\u0026thinsp;0.60 (-12- 1*8) -0.30 (33\u0026thinsp;\u0026minus;\u0026thinsp;8) = -1.50\u003c/p\u003e\n \u003cp\u003eThe new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e for the remaining solutions are determined similarly. The new values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, along with the corresponding values of the objective function, are displayed in Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNew values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003ef(x)\u003c/em\u003e during the first iteration of the BWR algorithm.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSolution\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e557.14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1867.41\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-34.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1265.94\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-23.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-7.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e596.18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAfter comparing the values of \u003cem\u003e(x)\u003c/em\u003e in Tables \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e is prepared, and it contains the updated values of \u003cem\u003ef(x)\u003c/em\u003e based on fitness comparison. The first iteration of the BWR algorithm is complete.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eUpdated values of \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003ef(x)\u003c/em\u003e after the first iteration of the BWR algorithm.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSolution\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ef\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStatus\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ebest\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e557.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e936\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eworst\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e388\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates that solution 1 is the best solution, while solution 3 is the worst. Additionally, it is evident that in just one iteration, the objective function\u0026apos;s value drops from 193 to 2.74. The known value of the objective function, or 0, can be reached in a few iterations if the number of iterations is increased. Problems involving either minimization or maximization can be handled by the BWR.\u003c/p\u003e\n \u003cp\u003eThis illustration pertains to an unconstrained optimization problem. Nonetheless, the same procedures can be employed when dealing with constrained optimization problems. The primary distinction is that in the constrained optimization problem, each violation of a constraint is handled by a penalty function that is applied to the objective function.\u003c/p\u003e\n \u003cp\u003eThe experimentation of the proposed algorithms on 26 real-life nonconvex constrained benchmark problems given in CEC 2020 [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] is explained in the following section.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Experiments on real-life nonconvex constrained benchmark problems of CEC 2020","content":"\u003cp\u003eTo demonstrate and prove the effectiveness of the BMR and BWR algorithms, 26 real-life constrained optimization problems (COPs) from the CEC 2020 competition [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] are considered. A detailed description of the 26 COPs is available in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] and hence is not provided here for space reasons. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents the COPs, the number of decision variables, the number of equality constraints, and the number of inequality constraints.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eDetails of 26 nonconvex COPs and the associated numbers of decision variables and constraints.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCOP designation\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo. of decision variables\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo. of equality constraints\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo. of inequality constraints\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eProcess synthesis and design problems\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eMechanical engineering problems\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRC33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe decision variables, objective functions, and constraints of the 26 considered nonconvex COPs are available in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. Kumar et al. [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] presented 57 COPs belonging to different domains, such as industrial chemical processes (RC01-RC07), process synthesis and design problems (RC08-RC14), mechanical engineering problems (RC15-RC33), power system problems (RC34-RC44), power electronics problems (RC45-RC50), and livestock feed ratio problems (RC51-RC57), and presented the results of the application of the improved unified differential evolution algorithm (IUDE) [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e], matrix adaptation evolution strategy (\u0026epsilon;MAgES) [\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e], and LSHADE44 with an improved 𝜖 constraint-handling method (iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e) [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]. Gurrola-Ramos [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e] used the COLSHADE algorithm, and Sallam et al. [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e] used the multi-operator differential evolution (EnMODE) algorithm to solve the same COPs. Rao and Pawar [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e] applied an improved Rao (I-Rao) algorithm for solving mechanical engineering problems (RC15-RC33) and compared their results with those given in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e], [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e], and [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e] and reported good performance of the I-Rao algorithm.\u003c/p\u003e\n\u003cp\u003eIn the present work, to demonstrate and prove the effectiveness of the BMR and BWR algorithms, the COPs numbered RC08-RC33 are attempted \u003cem\u003ebecause of the familiarity of the authors with these problems\u003c/em\u003e. These problems have decision variables ranging from 2 to 30, with inequality constraints ranging from 1 to 30 and equality constraints ranging from 0 to 4. All algorithms (i.e., IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, I-Rao, BMR, and BWR) use the same termination criterion based on the number of decision variables to end the optimization process. A set number of function evaluations are permitted throughout the optimization process. When the maximum number of function evaluations is reached, the algorithm\u0026rsquo;s optimization process concludes, and the optimal solution is returned. For every COP, the maximum function evaluations are determined using the following criteria [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eMaximum function evaluations\u0026thinsp;=\u0026thinsp;1 x 10\u003csup\u003e5\u003c/sup\u003e if \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;10\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003e=\u0026thinsp;2 x 10\u003csup\u003e5\u003c/sup\u003e if 10\u0026thinsp;\u003cem\u003e\u0026lt;\u0026thinsp;D\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;30\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eIn the present work, MATLAB r2024a was used to implement the BMR and BWR algorithms to evaluate the COPs. A laptop with a Microsoft Windows 10 operating system with AMD Ryzen 7- CPU and 24 GB RAM was used for the computational experiments.\u003c/p\u003e\n\u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e presents the results of the application of the IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, BMR, and BWR algorithms to the process synthesis and design problems after 25 runs of each algorithm. A static penalty method is used to address constraint violations. For example, in the case of the minimization of a COP designated RC08, which has two constraints \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e and \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e, the penalized value of \u003cem\u003ef(x)\u003c/em\u003e is calculated as, penalized \u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;+\u0026thinsp;10*\u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e+\u003cem\u003e10*g\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e. In the case of maximization of a COP designated as RC26, which has 9 constraints from \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e to \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e9\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e, the penalized value of \u003cem\u003ef(x)\u003c/em\u003e is calculated as, Penalized \u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ef(x)\u003c/em\u003e-10*\u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e-\u003cem\u003e10*g\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e-\u003cem\u003e10*g\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e-\u0026hellip;\u0026hellip;\u0026hellip;.-\u003cem\u003e10*g\u003c/em\u003e\u003csub\u003e\u003cem\u003e8\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e-\u003cem\u003e10*g\u003c/em\u003e\u003csub\u003e\u003cem\u003e9\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e. A similar approach is followed in the case of equality constraints. For example, in the case of minimization of RC09, which has an inequality constraint \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e and an equality constraint \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e, the penalized value of \u003cem\u003ef(x)\u003c/em\u003e is calculated as, penalized \u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;+\u0026thinsp;10*\u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e+\u003cem\u003e10*h\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(x)\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e. If there is no constraint violation, then there will not be any penalty, and the penalized \u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ef(x)\u003c/em\u003e. It may be noted here that the user can decide which type of penalty can be imposed for constraint violation.\u003c/p\u003e\n\u003cp\u003eThe statistical results are expressed in terms of \u0026ldquo;best\u0026rdquo; \u0026ldquo;median,\u0026rdquo; \u0026ldquo;mean,\u0026rdquo; \u0026ldquo;worst,\u0026rdquo; \u0026ldquo;standard deviation,\u0026rdquo; \u0026ldquo;feasibility rate (FR),\u0026rdquo; \u0026ldquo;mean constraint violation (MV),\u0026rdquo; and \u0026ldquo;success rate (SR)\u0026rdquo; in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. The FR is defined as the ratio of total runs to the number of runs in which at least one workable solution is found within the maximum function evaluations. The SR represents the ratio between the total number of runs and the number of viable solutions (x) that an algorithm was able to obtain, meeting \u003cem\u003ef(x)\u003c/em\u003e\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ef (x\u0026lowast;)\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e within the maximum function evaluations. The equation for computing the MV is available in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eIncluding all the results of the IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, and EnMODE algorithms in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e for the RC08-RC14 problems will, unfortunately, increase the similarity content of this paper (even though such inclusion will provide much clarity). Hence, for illustration, the results of all the algorithms are shown for the RC08 and RC09 problems only. For the remaining problems (i.e., RC10-RC14), only the results of the BMR and BWR algorithms are shown. The bold values in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e indicate better values compared to the corresponding values given by the other algorithms.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eStatistical results of the application of different algorithms for the RC08-RC14 problems.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"10\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProblem\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBest\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWorst\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStd. Dev.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMV\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSR\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"7\"\u003e\n \u003cp\u003eRC08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIUDE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.41E-17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026epsilon;MAgES\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.99E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.29E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.52E-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.58E-03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eiLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCOLSHADE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEnMODE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBMR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBWR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.625E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"7\"\u003e\n \u003cp\u003eRC09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIUDE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.56E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.56E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.56E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n 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align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.0539E-16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBWR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.900126E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRC13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBMR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22586.82857\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.713E-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBWR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e22586.82857\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22586.82857\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.713E-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRC14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBMR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28336.49265\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.1647E-11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBWR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e28336.49265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28336.49265\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.2755E-11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003csup\u003eThe results of IUDE, \u0026epsilon;MAgES, and iLSHADE\u0026epsilon; are taken from [14]; COLSHADE results from [18]; and EnMODE results from [19]; \u0026minus;\u0026minus;\u0026minus;: not available; The bold numbers denote better values in comparison to the similar values provided by the other algorithms\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e displays the convergence behavior of the BMR and BWR algorithms for the RC08\u0026ndash;RC14 functions. The 0e\u0026thinsp;+\u0026thinsp;00 shown at the origin of the graphs indicates the iteration during which the population is randomly generated. Complete convergence until the end is not clearly visible in the graphs in certain cases (because of the scale step size taken on the x- and y-axes); however, the readers may understand that the convergence occurred at the mean function values shown in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eTo further test the proposed BMR and BWR algorithms, 19 nonconvex COPs are tested for the mechanical engineering of RC15-RC33. Computational experiments are carried out to evaluate the performances of the BMR and BWR algorithms, and the performances are compared with those of the IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, and I-Rao algorithms. A common platform is offered by maintaining the same function evaluations for all the algorithms for comparison. As a result, the consistency of the comparison is maintained while comparing the performances of the BMR and BWR algorithms with those of the other optimization algorithms\u003c/p\u003e\n\u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e shows the results, and these results include the results of the I-Rao algorithm [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e] for comparison in addition to the IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, BMR, and BWR algorithms. However, including all the results of the IUDE, \u0026epsilon;MAgES, iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, and I-Rao algorithms in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e for the RC15-RC33 problems will, unfortunately, increase the plagiarism content of this paper (even though such inclusion will provide much clarity). Hence, for illustration, the results of all the algorithms are shown for the RC15 problem only. For the remaining problems (i.e., RC16-RC33), only the results of the BMR and BWR algorithms are shown.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab8\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eStatistical results of the application of different algorithms for the RC15-RC33 problems.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"10\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProblem\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBest\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWorst\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStd. Dev.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMV\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSR\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\n \u003cp\u003eRC15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIUDE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.64E-13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026epsilon;\u003c/em\u003eMAgES\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.99E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n 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\u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.21641E\u0026thinsp;+\u0026thinsp;04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.42599E-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRC33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBMR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBWR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.639346497E\u0026thinsp;+\u0026thinsp;00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e100\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003csup\u003eThe results of IUDE, \u0026epsilon;MAgES, and iLSHADE\u0026epsilon; are taken from [14]; COLSHADE results from [18]; EnMODE results from [19]; and I\u0026minus;Rao results from [20]; \u0026minus;\u0026minus;\u0026minus;: not available; The bold values indicate better values compared to the corresponding values given by the other algorithms\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe graphs showing the convergence behavior of the BMR and BWR algorithms corresponding to the RC15-RC33 functions are shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eTable 9 summarizes the performances of the BMR and BWR algorithms compared to those of the other algorithms, namely,\u0026nbsp;IUDE,\u0026nbsp;\u0026epsilon;MAgES,\u0026nbsp;iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e, COLSHADE, EnMODE, and I-Rao. The comparison summary shows how many times the BMR and BWR algorithms performed \u0026ldquo;better\u0026rdquo;, \u0026ldquo;similar or equal\u0026rdquo; or \u0026ldquo;inferior\u0026rdquo; to the other algorithms. The \u0026ldquo;success %\u0026rdquo; is calculated as follows: Success % = (summation of the no. of times a particular algorithm performed \u0026ldquo;better\u0026rdquo;, \u0026ldquo;similar or equal\u0026rdquo;)/total no. of optimization problems.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab10\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSummary of the performances of the BMR and BWR algorithms for 26 problems (i.e., RC08-RC33).\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlgorithms\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBest\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMV\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSR\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. IUDE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20 (21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21(22)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21(22)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100(96.15)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. \u0026epsilon;MAgES\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e92.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. iLSHADE\u003csub\u003e\u0026epsilon;\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20(21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20(21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23(22)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e92.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(92.31)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. COLSHADE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20(21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. EnMODE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e---\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eBMR and BWR Vs. I-Rao*\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBetter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12(14)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13(14)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimilar or equal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInferior\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1(0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSuccess %\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e89.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e89.47(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e94.73(100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003csup\u003e*Results of I\u0026minus;Rao [20] are available for 19 RC problems only (i.e., RC15\u0026minus;RC33). The tabulated summary is applicable for both the BMR and BWR algorithms. However, wherever the values are shown in brackets, those values are exclusively applicable to BWR\u003c/sup\u003e.\u003c/p\u003e"},{"header":"5. Experiments on 12 constrained engineering optimization problems","content":"\u003cp\u003e \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVery recently, Ghasemi et al.\u003c/span\u003e [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eproposed a metaphor-based algorithm named \u0026ldquo;flood algorithm (FLA)\u0026rdquo; and compared its performance with that of\u003c/span\u003e \u003cspan type=\"ItalicUnderline\" class=\"ItalicUnderline\" name=\"Emphasis\"\u003emany\u003c/span\u003e \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eoptimization algorithms (in some problems, more than 30 algorithms) for solving certain CEC functions along with 12 constrained engineering problems. The decision variables, objective functions, constraints, and bounds of the decision variables are available in Ghasemi et al.\u003c/span\u003e [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eand hence are not reproduced here for space reasons and to avoid similarity issues. Now, the proposed BMR and BWR algorithms are applied to the same 12 constrained engineering problems under the same conditions as those used by FLA and other optimization algorithms.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e10\u003c/span\u003e presents the \u003cem\u003emany optimization algorithms\u003c/em\u003e with which the FLA was compared by Ghasemi et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of the optimization algorithms* previously applied to 12 constrained engineering problems.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"12\" nameend=\"c12\" namest=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eProblem numbers and the optimization algorithms used\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e2\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e3\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e4\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e5\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e6\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e7\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e8\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e9\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e10\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e11\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e12\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBLPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003emGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eYDSE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eYDSE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAD-IFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAEFA-C\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMPDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eIAS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMBWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBES\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVCO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSRS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLS-LF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFPSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMGO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAMO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCCEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eBP-εMAg-ES\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMBA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAD-IFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRAO-3\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eIAS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEBS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCOLSHA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSOS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLS-LF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eESOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMPDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eUPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEEFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDE\u0026thinsp;\u0026minus;\u0026thinsp;QL\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eER-WCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHPSO-Q\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eiLSHADEε\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVCO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVMCH\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eALO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eKOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSNS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRL-BA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEEFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGGO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eUPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLFD\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDBB-BC\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMBA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAD-IFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAD-IFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eESOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eG-QPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eACVO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVCO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLS-LF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLS-LF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEChOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eER-WCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSAO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDE\u0026thinsp;\u0026minus;\u0026thinsp;QL\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003emGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eI-GWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eALO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eVMCH\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHFPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMMLA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGCHHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEnMODE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHEAA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eT-CSS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAD-IFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003emGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eQS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCDE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCSS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLS-LF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePSO-HBF\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGCHHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDHOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSETO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFACSS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLF-FA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSMA-AGDE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLFD\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSMA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCOOT\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSELO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003em-SCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAHA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003emGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMBWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCCEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eG-QPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMPDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eTEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eWCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCHO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCDE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eDDAO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGAO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eUPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCDE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eYDSE\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePFA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e(l\u0026thinsp;+\u0026thinsp;λ)-ES\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLEA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHGS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eGWO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eINFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMVO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eIPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eNRBO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHMS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eIMSCSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ePOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eLSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003ehHHO-SCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCPO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eEBS\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAOA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHGA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eTDO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eUPSO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eCSA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eSCA\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMVO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eMFO\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cb\u003e*\u003c/b\u003eThe abbreviations of the optimization algorithms are available in Ghasemi et al. [21]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e11\u003c/span\u003e \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003epresents the results of the BMR and BWR algorithms along with the results of FLA.\u003c/span\u003e \u003cspan type=\"ItalicUnderline\" class=\"ItalicUnderline\" name=\"Emphasis\"\u003eThe results of so many other algorithms are not included in\u003c/span\u003e Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e11\u003c/span\u003e, \u003cspan type=\"ItalicUnderline\" class=\"ItalicUnderline\" name=\"Emphasis\"\u003eas FLA has already claimed its supremacy over those algorithms, and it is felt that comparison with FLA is sufficient to check the performance of the BMR and BWR algorithms.\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical results obtained by the BMR and BWR algorithms and FLA for 12 constrained engineering problems.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eName of the problem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eWorst\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eStd. dev.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWelded beam optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.6981\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.7010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.7032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.5674\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e6979\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e6979\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e6979\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.7043\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.7248523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.7248527\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.7248536\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.08E-06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThree-bar truss optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.4504\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e085211\u003c/b\u003e\u003cb\u003eE\u003c/b\u003e\u0026thinsp;\u003cb\u003e+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.8346\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e263.89584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e263.89586\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e263.89665\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e7.10E-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCantilever beam optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.9342\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e.\u003cb\u003e3351\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.5367\u003cem\u003eE\u0026thinsp;\u0026minus;\u003c/em\u003e\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.339956\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.339958\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.339963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.48E-07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOptimal design of gear train\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.287642E\u0026thinsp;\u0026minus;\u0026thinsp;22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.4497E\u0026thinsp;\u0026minus;\u0026thinsp;18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.4131E\u0026thinsp;\u0026minus;\u0026thinsp;17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.21E\u0026thinsp;\u0026minus;\u0026thinsp;18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.3856E\u0026thinsp;\u0026minus;\u0026thinsp;25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e7.1755E\u0026thinsp;\u0026minus;\u0026thinsp;21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.3061E\u0026thinsp;\u0026minus;\u0026thinsp;20\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.121E\u0026thinsp;\u0026minus;\u0026thinsp;20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.700857E-12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.7526E-10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.4069E-09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.76E-09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTension/compression spring optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.0429E\u0026thinsp;\u0026minus;\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.012648\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0126652\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.012666\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.012667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.29E-07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePressure vessel optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.6409E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.840545E\u0026thinsp;+\u0026thinsp;02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.6409E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.059714E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.06021E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.09052E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpeed reducer optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e2.35748E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2.357481E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.35748E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.2825E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e2.35748E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2.35748E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.35748E\u0026thinsp;+\u0026thinsp;03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.2825E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.99447E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.994471E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.994473E\u0026thinsp;+\u0026thinsp;03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.09E-04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI-beam vertical deflection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.6394E\u0026thinsp;\u0026minus;\u0026thinsp;19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.0016369\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.6394E\u0026thinsp;\u0026minus;\u0026thinsp;19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.013074\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01307445\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01307579\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.91E-06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTubular column optimal design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.2825E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1.03168E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.2825E\u0026thinsp;\u0026minus;\u0026thinsp;13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.64995E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.64995E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.651003E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.41E-04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePiston lever optimal design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.585\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e7.585\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e7.5851\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.4052E\u0026thinsp;\u0026minus;\u0026thinsp;05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.585\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e7.585\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e7.585\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.054E-14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.412698\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.821251\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e167.232196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e47.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrugated bulkhead optimal design\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e6.5795\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e6.5795\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.5795\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.7195E\u0026thinsp;\u0026minus;\u0026thinsp;15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e6.5795\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e6.5795\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.5795\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.7195E\u0026thinsp;\u0026minus;\u0026thinsp;15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.842958\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.8429676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.8432916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.25E-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCar side impact optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.0534E\u0026thinsp;\u0026minus;\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.22857E\u0026thinsp;+\u0026thinsp;01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.0534E\u0026thinsp;\u0026minus;\u0026thinsp;14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFLA [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.284297E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.288914E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.317638E\u0026thinsp;+\u0026thinsp;01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e7.38E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003eThe \u003cb\u003ebold\u003c/b\u003e numbers denote better values in comparison to the similar values provided by the FLA [21]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe BMR and BWR algorithms outperformed the very recently published FLA [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Interestingly, \u003cb\u003ethe FLA was shown by Ghasemi et al.\u003c/b\u003e [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] \u003cb\u003eto be superior to 32 other algorithms for problem 1; 14 other algorithms for problem 2; 17 other algorithms for problem 3; 5 other algorithms for problem 4; 39 other algorithms for problem 5; 14 other algorithms for problem 6; 32 other algorithms for problem 7; 4 other algorithms for problem 8; 7 other algorithms for problem 9; 6 other algorithms for problem 10; 6 other algorithms for problem 11; and 14 other algorithms for problem 12. The proposed BMR and BWR algorithms have shown better performance in outperforming the FLA algorithm on all 12 engineering problems, which was recently published in June 2024.\u003c/b\u003e\u003c/p\u003e \u003cp\u003eThe convergence behavior behaviors of the BMR and BWR algorithms are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. It may be noted that the 0e\u0026thinsp;+\u0026thinsp;00 shown at the origin of the graphs indicates the iteration during which the population is randomly generated. Complete convergence until the end is not clearly visible in the graphs in certain cases (because of the scale step size taken on the x- and y-axes); however, the readers may understand that the convergence occurred at the mean function values shown in Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn a preprint [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], the results of the application of the BMR and BWR algorithms on 26 real-life nonconvex constrained optimization problems of CEC 2020 were presented. In another preprint [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], the results of the application of the BMR and BWR algorithms on 12 engineering problems were presented.\u003c/p\u003e"},{"header":"6. Experiments on 30 unconstrained optimization problems","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e6.1 Experiments on 25 unconstrained standard benchmark functions\u003c/h2\u003e \u003cp\u003eTo test the performance of the BMR and BWR algorithms on unconstrained optimization problems, 25 standard benchmark functions frequently used by researchers are considered. These benchmark functions are separable, nonseparable, multimodal, and unimodal. The algorithms are coded in Python 3.11.5. Thirty separate runs of each function and a maximum of 500000 function evaluations were used in the computational studies. Table\u0026nbsp;\u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003e12\u003c/span\u003e displays the \"best\", \"mean\", \"worst\", \"standard deviation (std. dev.)\", and \"mean function evaluations (MFE)\" results for the BMR and BWR algorithms.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab13\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical results obtained by the BMR and BWR algorithms for 25 unconstrained standard benchmark problems.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnconstrained\u003c/p\u003e \u003cp\u003efunction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOptimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWorst\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eStd. dev.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMFE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSphere\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e125018\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e68256\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSumSquares\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e124709\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e62936\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBeale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10317\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4535\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEasom\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5174\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2891\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMatyas\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e13610\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e23663\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eColville\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e23195\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e14469\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTrid 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e18496\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e13793\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTrid 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e55635\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e52834\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZakharov\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e128387\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e79267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSchwefel 1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e129580\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e80000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRosenbrock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.62E-29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.09E-29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.44E-29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e434010\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e167089\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDixon-Price\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e19000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.24906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e14300\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBranin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e22330\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.397887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e11080\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBohachevsky 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2746\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1788\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBohachevsky 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2738\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1761\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBohachevsky 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2757\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1749\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBooth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7862\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3910\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMichalewicz 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1819\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.8013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1157\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMichalewicz 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.76E-07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e180120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-4.6877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.38E-15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e23600\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGoldStein-Price\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.94E-14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e12517\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.87E-14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4317\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePerm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e55635\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e38393\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAckley\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e11350\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.44E-16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2300\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFoxholes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e741\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.998004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHartmann 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1784\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.86278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e780\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF 25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePenalized 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e402120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.50E-33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e150000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eRecently, Rao and Pawar [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] used the I-Rao algorithm for solving the above 25 unconstrained functions and proved that I-Rao performed better than the three Rao algorithms reported by Rao [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Hence, the results of the BMR and BWR algorithms are now compared with those of the I-Rao. Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e13\u003c/span\u003e summarizes the performances of the BMR and BWR algorithms compared to that of the I-Rao algorithm. The comparison summary shows how many times the BMR and BWR algorithms performed \u0026ldquo;better\u0026rdquo;, \u0026ldquo;similar or equal\u0026rdquo; or \u0026ldquo;inferior\u0026rdquo; to the I-Rao algorithm. The \u0026ldquo;success %\u0026rdquo; was calculated similarly to what was explained in section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab14\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of the performances of the BMR and BWR algorithms for 25 unconstrained problems.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCriterion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWorst\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMFE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eBMR vs. I-Rao*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBetter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimilar or equal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInferior\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSuccess %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eBWR vs. I-Rao*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBetter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimilar or equal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInferior\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSuccess %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eBWR vs. BMR\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBetter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimilar or equal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInferior\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSuccess %\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e*Results of I\u0026minus;Rao are taken from [20]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe convergence behavior of the BMR and BWR algorithms for 4 selected unconstrained functions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. These graphs give an idea about the convergence behavior. The convergence graphs for the remaining 21 unconstrained problems are not shown for space reasons.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Experiments on 5 new unconstrained standard benchmark functions\u003c/h2\u003e \u003cp\u003eTo further demonstrate the potential of the proposed BMR and BWR algorithms for unconstrained optimization problems, 5 out of the 10 latest benchmark functions recently proposed by Yang [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] are considered. Thirty separate runs of each function and a maximum of 500000 function evaluations were used in the computational studies. The \u0026ldquo;best\u0026rdquo;, \u0026ldquo;mean\u0026rdquo;, \u0026ldquo;worst\u0026rdquo; \u0026ldquo;standard deviation (std. dev.)\u0026rdquo;, and \u0026ldquo;mean function evaluations (MFE)\u0026rdquo; values corresponding to the BMR and BWR algorithms are shown in Table\u0026nbsp;\u003cspan refid=\"Tab15\" class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab15\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 14\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical results of the BMR and BWR algorithms for the latest benchmark functions of Yang [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS. No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNew benchmark function\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOptimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWorst\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eStd. dev.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMFE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComplex Noisy Function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2787\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2772\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNon-differentiable function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.21228E-06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.21228E-06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.21228E-06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e250380\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.8488E-07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.8488E-07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.8488E-07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e221840\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHyperboloid Function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e471400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e222030\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNon-Smooth Multi-Layered Function (D\u0026thinsp;=\u0026thinsp;1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e155\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e232\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShortest-Path Problem\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBMR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBWR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e209\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo understand the convergence behavior, the convergence graph for the \u0026ldquo;nonsmooth multilayered function\u0026rdquo; is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"7. Discussion on the results obtained for nonconvex COPs (RC08-RC33) and unconstrained problems","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e7.1 Nonconvex constrained optimization problems\u003c/h2\u003e \u003cp\u003eIn the case of constrained problems of process synthesis and design (i.e., RC08-RC14), Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e clearly shows that compared to the IUDE, εMAgES, iLSHADE\u003csub\u003eε\u003c/sub\u003e, COLSHADE, and EnMODE algorithms, the BMR and BWR algorithms performed better in terms of \"Best,\" \"Median,\" \"Mean,\" \"FR,\" \"MV,\" and \"SR\". Both the BMR and BWR algorithms performed equally well on these 7 problems. The convergence graphs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (drawn between the mean fitness value on the y-axis and the number of generations on the x-axis) indicate the better convergence behavior of the BMR and BWR algorithms. These algorithms converge much faster in the cases of RC08-RC10 and RC13.\u003c/p\u003e \u003cp\u003eIn the case of constrained problems of mechanical engineering (i.e., RC14-RC33), once again, Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows that the proposed BMR and BWR algorithms mostly outperformed the remaining algorithms (i.e., the IUDE, εMAgES, iLSHADE\u003csub\u003eε\u003c/sub\u003e, COLSHADE, EnMODE, and I-Rao) in terms of \u0026ldquo;Best\u0026rdquo;, \u0026ldquo;Median\u0026rdquo;, \u0026ldquo;Mean\u0026rdquo;, \u0026ldquo;FR\u0026rdquo;, \u0026ldquo;MV\u0026rdquo;, and \u0026ldquo;SR\u0026rdquo;, respectively. In the case of RC21 and RC24, Kumar [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] provided the results of IUDE, εMAgES, and iLSHADE\u003csub\u003eε\u003c/sub\u003e only up to two digits after the decimal point (e.g., 2.35E-01 in the case of RC21, and 2.54E\u0026thinsp;+\u0026thinsp;00 in the case of RC24). However, the values provided by the BMR and BWR algorithms are precisely 2.352398E-01 and 2.54378555, respectively, for RC24. In these two RCs, the performances of the IUDE, εMAgES, and iLSHADE\u003csub\u003eε\u003c/sub\u003e algorithms are considered similar or equal to those of the BMR and BWR algorithms.\u003c/p\u003e \u003cp\u003eThe convergence graphs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (drawn between the mean fitness value on the y-axis and the number of generations on the x-axis) indicate the better convergence behavior of the BMR and BWR algorithms for RC15-RC33 problems. These algorithms converge much faster in the cases of the RC18, RC20-RC25, RC27, RC29, and RC31-RC33 functions. In the case of other RC problems, the convergence behavior is appreciable.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows a summary of the performances of the BMR and BWR algorithms for 26 problems (i.e., RC08-RC33) compared to those of the IUDE, εMAgES, iLSHADE\u003csub\u003eε\u003c/sub\u003e, COLSHADE, EnMODE, and I-Rao algorithms. The comparison summary shows how many times the BMR and BWR algorithms performed \u0026ldquo;better\u0026rdquo;, \u0026ldquo;similar or equal\u0026rdquo; or \u0026ldquo;inferior\u0026rdquo; to the other algorithms. It is clear from Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e9\u003c/span\u003e that the success percentages of the BMR and BWR algorithms are very high, at more than 90% (i.e., 100%, 96.15%, 94.73%, and 92.31%). Furthermore, both the BMR and BWR algorithms performed well on these RC08-RC33 problems. However, the performance of BWR may be slightly better than that of the BMR algorithm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e7.2 Constrained engineering problems\u003c/h2\u003e \u003cp\u003eIn the case of 12 constrained engineering problems, Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e11\u003c/span\u003e clearly shows that, compared to FLA [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and \u003cem\u003emany other algorithms\u003c/em\u003e in which FLA outperformed the other algorithms, the BMR and BWR algorithms performed much better in terms of \"best,\" \"mean,\" and \"worst\". Both the BMR and BWR algorithms performed equally well on these 12 problems. The convergence graphs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e indicate the better convergence behavior of the BMR and BWR algorithms.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e7.3 Unconstrained optimization problems\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e7.3.1 Standard unconstrained optimization problems\u003c/h2\u003e \u003cp\u003eIn the case of 25 standard unconstrained optimization problems, the selected convergence graphs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e for Beale, Easom, Bohachevsky 2, and Bohachevsky 2 indicate the better convergence behavior of the BMR and BWR algorithms. In the case of other unconstrained problems, the convergence behavior is also appreciable (however, those graphs are not shown in this paper for space reasons).\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows summary of the performances of the BMR and BWR algorithms for 25 problems compared to the recently published I-Rao algorithm of Rao and Pawar [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The comparison summary shows how many times the BMR and BWR algorithms performed \u0026ldquo;better\u0026rdquo;, \u0026ldquo;similar or equal\u0026rdquo;, or \u0026ldquo;inferior\u0026rdquo; to the other algorithms. It is clear from Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e13\u003c/span\u003e that the success percentages of the BMR and BWR algorithms are very high, at more than 90% (i.e., 100% and 96%). In the case of MFE, compared to those of the I-Rao algorithm, the success percentages of the BMR and BWR algorithms are 68 and 88, respectively. Furthermore, both the BMR and BWR algorithms performed well on these 25 unconstrained problems. However, the performance of BWR may be somewhat better than that of the BMR algorithm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e7.3.2 New unconstrained optimization problems proposed by Yang [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/h2\u003e \u003cp\u003eThe statistical results of the BMR and BWR algorithms for the 5 latest benchmark functions of Yang [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] presented in Table\u0026nbsp;\u003cspan refid=\"Tab15\" class=\"InternalRef\"\u003e14\u003c/span\u003e show that the proposed BMR and BWR algorithms produced the optimum results. The MFE required by the BWR algorithm is less than that required by the BMR algorithm. The convergence behavior is also found to be good.\u003c/p\u003e \u003cp\u003eNormally, statistical tests such as the Friedman test, and the Home-Sidak test, etc. are used to determine the significance of the algorithms and to rank the competing optimization algorithms. \u003cem\u003eHowever, these tests are not necessary here, as for the constrained and unconstrained problems presented in this paper, the BMR and BWR algorithms have established their competitiveness\u003c/em\u003e by providing better Best, Median, Mean, FR, MV, SR, and MFE values (with the performance of the BWR algorithm being slightly better than that of the BMR algorithm in some problems).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"8. Conclusions","content":"\u003cp\u003eThe proposed BMR algorithm is based on \u0026ldquo;best\u0026rdquo;, \u0026ldquo;mean\u0026rdquo;, and \u0026ldquo;random\u0026rdquo; values in the population of a given iteration, and the proposed BWR algorithm is based on \u0026ldquo;best\u0026rdquo;, \u0026ldquo;worst\u0026rdquo;, and \u0026ldquo;random\u0026rdquo;. These two algorithms are developed in the present work without using any metaphors (as explained in section \u003cspan refid=\"Sec1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and it was proven that there is no need to depend on metaphors to develop new optimization algorithms. The metaphor-free and algorithm-specific parameter-free BMR and BWR algorithms are simple to understand and easy to implement. The efficiency of the proposed algorithms is demonstrated in terms of convergence and results on real-life nonconvex constrained optimization problems (such as CEC 2020 problems), 12 constrained engineering problems, and a range of standard unconstrained optimization problems, including the most recent benchmark functions, each with unique characteristics. Thus, the objectives mentioned in section \u003cspan refid=\"Sec1\" class=\"InternalRef\"\u003e1\u003c/span\u003e are met.\u003c/p\u003e \u003cp\u003eIt is important to understand that the proposed BMR and BWR algorithms are not claimed as the \"best\" optimization algorithms available from all of the algorithms published in the optimization literature. An \"optimal\" algorithm may not exist for every type of optimization problem! However, the BMR and BWR algorithms demonstrate great potential for tackling optimization problems that are both constrained and unconstrained. Currently, we can say that the BMR and BWR algorithms produce the best results in a comparatively small number of function evaluations, are simple to comprehend and apply, and have no algorithm-specific parameters.\u003c/p\u003e \u003cp\u003eThe preliminary investigations serve as the foundation for the proposed algorithm outcomes, which are given in this work. In-depth investigations are planned to be conducted in the upcoming days on more real-life constrained and new unconstrained benchmark problems. Testing the effectiveness of the proposed algorithms on a range of intricate and computationally demanding benchmark functions involving high dimensions as well as real-life engineering optimization problems will be part of these investigations. The results are compared with those of other well-known and well-established optimization algorithms, and statistical analyses are also carried out. The application of the BMR and BWR algorithms for fine-tuning and training deep neural networks in machine learning will also be investigated.\u003c/p\u003e \u003cp\u003eThe objective of this paper is NOT to insult researchers who have developed (and who are developing) metaphor-based optimization algorithms. The objective is to prove that there is no need to depend on metaphors to develop new optimization algorithms.\u003c/p\u003e \u003cp\u003eThe preliminary investigations serve as the foundation for the proposed algorithm outcomes, which are given in this work. In-depth investigations of more real-life constrained and unconstrained engineering problems are planned to be conducted in the upcoming days. Testing the effectiveness of the proposed algorithms on a range of intricate and computationally demanding problems involving high dimensions, as well as investigating the convergence behavior, will be part of these investigations. The results are compared with those of other well-known and well-established optimization algorithms, and statistical analyses are also carried out. The application of the BMR and BWR algorithms for fine-tuning and training deep neural networks in machine learning will also be investigated.\u003c/p\u003e \u003cp\u003eThe optimization community researchers may attempt to enhance these two algorithms to increase their potency. We hope that researchers from various technical and scientific fields\u0026mdash;including the physical, biological, and social sciences\u0026mdash;will find the BMR and BWR algorithms to be effective instruments for optimizing systems and processes. If certain flaws in these algorithms are found, researchers may offer suggestions to address the drawbacks.\u003c/p\u003e \u003cp\u003eThe codes of the BMR and BWR algorithms are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://sites.google.com/view/bmr-bwr-optimization-algorithm/home?authuser=0\u003c/span\u003e\u003cspan address=\"https://sites.google.com/view/bmr-bwr-optimization-algorithm/home?authuser=0\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe research is supported by the Department of Science and Technology (DST) of the Government of India under the Mathematical Research Impact Centric Scheme (MATRICS) with the project number MTR/2023/000071.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eK. 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Yang, \u0026ldquo;Ten new benchmarks for optimization\u0026rdquo;, in: Benchmarks and Hybrid Algorithms in Optimization and Applications (Ed. X-S Yang), \u003cem\u003eSpringer Tracts in Nature-Inspired Computing\u003c/em\u003e, pp. 19 \u0026ndash; 32, 2023 (arXiv:2309.00644v1).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"S. V. NATIONAL INSTITUTE OF TECHNOLOGY","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Optimization, BMR algorithm, BWR algorithm, CEC 2020, Real-life nonconvex constrained problems, Constrained engineering problems, Unconstrained problems, New benchmarks","lastPublishedDoi":"10.21203/rs.3.rs-4970235/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4970235/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTwo simple yet powerful optimization algorithms, named the Best-Mean-Random (BMR) and Best-Worst-Random (BWR) algorithms, are developed and presented in this paper to handle both constrained and unconstrained optimization problems. These algorithms are free of metaphors and algorithm-specific parameters. The BMR algorithm is based on the best, mean, and random solutions of the population generated for solving a given problem, and the BWR algorithm is based on the best, worst, and random solutions. The performances of the proposed two algorithms are investigated by implementing them on 26 real-life nonconvex\u003cu\u003e \u003c/u\u003econstrained optimization problems given in the Congress on Evolutionary Computation (CEC) 2020 competition, and comparisons are made with those of the other prominent optimization algorithms. The performances on 12 constrained engineering problems are also investigated, and the results are compared with those of very recent algorithms (in some cases, compared with more than 30 algorithms). Furthermore, computational experiments are conducted on 30 unconstrained standard benchmark optimization problems, including 5 recently developed benchmark problems with distinct characteristics. The results demonstrated the superior competitiveness and superiority of the proposed simple algorithms. The optimization research community may gain an advantage by adapting these algorithms to solve various constrained and unconstrained real-life optimization problems across various scientific and engineering disciplines.\u003c/p\u003e","manuscriptTitle":"Development and testing of two simple metaphor-free optimization algorithms for solving real-life nonconvex constrained and unconstrained engineering problems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-27 11:09:59","doi":"10.21203/rs.3.rs-4970235/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b9eb4d6b-d3c7-49ab-b399-d237b6938980","owner":[],"postedDate":"August 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":36527714,"name":"Operations Research"},{"id":36527715,"name":"Artificial Intelligence and Machine Learning"},{"id":36527716,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2024-08-27T11:10:00+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-27 11:09:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4970235","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4970235","identity":"rs-4970235","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}