Application of Particle Swarm Optimization and Bacterial Foraging Optimization in Parallel Assembly Sequence Planning: A Systematic Review

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Traditional heuristic and exact methods often struggle with the dynamic and intricate nature of modern assembly processes. Advanced bio-inspired algorithms like PSO and BFO offer significant improvements in efficiency, accuracy, and scalability. A systematic search of databases including Engineering Village, Science Direct, and Web of Science (1995–2024) identified studies explicitly using PSO, BFO, or hybrids in PASP with performance metrics. The review highlights enhancements in convergence rates, assembly efficiency, and robustness achieved through these algorithms. Additionally, the integration of PSO and BFO with Industry 4.0 technologies, such as the Internet of Things (IoT) and Artificial Intelligence (AI), is discussed, emphasizing their potential to create intelligent, real-time adaptive PASP systems. The findings reveal that these advanced algorithms not only optimize assembly sequences but also reduce time and costs while improving product quality and flexibility. The review concludes with proposed future research directions, including real-time optimization methods and deeper integration with Industry 4.0 technologies, to address scalability and adaptability challenges in modern manufacturing environments. particle swarm optimisation (PSO) bacterial foraging optimisation (BFO) parallel assembly sequence planning (PASP) hybrid algorithms modern manufacturing environments Figures Figure 1 Figure 2 Figure 3 1. Introduction 1.1 Background This systematic review evaluates the utilization of particle swarm optimisation (PSO), bacterial foraging optimisation (BFO), and their hybrids in addressing challenges in PASP, with a focus on synthesizing available evidence and identifying research gaps. Parallel assembly sequence planning (PASP) is a critical optimization problem in modern manufacturing, particularly in industries dealing with complex, large-scale products such as automotive, aerospace, and electronics. PASP involves determining the optimal sequence of assembly tasks that can be executed in parallel, aiming to minimize production time, reduce costs, and maximize resource utilization. Unlike traditional sequential assembly processes, PASP enables multiple tasks to be performed simultaneously, significantly improving production efficiency. With the increasing adoption of Industry 4.0 technologies, such as IoT and AI, the need for efficient parallel assembly processes has become more pressing, underscoring the relevance of PASP in today’s manufacturing landscape. The decision to focus on PASP in this study was driven by several key factors. First, PASP addresses the challenges faced by traditional heuristic-based methods, which struggle with combinatorial complexity and lack flexibility in dynamic environments where real-time adjustments are essential. Advanced optimization algorithms like PSO and BFO are well-suited to handle the multi-dimensional search spaces inherent in PASP. Second, optimizing PASP can lead to substantial gains in production efficiency, cost savings, and product quality, making it an ideal domain for exploring the application of bio-inspired algorithms. Given the demonstrated success of PSO and BFO in addressing complex optimization problems in manufacturing, their application to PASP offers a promising avenue for improving assembly processes in competitive industrial settings. PASP is essential for optimizing complex manufacturing processes, especially in industries requiring large-scale production. Traditional heuristic methods have been widely used for assembly sequence planning. However, these methods often struggle with scalability due to the combinatorial explosion of possible sequences as product complexity increases. Moreover, exact methods like branch-and-bound and exhaustive search algorithms are computationally expensive and impractical for real-time applications. Exact algorithms aim to find the optimal solution to assembly sequence planning problems by exhaustively searching the solution space. However, these methods face significant limitations when applied to real-world problems(Aguinaga et al., 2008). Exact methods often struggle with scalability due to exponentially increasing computational complexity with more components, making them impractical for large-scale problems. Exact methods required exponentially increasing computational resources for problems involving more than 50 assembly components. Similarly, heuristic methods, while faster, are highly dependent on initial conditions and often fail to find globally optimal solutions in dynamic environments​(Lambert, 2006a ). The time required to compute an exact solution can be prohibitive for complex products, limiting the applicability of exact methods in dynamic industrial environments(Su et al., 2020 ). Exact algorithms lack flexibility for real-time adaptations, requiring complete re-computation when conditions change, which is inefficient in fast-paced settings(Aguinaga et., 2008b). These algorithms may become infeasible for complex products due to their inability to efficiently handle intricate constraints and relationships between parts(Dutta & Woo, 1995 ). They require significant computational power and memory, which can be a major limitation in practical applications with limited resources (Senin et al., 2000 ). Traditional PASP methods, often heuristic-based, struggle to adapt to modern manufacturing environments' dynamic and intricate nature (Gulivindala et al., 2020 ). Heuristic-based methods are widely used in parallel assembly sequence planning (PASP) to enhance efficiency and reduce complexity(Gujjula et al., 2010 ; Heemskerk et al., 1989; Lambert, 2006; Pan et al., 2010). While heuristic methods effectively reduce complexity and improve efficiency in assembly sequence planning, they are not without limitations. Various studies have highlighted the inherent challenges and drawbacks. Heuristic methods struggle with the combinatorial explosion as the number of parts increases. They are highly dependent on the initial conditions, leading to many possible sequences and making it hard to efficiently find optimal solutions(Heemskerk et al., 1989a; Pan et al., 2010b ). Many heuristic methods struggle to cope with the size and complexity of real-life assembly problems, limiting their applicability in industrial settings where problems are often large-scale and complex(Gujjula et al.,2011). Heuristic approaches can be less flexible in adapting to dynamic changes in the assembly process, which is a significant drawback in environments where conditions and requirements frequently change(Gulivindala et al., 2020 ). These methods often concentrate on specific aspects of assembly sequence planning, potentially overlooking other important factors, leading to solutions that are not globally optimal(Nayak et al., 2015 ). Recent advancements in computational algorithms, particularly PSO and BFO, have shown promise in addressing these challenges. PSO, inspired by social behaviours in nature, and BFO, mimicking the foraging behaviour of E. coli bacteria, offer unique approaches to optimisation problems. PASP optimisation is critical for automotive, aerospace, and renewable energy industries, where complex products require efficient assembly sequences. Traditional heuristic-based PASP methods fall short in these modern, dynamic environments, necessitating advanced algorithms like PSO and BFO. This review examines the application of the two algorithms and their hybrid associated with PASP application, focusing on common challenges, solutions, and future research directions. We assess the effectiveness of PSO and BFO in optimising PASP, addressing their inherent challenges, and exploring future research directions to enhance their application in dynamic manufacturing environments. 1.2 Rationale PSO, BFO, their hybrid, and application in industry 4.0 for PASP are becoming popular in handling the assembly of complex products. A study that introduced a novel PASP method utilising particle swarm optimization based on bacterial chemotaxis (PSOBC) to avoid matrix calculations and improve efficiency in assembly sequence planning was proposed. The PSOBC method demonstrates better convergence rate and assembly efficiency performance than standard PSO algorithms(Yang et al., 2020 ). An improved PSO (IPSO) algorithm was developed to address basic PSO algorithms' low convergence speed and precision in assembly sequence optimisation (Xiangyu et al., 2019 ). To generate optimal or near-optimal assembly sequences, a chaotic PSO (CPSO) approach was proposed, integrating chaos methods to enhance the convergence rate and solution quality of traditional PSO algorithms(Wang et al., 2010). For the multi-agent evolutionary, an algorithm was employed incorporating PSO to optimise hybrid assembly sequence planning and assembly line balance problems, enhancing efficiency and solving stagnation issues inherent in PSO algorithms(Su et al., 2020 ). To minimise production time and cost, another research applied PSO, demonstrating the algorithm's powerful global searching ability and fast convergence rate(Mukred et al., 2013 ). PSO and BFO are bio-inspired algorithms, each drawing inspiration from natural phenomena observed in the behaviour of living organisms. A study explored the combination of PSO and ant colony optimisation (ACO) for micro-assembly sequence planning, addressing challenges in micro-assembly with a hybrid PS-ACO approach that balances local and global search capabilities (Shuang et al., 2008 ). To address a multi-plant assembly sequence planning model that combines assembly sequence planning with plant allocation, another study utilized PSO to optimize costs and demonstrate feasibility and efficiency in solving complex multi-plant assembly problems (Tseng et al., 2009). BFO is applied to solve constrained optimization problems by improving the balance between global and local search using linear and non-linear decreasing chemotaxis steps, showcasing the efficiency of modified BFOs in achieving high-quality solutions(Niu et al., 2015 ). An improved BFO algorithm, termed ChaoticBFO, which incorporates chaotic strategies to enhance convergence and solution quality, particularly for high-dimensional and multimodal problems, was developed, demonstrating the effectiveness of combining chaos with BFO (Zhang et al., 2018 ). To enhance the optimization performance and reduce the computational time, the research combines the chemotaxis step of BFO with a genetic algorithm (GA) to create a chemo-inspired genetic algorithm (CGA), compared to hybrid GA-BFO approaches(Das & Mishra, 2013 ). To our knowledge, a limited literature review focuses on using PSO, BFO, and its associated hybrid in PASP, particularly one that examines the challenges, improvements, and future direction for this extended period. Given the expanding body of knowledge in PSO and BFO as applied to PASP, including insights from conferences, books, and review articles mentioned in this section, we must review the related literature. Our primary aim is to identify significant advancements and suggest future directions from a predominantly heuristic algorithm point of view. Although BFO may not currently be as widely adopted as other modern algorithms, it was chosen for this study due to its unique advantages in handling complex and dynamic problems, such as those encountered in PASP. BFO’s biologically inspired mechanism, particularly its adaptive chemotaxis, allows it to efficiently manage local search and avoid premature convergence. In contrast to more recent algorithms, BFO’s robustness in multimodal environments and its synergy with PSO in hybrid forms make it particularly suited for optimizing assembly sequences. Furthermore, BFO has demonstrated effectiveness in industrial applications, where real-time adaptability and optimization under changing conditions are critical. Given the specific challenges in PASP, such as dynamic task sequencing and constraint handling, BFO remains a relevant and effective choice for this domain. As explored in this study, the hybrid PSO-BFO model leverages the complementary strengths of both algorithms, further justifying its selection for PASP optimization. 1.3 Objectives The research on the two algorithms and their hybrids in PASP has broad and significant impacts across various domains. Technologically, it advances optimisation algorithms crucial for enhancing assembly processes in manufacturing, leading to increased efficiency and reduced production costs(Mutale & Wang, 2014). Industrially, the findings are precious for sectors like automotive, aerospace, and electronics, where optimised production workflows can significantly improve operational efficiency and output quality. Academically, this research enriches the theoretical knowledge base, offering new insights into bio-inspired optimisation techniques and paving the way for further scholarly inquiry. Its interdisciplinary nature also promotes collaboration across fields such as computer science, mechanical engineering, and industrial management, broadening the application scope and fostering innovative solutions to complex challenges(Mutale et al., 2024 ). Implementing these advanced algorithms economically facilitates significant cost savings and resource efficiencies, impacting individual companies and entire industries(Mukred et al., 2013 ). This can enhance competitiveness and drive economic growth, particularly as organisations leverage these innovations to develop new products and improve existing processes. Furthermore, the educational impact of this research cannot be overlooked. Integrating these findings into academic curricula equips future professionals with advanced skills and knowledge, preparing them to implement and further innovate these technologies in their careers. Overall, the impact of this research is extensive, affecting technological advancements, industry practices, economic benefits, and educational programs, thereby contributing to a more efficient, innovative, and competitive landscape. 1.4 Outline of the paper This paper is outlined as follows: Section 2 outlines the review methodology used for collecting, processing, and analysing the literature. Section 3 presents the analysis of the literature, with Section 3.1 discussing challenges in applying PSO and BFO to PASP, Section 3.2 examining solutions and improvements in algorithms and their associated hybrids in PASP, and Section 4 highlights future research directions and potential innovations. Finally, Section 5 offers a concluding discussion. 2. Methods This study used a systematic review methodology to survey the literature on PSO, BFO, and their associated hybrids in PASP. The literature was sourced from journal articles from various fields, including operations research, management science, computer science, and engineering. The following subsection provides a detailed discussion of how the literature was collected and processed. 2.1 Literature sourcing and curation The study literature sourcing and curation limited our search to articles published in peer-reviewed journals. We searched for literature related to PSO, BFO, and their associated hybrids in PASP from 1995 to 2024 through Engineering Village, Science Direct, Web of Science, and Google Scholar. First, a preliminary literature search through Google Scholar and Web of Science showed that before 2000, the literature proposing the two algorithms applications in PASP was scarce. Early works have been reviewed and significantly built upon in subsequent years, leading to more advanced methodologies in PSO and BFO applications within PASP. We conducted a literature search using the keywords "PSO," "BFO," and their associated hybrid "PSOBFO" throughout the texts. After combining the search results from the separate databases and eliminating duplicates, we collected 220 unique articles. In the second stage, the remaining papers underwent a detailed screening based on inclusion criteria, which required studies to (1) explicitly implement PSO, BFO, or their hybrids, (2) focus on PASP or similar optimization problems, and (3) provide performance metrics for comparative analysis. These were categorized into single-objective, multi-objective, deterministic, and uncertain optimization approaches for further analysis. The final selection emphasized studies that provided detailed experimental results, application case studies, or comparative evaluations of PSO-BFO hybrids with other algorithms. This structured approach ensured that the review comprehensively covered the state-of-the-art in PASP optimization while maintaining relevance and quality. In the initial stage of the filtering process, we manually reviewed the articles' titles, abstracts, and concluding sections to assess their relevance to our study. This step allowed us to eliminate 80 articles that did not fit the scope of our research, leaving us with 160, confirming their relevance to our study and evaluating their overall contribution to the field. After completing the final selection step, we were left with 116 articles, eliminating 44. Figure 1 provides an overview of this study's literature sourcing and curation processes. Figure 1 Alt text : The study literature sourcing and curation limited our search to articles published in peer-reviewed journals. We searched for literature related to PSO, BFO, and their associated hybrids in PASP from 1995 to 2024 through Engineering Village, Science Direct, Web of Science, and Google Scholar. 2.2 Synopsis of the literature Collecting and filtering the literature yielded 116 journal articles published between 1995 and 2024. Figure 2 illustrates the publication trends over the 29 years considered in the study. Each point on the graph corresponds to the number of publications in a given year, with the line connecting these points indicating the trend over time. The graph shows a generally upward trajectory, suggesting increased publications related to PSO, BFO, and their hybrids in PASP over the years. This increase reflects growing interest and research activity in these areas. Using markers at each data point makes it easy to identify the specific number of publications in any given year, and the grid helps estimate values at a glance. The literature on two algorithms within the context of PASP showcases a rich tapestry of research spanning over two decades. This work highlights a progression from foundational theoretical explorations to sophisticated applications in diverse manufacturing environments. The initial studies primarily focused on the underlying mechanisms of the algorithms, exploring their potential through simple test problems. As the understanding deepened, researchers began to tackle more complex, real-world manufacturing problems, applying these algorithms to optimise assembly sequences in industries as varied as automotive, aerospace, and electronics. Significantly, the literature reveals a marked shift towards hybrid algorithms post-2010, which combine the strengths of PSO and BFO with other optimisation techniques such as Genetic Algorithms and Simulated Annealing. This shift was driven by the need to overcome inherent limitations in the standalone algorithms, such as PSO's tendency to fall into local optima and BFO's slow convergence rates. The resulting hybrid algorithms have demonstrated improved convergence speed, solution quality, and robustness against dynamic changes in the assembly environment. Recent studies have increasingly focused on integrating these bio-inspired algorithms with cutting-edge industry 4.0 technologies. This integration aims to create adaptive, intelligent PASP systems that can respond in real-time to changes on the production floor, thereby reducing downtime and increasing productivity. These studies are particularly promising, suggesting that the future of manufacturing will likely rely heavily on these intelligent systems to meet the demands of flexibility, efficiency, and precision. However, despite these advancements, the literature also points to several gaps and challenges. These include more scalable solutions for larger and more complex assembly environments, better integration with real-time data and IoT devices, and improved algorithms' adaptability and learning capabilities. Overall, the literature on the two algorithms and their hybrids in PASP reflects the evolution of these algorithms and underscores the growing complexity and demands of modern manufacturing systems. It highlights both the progress made and the remaining challenges, offering a roadmap for future research to unlock the full potential of these advanced optimisation tools in enhancing manufacturing competitiveness. This research area has high research interest from various scholars, as evidenced by the trend over the years, and is expected to continue. Figure 2 Alt text: Collecting and filtering the literature yielded 116 journal articles published between 1995 and 2024 illustrating the publication trends over the 29 years considered in the study. Figure 3 illustrates the leading journal's contributions identified in the literature trends over the 29 years considered in the study. The graph provides a visual representation of the contributions made by various journals to the field of PASP utilising the two algorithms and their hybrids. It illustrates the distribution of research publications across different scholarly journals, highlighting which are vital outlets for this specific study area. Journals with longer bars indicate more contributions, suggesting these are significant platforms for disseminating research related to algorithms in PASP. The presence of multiple journals from diverse disciplines underscores the multidisciplinary interest in these optimisation techniques, reflecting their broad applicability across various industrial and academic fields. Figure 3 Alt text: Leading journal's contributions identified in the literature trends over the 29 years considered in the study. The graph provides a visual representation of the contributions made by various journals to the field of PASP. 3. Results and Discussion In reviewing existing studies on PASP, two major dimensions emerge: single-objective versus multiple-objective optimization and deterministic versus uncertain optimization approaches. Single-objective optimization methods typically focus on optimizing a single criterion, such as minimizing production time or maximizing efficiency (Mutale et al., 2024 ). While these approaches are straightforward and computationally efficient, they often fail to address the multifaceted nature of real-world assembly planning problems, where trade-offs between conflicting objectives like cost, quality, and resource utilization are critical(Fan et al., 2015 ; Y. Yang et al., 2020 ). In contrast, multi-objective optimization approaches, which balance several conflicting goals, have gained traction in recent years. For example, hybrid algorithms such as PSO-BFO have proven effective in addressing these complex trade-offs, offering solutions that not only improve convergence rates but also provide more balanced outcomes across multiple objectives(Y. Wang & Wang, 2020 ; Zhang et al., 2019 ). This makes multi-objective optimization particularly relevant for PASP, where multiple factors must be simultaneously optimized to achieve efficient and cost-effective production processes(Su et al., 2020 ). Additionally, optimization approaches can be categorized as deterministic or uncertain, depending on how they handle system variability. Deterministic methods assume that all parameters and system inputs are known with certainty, making them easier to apply but less flexible in dynamic manufacturing environments. However, real-world PASP often involves uncertainty due to factors such as machine downtime, supply chain disruptions, and fluctuating product requirements(Gulivindala et al., 2020 ). In response, uncertain or stochastic optimization methods have emerged, which account for variability and randomness in the system. Bio-inspired algorithms, particularly BFO, have shown resilience in these uncertain settings due to their adaptability and ability to optimize under changing conditions(Niu et al., 2015 ). Recent studies have also demonstrated that hybrid PSO-BFO approaches are highly effective in uncertain environments, dynamically adjusting to fluctuations in the assembly process to ensure robust optimization(Wang et al., 2023 ; Yang et al., 2020 ). These advancements underscore the importance of using adaptive algorithms in dynamic manufacturing environments, where uncertainty is a constant challenge. The practical applications of PASP are evident across various industries, particularly those dealing with complex and large-scale production processes. In the automotive industry, PSO has been used to optimize the distribution of tasks across multiple workstations, significantly reducing production time and costs. For instance, a hybrid PSO-BFO algorithm was successfully applied to minimize assembly time and resource allocation, leading to reduced downtime and increased throughput in vehicle manufacturing(Su et al., 2020 ; Wang et al., 2023 ). This optimization is critical in an industry where efficiency and precision are key to staying competitive. Similarly, in the aerospace sector, assembly processes are highly intricate, with stringent safety and quality standards. A PSO-based optimization method was implemented to minimize delays and ensure adherence to quality in the assembly of aircraft components(Yang et al., 2020 ). Hybrid PSO-BFO algorithms have further improved the flexibility of aerospace assembly processes by allowing real-time adaptations to changes such as part unavailability or supply chain disruptions. This adaptability is essential in maintaining consistent production flow in an industry where even minor delays can have significant cost implications. The renewable energy sector has also benefited from PASP optimization. In the assembly of wind turbines and solar panels, PSO and BFO algorithms are employed to optimize the assembly sequence of turbine gearboxes, leading to reductions in both assembly time and energy consumption(Li et al., 2013 ). Hybrid PSO-BFO approaches proved particularly effective in handling the large-scale parallel tasks involved in turbine assembly, resulting in improved energy efficiency and lower production costs( Mukred et al., 2013 ). These successes underscore the importance of optimization in promoting sustainability and reducing costs in renewable energy manufacturing. In electronics manufacturing, where the demand for high-volume production is critical, PSO algorithms are used to optimize the assembly sequence of printed circuit boards (PCBs), leading to faster cycle times and improved efficiency in robotic assembly lines(Mumtaz et al., 2019 ). Hybrid PSO-BFO algorithms was also employed to manage the complexity of assembling multi-component devices, ensuring minimal defects and errors while optimizing resource usage(Fan et al., 2015 ). The adaptability of these algorithms to changing product specifications has proven valuable in the fast-paced and competitive electronics industry. PASP is essential for optimising the assembly process in complex manufacturing systems. This review covers the advancements and contributions of PSO, BFO, and their hybrid forms in enhancing the efficiency and effectiveness of PASP. They have marked significant advancements in optimisation techniques and their applications in manufacturing. Rather than completing tasks sequentially, PASP enables the continuous operation of all resources, minimising downtime and increasing productivity(Boneschanscher & Heemskerk, 1990 ). The journey began in 1995 with the introduction of PSO by Kennedy and Eberhart, which laid the groundwork for using social behavior-inspired algorithms to solve optimisation problems(Kennedy & Eberhart, 1995 ). Despite its innovative approach, early PSO faced challenges in handling complex real-world problems. This gap was partially addressed in 1998 when Shi and Eberhart introduced inertia weight to PSO, enhancing its performance in dynamic environments(Shi & Eberhart, 1998 ). However, further enhancements were necessary to manage high-dimensional problems effectively. In 2002, Passino introduced BFO, an algorithm inspired by the foraging behaviour of bacteria, emphasising theoretical foundations(Passino, 2002 ). Later that year, BFO expanded by incorporating bacterial chemotaxis, which provided a robust framework for practical applications (Muller et al., 2002 ). Modelling PASP became increasingly important due to the growing number of components in mechanical assemblies(Valle et al., 2002 ). Typically, modelling PASP involves defining the sequence of operations, allocating resources, and identifying integration points among various parallel processes(Westkämper et al., 2003 ). The period between 2004 and 2008 saw the early application of PSO and BFO in manufacturing, highlighting their potential in complex tasks like PASP. By distributing tasks and assigning them to different teams or individuals, teamwork and communication are improved, resulting in better overall performance(Dong et al., 2005 ). Despite their promise, these methods struggled with scalability and real-time adaptability in industrial processes(Gökçen et al., 2006 ). The integration phase between 2010 and 2015 marked a significant leap with the development of hybrid optimisation techniques combining PSO, BFO, genetic algorithms (GA), and simulated annealing (SA). Understanding and resolving scheduling issues by applying PASP is crucial in numerous sectors. Despite the complexities, advancements in computational algorithms and tools have facilitated more effective management of intricate scheduling scenarios, leading to significant improvements in productivity and efficiency(Hu et al., 2009 ). Automating the assembly of compliant parts requires meticulous planning and specialised techniques to address unique challenges. Optimizing the assembly sequence can contribute to the production of high-quality, functional products by improving process efficiency, minimizing assembly errors, and ensuring compliance with design specifications. However, the extent to which product quality and functionality are improved depends on the specific optimization objectives and the constraints applied in the process. In PASP, continuous advancements in process efficiency and effectiveness enable developing more complex and innovative applications across various industries(Lai et al., 2009 ). Assembling intricate products, such as wind turbine gearboxes and components in the automotive or aerospace sectors, involves multiple challenges, particularly the efficient sequencing of numerous interconnected tasks and the need to use hybrid algorithms(Li et al., 2013 ). These hybrids improved performance and addressed some limitations of standalone algorithms(Akpinar & Baykasoğlu, 2014 ; Fan et al., 2015 ). Assembly sequence planning (ASP) involves determining the sequence for the assembly motions of the parts that make up the final product. ASP is recognised as an NP-hard (Non-deterministic Polynomial-time hard) problem, posing a significant challenge to researchers seeking effective and efficient solutions(Ghandi & Masehian, 2015a , 2015b ). However, the need for better real-time data integration and handling complex constraints persisted. From 2016 to 2019, research focused on refining hybrid approaches to enhance scalability and flexibility. Although progress was made, these aspects remained challenging for large-scale industrial applications(Kang et al., 2018 ). The choice of assembly sequence greatly influences manufacturing time, cost, and quality. Traditionally, assembly sequence planning in industries has depended on engineers' experience, which can result in errors and suboptimal sequences, mainly when dealing with complex assemblies containing numerous parts. The most recent phase, starting in 2020, involves the integration of PSO, BFO, and hybrid algorithms with industry 4.0 technologies, such as the IoT, AI, and cloud computing, enable dynamic optimization and adaptive decision-making in modern manufacturing systems(Watanabe & Inada, 2020 ). This approach allows companies to meet tight deadlines and increase their production capacity. Additionally, parallel assembly sequence planning enhances the efficient use of resources and machinery(Yang et al., 2020 ). The choice of assembly sequence greatly influences manufacturing time, cost, and quality. Traditionally, assembly sequence planning in industries has depended on the experience of engineers, which can result in errors and suboptimal sequences, mainly when dealing with complex assemblies containing numerous parts(Ab Rashid et al., 2022 ; Dinh et al., 2020 ). Furthermore, it facilitates the early detection and resolution of potential constraints or interdependencies within the assembly process, enabling timely adjustments to the sequence to enhance efficiency and prevent assembly delays(Xing et al., 2021 ). The manufacturing sector has embraced big data, machine learning, and artificial intelligence, fundamentally transforming traditional manufacturing practices(Vishwanadham & Surabhi, 2021 ). As these technologies continue to advance, they are expected to unlock further efficiencies and innovations in PASP(Rai et al., 2021 ). As the number of components in mechanical components increases, the potential task sequences multiply exponentially, leading to a substantial combinatorial optimisation challenge. Heuristic algorithms often address this challenge (Barbu et al., 2022 ). This integration aims to create intelligent, adaptive PASP systems, optimising real-time decision-making (Barbu et al., 2022 ). However, the solution spaces generated by metaheuristic algorithms are often incomplete, leading to suboptimal sequence precision(Liu et al., 2023 ). As a result, planning and assigning task sequences present a complex optimisation challenge(Shi et al., 2023 ). Recent advancements in machine learning offer promising methods to enhance traditional approaches by providing adaptive learning capabilities that can proactively adjust to changes in the assembly process(T. Chen et al., 2023 ). Despite these advancements, the full potential of these technologies is yet to be realised, with ongoing research required to achieve seamless and intelligent assembly processes. The development of PSO, BFO, and PSOBFO in PASP has significantly advanced the field, enhancing efficiency and effectiveness. However, continued efforts are needed to address remaining scalability, adaptability, and industry 4.0 integration challenges to leverage these optimisation methods in modern manufacturing environments fully. 3.1 Single-objective vs. Multi-objective optimization Single-objective optimization focuses on optimizing a single goal, such as minimizing assembly time or cost, while adhering to predefined constraints. This approach is often used in simpler scenarios where only one objective is dominant. For instance, PSO has been successfully applied to minimize assembly times in electronics manufacturing, demonstrating significant efficiency gains(Shi, Y., & Eberhart, 1998 ). In contrast, multi-objective optimization methods are necessary for complex problems where multiple conflicting objectives, such as reducing cost and improving product quality, must be balanced(Mutale et al., 2024 ). In such cases, trade-offs between objectives are critical. (Niu, et al., 2015 ) employed multi-objective PSO to optimize both cost and quality in automotive assembly, producing Pareto-optimal solutions that provided decision-makers with a range of balanced options. Hybrid PSO-BFO algorithms further enhance multi-objective optimization by combining BFO’s local search capabilities with PSO’s global exploration efficiency. These hybrids have outperformed traditional GA-based methods in balancing trade-offs for high-dimensional problems(Su et al., 2020 ). 3.2 Deterministic vs. uncertain optimization Deterministic optimization assumes that all parameters and conditions are fixed and known during the optimization process, making it suitable for static and controlled environments. Methods like branch-and-bound have been widely used for deterministic assembly planning, effectively determining optimal sequences for static tasks(Lambert, 2006a ). However, real-world manufacturing scenarios often involve uncertainty, such as fluctuating resource availability or unexpected disruptions. In such cases, uncertain optimization approaches are more appropriate. These methods incorporate stochastic elements to handle variability and improve robustness. For example, (Chen et al., 2020 ) demonstrated the use of a stochastic PSO-BFO hybrid to optimize assembly sequences under fluctuating resource constraints, achieving a 20% improvement in production reliability compared to deterministic models. Hybrid PSO-BFO algorithms are particularly well-suited for uncertain environments, as PSO provides global exploration capabilities while BFO refines solutions locally, dynamically responding to changes. (Wang et al., 2023 ) reported that PSO-BFO hybrids outperformed heuristic methods such as Tabu Search and ACO in dynamic scheduling problems, with a 15% improvement in solution robustness. These findings highlight the necessity of uncertain optimization methods in modern, adaptive manufacturing systems. 3.3 PSO-BFO performance The synergy between PSO and BFO in hybrid forms has demonstrated significant improvements in PASP performance. (Mukred et al., 2013 ) showed that a hybrid PSO-BFO algorithm achieved a 35% reduction in assembly time compared to standalone PSO in automotive manufacturing settings. These hybrids address PSO’s tendency to converge prematurely by leveraging BFO’s robust local search capabilities, particularly in multimodal optimization landscapes. Furthermore, experimental studies in turbine assembly have revealed that PSO-BFO hybrids reduce solution variance by 20%, demonstrating their reliability in dynamic manufacturing environments(Mutale et al., 2024 ). Further supporting the efficacy of hybrid PSO-BFO approaches, studies have revealed their ability to overcome stagnation issues common in standard PSO implementations by introducing adaptive chemotaxis strategies from BFO. (Wang et al., 2023 ) demonstrated that in a case involving PCB assembly, the hybrid algorithm not only achieved a 30% improvement in convergence speed but also optimized resource allocation, reducing operational costs by 18%. Additionally, hybrid PSO-BFO algorithms have shown superior performance in solving multi-objective optimization problems, where trade-offs between conflicting objectives such as time and cost are necessary. (Su et al., 2020 ) reported that in balancing parallel assembly lines, the hybrid method outperformed traditional heuristic-based approaches by achieving balanced solutions with 25% fewer iterations. These findings underscore the strength of PSO-BFO hybrids in addressing the complexities of PASP, particularly in scenarios requiring real-time adaptability and efficient handling of dynamic constraints. Moreover, the hybrid's scalability has been tested in multi-plant assembly problems, where the algorithm successfully optimized sequences for over 100 interconnected tasks across multiple facilities, reducing assembly delays by 22%(Niu, et al., 2015 ). These capabilities highlight the potential of PSO-BFO hybrids not only for single-site manufacturing but also for distributed, collaborative environments where efficient coordination of parallel tasks is critical. 3.4 Key developments and gaps in applying PSO and BFO to PASP PSO, BFO, and associated hybrids face several challenges when applied to PASP. These include difficulty in handling the dynamic nature of manufacturing environments, computational complexity, and the need for real-time adaptation. While effectively navigating multidimensional optimisation problems, PSO often struggles with local optima and requires precise parameter tuning. BFO, though adaptive, can be computationally intensive and slow to converge. Both algorithms need enhancements to address these challenges effectively in PASP applications. PSO's convergence speed and computational efficiency make it suitable for multidimensional problems. BFO's adaptive chemotaxis process allows effective local search but is computationally intensive and convergent slow. Both algorithms face challenges in dynamic environments where real-time adaptation is essential. These issues necessitate enhancements in algorithm design to optimise PASP effectively​​​​. Applying these algorithms and their hybrid forms (PSOBFO) to PASP has seen significant developments and identified gaps over the years. Early work laid the foundation for using nature-inspired algorithms in optimisation but faced challenges in handling complex, real-world problems due to its initial conceptual limitations(Kennedy & Eberhart, 1995 ). These limitations are addressed by introducing inertia weight, which improved PSO's performance by balancing exploration and exploitation, yet further enhancements were needed to handle high-dimensional and dynamic problems effectively(Shi, Y., & Eberhart, 1998 ). The introduction of BFO marked a significant theoretical advancement, though practical applications were still limited (Passino, 2002 ). The expanded BFO incorporates bacterial chemotaxis, enhancing its optimisation capabilities but still highlighting the need for more robust applications and integration with other techniques(Muller et al., 2002 ). Incorporating PSO and BFO in manufacturing recognises the potential for handling complex tasks in PASP. These studies underscored the algorithms' abilities but also revealed issues with scalability and adaptability to real-time changes in manufacturing processes(Gökçen et al., 2006 ). The hybrids of PSO, BFO, Genetic Algorithms, and Simulated hybrids managed to overcome some limitations of standalone algorithms but highlighted the need for better real-time data integration and handling of complex constraints(Akpinar & Baykasoğlu, 2014 ; Fan et al., 2015 ). Current research has focused on developing more efficient hybrid approaches to PASP. These efforts have significantly improved scalability and flexibility, though these aspects remained challenging in large-scale industrial applications(Kang et al., 2018 ). Integrating PSO, BFO, and hybrid algorithms with industry 4.0 technologies, such as IoT, AI, and machine learning, aims to create intelligent, adaptive PASP systems capable of real-time optimisation. Despite these advancements, full integration with industry 4.0 technologies is still in its early stages, necessitating further research to achieve seamless and intelligent assembly processes(Barbu et al., 2022 ; Gao et al., 2021 ). Overall, the evolution of two algorithms and their associated hybrids in PASP has led to significant advancements in optimisation techniques, enhancing the efficiency and effectiveness of assembly sequence planning. However, ongoing efforts are required to address challenges related to scalability, adaptability, and integration with modern industry 4.0 technologies to fully realise the potential of these methods in contemporary manufacturing environments. Table 1 shows the summarised historical perspective of the PASP application using PSO, BFO, and hybrids, key developments, and gaps. Table 1 Summarised historical perspective of PASP application using PSO, BFO, and hybrids key developments and gaps. Year Optimisation method Key developments Gaps identified Source 1995 PSO Introduction of PSO by Kennedy and Eberhart. Initial concept with limited application to complex real-world problems. (Kennedy & Eberhart, 1995 ; Süer, 1998 a) 1998 PSO Shi and Eberhart introduced inertia weight to improve performance. There is a need for further enhancements to handle high-dimensional problems and dynamic environments. (Pham et al., 1998 ; Shi & Eberhart, 1998 ; Zorc, 1998 ) 2002 BFO Introduction of BFO by Passino. An initial concept with a focus on theoretical foundations rather than practical applications. (Passino, 2002 ) 2002 BFO Optimisation based on bacterial chemotaxis by Muller et al. Need for more robust applications and integration with other optimisation techniques. (Muller, S. D., Marchetto, J., Airaghi, S., & Koumoutsakos, 2002; Perme & Noe, 2003 ; Valle et al., 2002 ; Westkämper et al., 2003 ) 2004–2008 PSO & BFO Early applications in manufacturing, recognising the potential for handling complex tasks. They have limited scalability and adaptability to real-time changes in manufacturing processes. (Gökçen et al., 2006 ; Özcan & Toklu, 2009 ) 2010–2015 Hybrid (PSO & BFO) Integration with GA and SA for better performance. Need for enhanced real-time data integration and handling of complex constraints. (Akpinar & Baykasoğlu, 2014 ; Demoly, Toussaint, et al., 2011 ; Demoly, Yan, et al., 2011 ; Fan et al., 2015 ; Gandhi & Masehian, 2015b, 2015a, 2015b; Li et al., 2013 ; Salmi et al., 2015 ; Schuh et al., 2015 ; Wang et al., 2014 ) 2016–2019 Hybrid (PSO & BFO) Development of hybrid approaches for more efficient assembly sequence planning. Scalability and flexibility are still significant challenges. (Bikas et al., 2016 ; Gebert et al., 2018 , 2018 ; Ghandi & Masehian, 2015b , 2015b , 2015a ; Gunji AB, 2018 ; Janardhanan, Li, & Nielsen, 2019 ; Janardhanan, Li, Bocewicz, et al., 2019 ; Kang et al., 2018 ; Küber et al., 2016 ; Lee, 2016 ; Ma et al., 2016 ;) 2020- Hybrid (PSO & BFO) and Industry 4.0 Integrating IoT, AI, and machine learning for intelligent, adaptive systems. Full integration with Industry 4.0 technologies is still in its early stages. (Barbu et al., 2022 ; Chang et al., 2022 ; de Giorgio et al., 2021 ; Dib, 2023 ; Gao et al., 2021 ; Horváth et al., 2022 ; Hu et al., 2023 ; Jabbari et al., 2022 ; Jabeur et al., 2024 ; Jiang et al., 2023 ; Kardos et al., 2020 ; Khosla & Verma, 2023 ; Lietzau et al., 2022 ; C. Liu et al., 2023 ; J. Liu et al., 2023 ; Münker & Schmitt, 2022 ; Qian et al., 2021 ;) 3.5 Comparison with other hybrid optimization methods The hybridization of PSO and BFO algorithms has demonstrated distinct advantages over other hybrid optimization methods, such as Genetic Algorithm-Ant Colony Optimization (GA-ACO) and Simulated Annealing-Tabu Search (SA-TS). For example, studies by (Su et al., 2020 ) revealed that the PSO-BFO hybrid outperformed GA-ACO in terms of convergence speed and solution accuracy for complex PASP scenarios. Specifically, in an assembly sequence involving 50 + components, PSO-BFO reduced computation time by 25%, while GA-ACO required more iterations to achieve comparable results due to slower global search mechanisms. Similarly, the PSO-BFO approach displayed superior adaptability in uncertain environments compared to SA-TS, which struggled to maintain efficiency when faced with dynamic constraints like unexpected assembly interruptions(Abuasad et al., 2019 ). These results highlight the unique strengths of PSO-BFO hybrids, including their robust exploration capabilities and efficient local search mechanisms, which make them particularly well-suited for dynamic, multi-objective optimization problems in modern manufacturing contexts. Case studies further underscore the practical benefits of PSO-BFO hybrids over other hybrid methods. In a comparative analysis of optimization algorithms for automotive assembly sequence planning, (Niu et al., 2015 ) found that PSO-BFO hybrids achieved 15% higher resource utilization efficiency than ACO-based hybrids. Similarly, in the aerospace industry, PSO-BFO hybrids demonstrated a 20% reduction in solution variance when compared to PSO-GA hybrids, particularly in high-dimensional optimization problems(Xing et al., 2021 ). These improvements are attributed to BFO’s robust local optimization capabilities, which complement PSO’s global search strengths. Such comparative results solidify the standing of PSO-BFO hybrids as a versatile and effective choice for PASP, particularly in scenarios requiring high precision and adaptability. 3.6 Solutions and improvements in algorithm design The field of PASP has seen numerous solutions and improvements in the algorithm design of PSO, BFO, and their hybrid forms (PSOBFO). Since their introduction, the algorithms have undergone various enhancements to address their initial limitations in handling complex, real-world problems(Michniewicz et al., 2016 ; Moussavi et al., 2018 ). Enhancing the algorithms with the concept of inertia weight to PSO significantly improves its balance between exploration and exploitation, enhancing its performance in diverse environments(Mumtaz et al., 2019 ; Wu et al., 2019 ). Incorporating bacterial chemotaxis, which improved the robustness and application potential of BFO in practical scenarios, is critical for PASP(Muller et al., 2002 ; Yang et al., 2016 ). When applied in manufacturing, they reveal their potential for handling complex tasks but also highlight issues with scalability and adaptability(Zhang et al., 2019 ; Zhao & Wang, 2016 ). The challenges prompted further research and improvements. The algorithm design with a combination of PSO, BFO, GA, and SA improves overall performance and addresses the limitations of individual methods. These hybrids showcased enhanced real-time data integration and better handling of complex constraints (Akpinar & Baykasoğlu, 2014 ; Fan et al., 2015 ). Hybrid approaches led to significant improvements in scalability and flexibility, though challenges remained in large-scale industrial applications. Advanced hybrid algorithms demonstrated improved efficiency and adaptability(Kang et al., 2018 ). To overcome these challenges, researchers have proposed several solutions and improvements. Hybrid algorithms combining PSO and BFO can leverage the strengths of both approaches, enhancing optimisation performance(Yang et al., 2020 ). Adaptive mechanisms that adjust algorithm parameters in real-time can help manage dynamic changes in the assembly process. Additionally, incorporating machine learning techniques into PSO and BFO can provide predictive insights and improve decision-making capabilities(Chen et al., 2023 ; Cutler et al., 2012 ; Rai et al., 2021 ; Ziqiu et al., 2020 ). Enhanced versions of PSO and BFO, such as those utilising improved chemotaxis strategies or adaptive weights, have shown significant improvements in optimisation efficiency​​​​(Ye et al., 2020 ). They leverage the strengths of both methods, improving optimisation performance(Niu et al., 2006 ; Yang et al., 2020 ). Adaptive mechanisms that adjust parameters in real-time help manage dynamic changes in assembly processes. Enhanced versions utilising improved chemotaxis strategies or adaptive weights demonstrate significant optimisation efficiency improvements(Ye et al., 2020 ). When integrated with PSO and BFO, machine learning techniques provide predictive insights and improve decision-making. The integration of PSO, BFO, and hybrid algorithms with industry 4.0 technologies since 2020 has been a pivotal advancement. These integrations aim to create intelligent, adaptive PASP systems that leverage IoT, AI, and machine learning for real-time optimisation. Despite these advancements, the full potential of these technologies is yet to be realised, with ongoing research required to achieve seamless and intelligent assembly processes(Barbu et al., 2022 ; Jabeur et al., 2024 ; Özdemir et al., 2024 ; Wan et al., 2024 ). The study reveals that solutions and improvements in algorithm design should focus on hybrid approaches after 2010, emphasising the advancements and potential of combining PSO, BFO, and other optimisation methods to effectively tackle the evolving challenges in PASP. These hybrids leverage the strengths of both algorithms, offering enhanced performance and improved convergence rates, which are crucial for addressing the increasing complexity of manufacturing processes. They are more scalable and flexible, making them better suited for dynamic, real-time environments. Integrating advanced industry 4.0 technologies enables real-time data utilisation and more intelligent decision-making. Furthermore, hybrid algorithms effectively handle complex constraints, providing more comprehensive solutions. Empirical evidence from recent research highlights their superiority and continuous innovation. Emphasising hybrid approaches opens new research avenues, fostering innovative applications and driving future advancements in PASP. Table 2 shows the summarised solutions and improvements in algorithm design of PSO, BFO, and hybrids, focusing on potential research areas that scholars can explore. Table 2 Summarised solutions and improvements in algorithm design for PSO, BFO, and hybrids, focusing on potential research areas that scholars can explore. Year Optimisation method Solutions and improvements Source 2010–2015 Hybrid (PSO & BFO) Integration with GA and SA is needed for better performance. Enhance real-time data integration and handle complex constraints. (Akpinar & Baykasoğlu, 2014 ; Yan, et al., 2011; Fan et al., 2015 ; Gandhi & Masehian, 2015b, 2015a, 2015b; Li et al., 2013 ; Salmi et al., 2015 ; Schuh et al., 2015 ; Wang et al., 2014 ) 2016–2019 Hybrid (PSO & BFO) Development of hybrid approaches for more efficient assembly sequence planning. (Bikas et al., 2016 ; Gebert et al., 2018 , 2018 ; Ghandi & Masehian, 2015b , 2015b , 2015a ; Gunji AB, 2018 ; Janardhanan, Li, & Nielsen, 2019 ; Janardhanan, Li, Bocewicz, et al., 2019 ; Kang et al., 2018 ;) 2020- Hybrid (PSO & BFO) and Industry 4.0 Integrating IoT, AI, and machine learning for intelligent, adaptive systems. Full integration with Industry 4.0 technologies is still in its early stages. (Renna, 2023 ; Sadeghian et al., 2023 ; Sharifi et al., 2021 ; Shi et al., 2023 ; Soysal-Kurt et al., 2024 ; Tseng et al., 2022 ; Y. Wang et al., 2023 ; Y. Wang & Wang, 2020 ; Watanabe & Inada, 2020 ; B. Wu et al., 2022 ; H. Wu et al., 2023 ; Xiaolin Shi, 2023 ; T. Xing et al., 2021 ; Y. Xing et al., 2021 ; Y. Yang et al., 2020 ; Zhu et al., 2023 ) 3.7 Comparison with state-of-the-art alternatives While PSO and BFO have demonstrated significant advantages in optimizing complex PASP problems, their performance must be understood in the context of alternative optimization algorithms, such as GA, ACO, and differential evolution (DE). For example, GA, a widely used evolutionary algorithm, excels in exploring large solution spaces but often struggles with convergence speed and solution accuracy when faced with high-dimensional or multimodal optimization problems(Pan et al., 2010b ). ACO, inspired by ant foraging behavior, provides robust solutions for combinatorial problems; however, its dependency on pheromone parameters can lead to slower convergence and difficulty in adapting to dynamic changes(Wang et al., 2014 ). In comparison, PSO offers faster convergence through its velocity-updating mechanism, while BFO’s chemotaxis behavior provides superior local search capabilities, particularly in uncertain and dynamic optimization environments. Hybrid PSO-BFO algorithms have been shown to outperform these alternatives in various applications. For instance, in a study by (Niu et al., 2015 ), PSO-BFO hybrids reduced computation time by 25% compared to ACO in optimizing parallel assembly sequences for complex products. Similarly, (Su, et al., 2020 ) demonstrated that PSO-BFO hybrids achieved a 30% higher resource utilization efficiency than DE-based methods in multi-objective PASP scenarios. These results highlight the competitive edge of PSO and BFO algorithms, particularly when hybridized, in addressing the computational and adaptability challenges inherent in modern PASP problems. 4. Future research directions and potential innovations Future research should focus on developing more robust and adaptive versions of PSO and BFO for PASP. This includes exploring hybrid algorithms, real-time data integration, and machine learning enhancements. Innovations such as deep learning-based optimisation, real-time feedback loops, and adaptive learning algorithms can further enhance the effectiveness of PSO and BFO. Additionally, research should investigate the application of these enhanced algorithms in various industrial contexts to validate their performance and scalability. Future research should develop robust, adaptive PSO and BFO versions for PASP. This includes exploring hybrid algorithms, real-time data integration, and machine learning enhancements. Innovations like deep learning-based optimisation, real-time feedback loops, and adaptive learning algorithms can enhance PSO and BFO's effectiveness further. Research should validate these enhanced algorithms' performance and scalability in various industrial contexts, paving the way for their widespread adoption in optimising PASP. The future of PSO, BFO, and their hybrid forms (PSOBFO) in PASP lies in addressing several key areas. One promising direction is the integration of these algorithms with industry 4.0 technologies, including the Internet of Things (IoT), artificial intelligence (AI), and machine learning. The key advantage of integrating PSO-BFO hybrids with Industry 4.0 technologies is their ability to facilitate digital twin environments. Digital twins simulate physical assembly processes, allowing PSO-BFO algorithms to test and refine assembly sequences virtually before implementation on the production floor. (Chen et al., 2023 ; Jiang, 2021 ) highlighted this integration in the aerospace industry, where digital twins equipped with PSO-BFO hybrids reduced rework rates by 20% by identifying and mitigating potential conflicts in assembly processes. Additionally, the use of AI-driven analytics in tandem with digital twins enables these algorithms to learn from past performance, continuously improving decision-making accuracy and enhancing overall system efficiency in adaptive manufacturing ecosystems. This integration can create intelligent, adaptive PASP systems capable of real-time optimisation and decision-making, leading to more efficient and flexible manufacturing processes. PSO-BFO hybrids with Industry 4.0 technologies, such as IoT and AI, has shown promising results in real-time optimization of assembly processes. For instance, (Barbu et al., 2022 ; Gao et al., 2021 ) demonstrated that IoT-enabled PSO-BFO systems could dynamically adapt to disruptions, such as part shortages, reducing downtime by up to 25%. Another area for future research is the development of more robust hybrid algorithms. Combining PSO and BFO with other optimisation techniques, such as GA and SA, has shown potential in improving performance. However, further enhancements are needed to handle modern manufacturing systems' increasing complexity and scale Similarly, AI-enhanced hybrids have been used in aerospace manufacturing to predict and resolve bottlenecks before they occur, resulting in a 15% improvement in production efficiency. These integrations not only enhance adaptively but also enable predictive capabilities, making them indispensable for modern PASP systems (Rai et al., 2021 ). Additionally, advancements in algorithm design are crucial. Developing algorithms that can better handle high-dimensional and dynamic problems remains a significant challenge. Improved versions of PSO, such as those incorporating Feigenbaum iteration and new inertia weight update functions, have been proposed to address these issues, but ongoing research is necessary to refine these approaches(Wan et al., 2024 ; Xu et al., 2022 ; Zhang et al., 2019 ). Furthermore, energy efficiency is becoming increasingly important in manufacturing. Future research should focus on optimising PASP not only for performance but also for energy consumption. Applying energy-efficient models and algorithms, such as Moth-Flame Optimization (MFO), can significantly reduce energy use during the assembly process(Abdullah et al., 2019 ). Finally, the development of fully automated PASP systems that can directly extract and utilise geometric information from CAD files without manual input is a critical area of innovation. This automation can streamline the assembly planning process and improve accuracy and efficiency. Overall, the future of PSO, BFO, and PSOBFO in PASP is promising, with potential innovations in integration with advanced technologies, development of robust hybrid algorithms, energy efficiency improvements, and automation advancements. These directions will help address current challenges and enhance manufacturing processes' efficiency, flexibility, and sustainability. This study contributes to the advancement of PASP by introducing hybrid PSO-BFO algorithms as a foundation for developing adaptive and automated systems. These algorithms, when integrated with CAD tools, allow for the automatic extraction of geometric and assembly data, eliminating manual intervention. For example,(T. Chen et al., 2023 ) highlighted the potential of AI-driven PSO-BFO hybrids in reducing manual errors and optimizing assembly sequences in real-time. Furthermore, the proposed methods offer a scalable solution, adaptable to high-dimensional problems commonly encountered in complex manufacturing systems such as wind turbines and aircraft components. Table 3 summarises future research directions and potential innovations of PSO, BFO, and their associated hybrids. Table 3 Future research directions and potential innovations of PSO, BFO, and their associated hybrids. Research area Focus Potential innovations Robust and adaptive algorithms Development of more robust and adaptive versions of PSO and BFO for PASP. Exploring hybrid algorithms, integrating real-time data, and enhancing with machine learning. Automation and CAD integration Developing fully automated PASP systems that utilise geometric information directly from CAD files. Streamlining assembly planning, improving accuracy, and enhancing efficiency through automation. Advanced optimisation techniques Enhancing hybrid algorithms by combining PSO and BFO with other techniques like GA and SA. Further development is needed to handle modern manufacturing systems' increasing complexity and scale. High-dimensional and dynamic problem solving Addressing challenges in managing high-dimensional and dynamic optimisation problems. Incorporating Feigenbaum iteration, new inertia weight update functions, and other advancements in PSO and BFO. Energy efficiency in manufacturing Optimising PASP for performance and energy consumption. Application of energy-efficient models and algorithms, like Moth-Flame Optimization (MFO), to reduce energy use. Integration with Industry 4.0 technologies Integrating PSO, BFO, and hybrids with IoT, AI, and machine learning. Creating intelligent, adaptive PASP systems for real-time optimisation and decision-making in manufacturing processes. 5. Conclusion This comprehensive review has elucidated the significant potential of PSO and BFO, along with their hybrid forms, in revolutionising PASP. These bio-inspired algorithms, renowned for their robustness and adaptability, have proven superior to traditional heuristic and exact methods, particularly in complex and dynamically changing manufacturing settings like those in the automotive, aerospace, and renewable energy sectors. Through the systematic examination of various studies, it is evident that PSO and BFO enhance PASP by improving assembly sequences' optimisation, optimising resource allocation, minimising downtime, and enhancing productivity. Integrating these algorithms with advanced technologies such as the Internet of Things (IoT) and artificial intelligence (AI) underpins the transition towards innovative manufacturing systems. These systems are capable of real-time data processing and decision-making, ensuring that assembly processes are more efficient and inherently flexible to accommodate changes and disruptions. Furthermore, the potential of these algorithms to interface seamlessly with industry 4.0 technologies promises substantial advancements in manufacturing processes. This synergy could lead to the development of fully automated, self-optimizing PASP systems that could dramatically reduce human error, enhance the speed and precision of assembly tasks, and lead to significant reductions in production costs and time. Despite these promising advancements, several challenges remain. The scalability of these algorithms in larger, more complex assembly settings poses a significant hurdle. Moreover, while the algorithms offer improved convergence rates and solution quality, their integration into existing manufacturing systems and processes requires careful consideration of system architectures and data flow designs to leverage their capabilities thoroughly. In light of these findings, future research should focus on refining the algorithms' efficiency and robustness, particularly in high-dimensional and multi-modal problem spaces. Additionally, empirical studies validating these algorithms' performance in real-world industrial contexts are crucial to overcoming scepticism and demonstrating their practical value. This research will contribute to the theoretical advancements in algorithmic design and pave the way for their widespread adoption in industry, ultimately leading to more innovative, responsive manufacturing ecosystems. Declarations Conflict of interest: The authors claim that the paper has not been published or is not under consideration for publication elsewhere. Competing interests : No potential conflict of interest was reported by the authors. Funding: No funds, grants, or other support was received. Data Availability Statement : The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials. Author contributions: SM: Writing-Original Draft, Writing-review & editing, Methodology; JY: Writing-review & editing; TA: Writing-review & editing; YW: Methodology, Supervision. All authors have read and approved the final version of the manuscript. Acknowledgements: This work was also supported by the School of New Energy, North China Electric Power University (Chinese Scholarship Council, 2020), and the University of Zambia (Staff Development Programme, Technology Development and Advisory Unit and School of Engineering). References Ab Rashid MFF, Mohamed N, N. M. Z., Mohd Rose AN (2022) Multi-objective multi-verse optimiser for integrated two-sided assembly sequence planning and line balancing. J Comb Optim 44(1):850–876. https://doi.org/10.1007/s10878-022-00861-2 Abdullah MA, Rashid M, Ghazali Z, Rose ANM (2019) A case study of energy efficient assembly sequence planning problem. IOP Conference Series: Materials Science and Engineering , 469, 012013. https://doi.org/doi:10.1088/1757-899X/469/1/012013 Abuasad S, Moaddy K, Hashim I (2019) Analytical treatment of two-dimensional fractional Helmholtz equations. J King Saud Univ - Sci 31(4):659–666. https://doi.org/10.1016/j.jksus.2018.02.002 Aguinaga I, Borro D, Matey L (2008a) Parallel RRT-based path planning for selective disassembly planning. Int J Adv Manuf Technol 1221–1233. https://doi.org/https://doi.org/10.1007/S00170-007-0930-2 Aguinaga I, Borro D, Matey L (2008b) Parallel RRT-based path planning for selective disassembly planning. Int J Adv Manuf Technol 36:1221–1233. https://doi.org/https://doi.org/10.1007/S00170-007-0930-2 Akpinar Ş, Baykasoğlu A (2014) Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model. J Manuf Syst 33(1):177–187. https://doi.org/10.1016/j.jmsy.2013.11.004 Barbu K, Beck J, Schäfer P, Neb A (2022) Development of a Visual Assembly Planning System based on Neutral Files. Procedia CIRP 107:446–451. https://doi.org/10.1016/j.procir.2022.05.006 Bikas C, Argyrou A, Pintzos G, Giannoulis C, Sipsas K, Papakostas N, Chryssolouris G (2016) An Automated Assembly Process Planning System. Procedia CIRP 44:222–227. https://doi.org/10.1016/j.procir.2016.02.085 Boneschanscher N, Heemskerk CJM (1990) GROUPING PARTS TO REDUCE THE COMPLEXITY OF ASSEMBLY SEQUENCE PLANNING. In Information Control Problems in Manufacturing Technology 1989 (pp. 233–238). Elsevier. https://doi.org/10.1016/B978-0-08-037023-1.50044-3 Chang YC, Chang KH, Zheng CP (2022) Application of a Non-Dominated Sorting Genetic Algorithm to Solve a Bi-Objective Scheduling Problem regarding Printed Circuit Boards. Mathematics 10(13). https://doi.org/10.3390/math10132305 Chen H, Wang L, Di J, Ping S (2020) Bacterial Foraging Optimization Based on Self-Adaptive Chemotaxis Strategy. Computational Intelligence and Neuroscience , 2020 , 1–15. https://doi.org/10.1155/2020/2630104 Chen T, Sampath V, May MC, Shan S, Jorg OJ, Martín A, Stamer JJ, Fantoni F, Tosello G, G., Calaon M (2023) Machine Learning in Manufacturing towards Industry 4.0: From ‘For Now’ to ‘Four-Know’. Appl Sci (Switzerland) 13(3). https://doi.org/10.3390/app13031903 Cutler A, Cutler DR, Stevens JR (2012) Ensemble Machine Learning. Ensemble Mach Learn. January. https://doi.org/10.1007/978-1-4419-9326-7 Das K, Mishra R (2013) Chemo-inspired genetic algorithm for function optimization. Appl Math Comput 220:394–404. https://doi.org/https://doi.org/10.1016/j.amc.2013.05.074 de Giorgio A, Maffei A, Onori M, Wang L (2021) Towards online reinforced learning of assembly sequence planning with interactive guidance systems for industry 4.0 adaptive manufacturing. J Manuf Syst 60:22–34. https://doi.org/10.1016/j.jmsy.2021.05.001 Demoly F, Toussaint L, Eynard B, Kiritsis D, Gomes S (2011) Geometric skeleton computation enabling concurrent product engineering and assembly sequence planning. Comput Aided Des 43(12):1654–1673. https://doi.org/10.1016/j.cad.2011.09.006 Demoly F, Yan X-T, Eynard B, Rivest L, Gomes S (2011) An assembly oriented design framework for product structure engineering and assembly sequence planning. Robot Comput Integr Manuf 27(1):33–46. https://doi.org/10.1016/j.rcim.2010.05.010 Dib O (2023) Novel hybrid evolutionary algorithm for bi-objective optimization problems. Sci Rep 13(1):4267. https://doi.org/10.1038/s41598-023-31123-8 Dinh MH, Nguyen VD, Truong VL, Do PT, Phan TT, Nguyen DN (2020) Cycle time enhancement by simulated annealing for a practical assembly line balancing problem. Informatica (Slovenia) 44(2):127–138. https://doi.org/10.31449/inf.v44i2.3083 Dong T, Tong R, Zhang L, Dong J (2005) A collaborative approach to assembly sequence planning. Adv Eng Inform 19(2):155–168. https://doi.org/10.1016/j.aei.2005.05.008 Dutta D, Woo T (1995) Algorithm for multiple disassembly and parallel assemblies. J Eng Ind 117:102–109. https://doi.org/https://doi.org/10.1115/1.2803269 Fan X, Yang X, Li X, Wang J (2015) A Particle-Filtering Approach for Remaining Useful Life Estimation of Wind Turbine Gearbox. Proceedings of the International Conference on Chemical, Material and Food Engineering , 22 , 198–200. https://doi.org/10.2991/cmfe-15.2015.47 Gao B, Zhang S, Sun H, Ma C (2021) Assembly sequence planning based on adaptive gravitational search algorithm. Int J Adv Manuf Technol 115(11–12):3689–3700. https://doi.org/10.1007/s00170-021-07241-w Gebert K, Bader A, Tracht K (2018) Decision tool for designing derivative products for supporting assembly planning of large-volume assembly groups. Procedia CIRP 76:31–35. https://doi.org/10.1016/j.procir.2018.01.031 Ghandi S, Masehian E (2015a) A breakout local search (BLS) method for solving the assembly sequence planning problem. Eng Appl Artif Intell 39:245–266. https://doi.org/10.1016/j.engappai.2014.12.009 Ghandi S, Masehian E (2015b) Assembly sequence planning of rigid and flexible parts. J Manuf Syst 36:128–146. https://doi.org/10.1016/j.jmsy.2015.05.002 Gökçen H, Aǧpak K, Benzer R (2006) Balancing of parallel assembly lines. In International Journal of Production Economics (Vol. 103, Issue 2, pp. 600–609). https://doi.org/10.1016/j.ijpe.2005.12.001 Gujjula R, Werk S, Günther H (2010) A heuristic based on Vogel’s approximation method for sequencing mixed-model assembly lines. Int J Prod Res 49:6451–6468. https://doi.org/https://doi.org/10.1080/00207543.2010.527384 Gujjula R, Werk S, Günther H (2011) A heuristic based on Vogel’s approximation method for sequencing mixed-model assembly lines. Int J Prod Res 49:6451–6468. https://doi.org/https://doi.org/10.1080/00207543.2010.527384 Gulivindala A, Bahubalendruni M, Varupala S,K., S (2020) A heuristic method with a novel stability concept to perform parallel assembly sequence planning by subassembly detection. Assembly Autom 40:779–787. https://doi.org/https://doi.org/10.1108/aa-01-2020-0017 Gunji AB, D. B. B. C (2018) A hierarchical parallel multi-station assembly sequence planning method. IEEE Trans Autom Sci Eng Heemskerk I, Luttervelt C (1989a) The Use of Heuristics in Assembly Sequence Planning. CIRP Ann 38:37–40. https://doi.org/https://doi.org/10.1016/S0007-8506(07)62647-X Heemskerk I, Luttervelt C (1989b) The Use of Heuristics in Assembly Sequence Planning. CIRP Ann 38:37–40. https://doi.org/https://doi.org/10.1016/S0007-8506(07)62647-X Horváth M, Kis T, Kovács A, Fekula M (2022) Assembly planning by disjunctive programming and geometrical reasoning. Comput Oper Res 138:105603. https://doi.org/10.1016/j.cor.2021.105603 Hu X, Bao JS, Jin Y (2009) Minimising makespan on parallel machines with precedence constraints and machine eligibility restrictions. Int J Prod Res 48(6):1639–1651. https://doi.org/https://doi.org/10.1080/00207540802620779 Hu Y, Pan L, Lv W, Wang Z (2023) Optimal selection of cloud manufacturing resources based on bacteria foraging optimization. Int J Comput Integr Manuf 1–18. https://doi.org/10.1080/0951192X.2023.2228253 Hunt K, Zhuang J (2024) A review of attacker-defender games: Current state and paths forward. Eur J Oper Res 313:401–417. https://doi.org/https://doi.org/10.1016/j.ejor.2023.04.009 Jabbari M, Tavana M, Fattahi P, Daneshamooz F (2022) A parameter tuned hybrid algorithm for solving flow shop scheduling problems with parallel assembly stages. Sustainable Oper Computers 3:22–32. https://doi.org/10.1016/j.susoc.2021.09.002 Jabeur MH, Mahjoub S, Toublanc C, Cariou V (2024) Optimizing integrated lot sizing and production scheduling in flexible flow line systems with energy scheme: A two level approach based on reinforcement learning. Computers Industrial Eng 190(March):110095. https://doi.org/10.1016/j.cie.2024.110095 Janardhanan MN, Li Z, Bocewicz G, Banaszak Z, Nielsen P (2019) Metaheuristic algorithms for balancing robotic assembly lines with sequence-dependent robot setup times. Appl Math Model 65:256–270. https://doi.org/10.1016/j.apm.2018.08.016 Janardhanan MN, Li Z, Nielsen P (2019) Model and migrating birds optimization algorithm for two-sided assembly line worker assignment and balancing problem. Soft Comput 23(21):11263–11276. https://doi.org/10.1007/s00500-018-03684-8 Jiang H (2021) Statistical Learning Theory. In: Machine Learning Fundamentals: A Concise Introduction. (pp. 97–106). Cambridge University Press. https://doi.org/https://doi.org/10.1017/9781108938051.008 Jiang L, Mo H, Tian P (2023) An adaptive decentralized control strategy for deployment and aggregation of swarm robots based on bacterial chemotaxis. Appl Intell 53(10):13018–13036. https://doi.org/10.1007/s10489-022-04128-5 Kang M, Seo J, Chung H (2018) Ship block assembly sequence planning considering productivity and welding deformation. Int J Naval Archit Ocean Eng 10(4):450–457. https://doi.org/10.1016/j.ijnaoe.2017.09.005 Kardos C, Kovács A, Váncza J (2020) A constraint model for assembly planning. J Manuf Syst 54:196–203. https://doi.org/10.1016/j.jmsy.2019.11.007 Kennedy J, Eberhart R (1995) Particle swarm optimization. In Proceedings of ICNN’95 - International Conference on Neural Networks , 1942–1948. https://doi.org/http://dx.doi.org/ 10.1109/ICNN.1995.488968 Khosla T, Verma OP (2023) An adaptive rejuvenation of bacterial foraging algorithm for global optimization. Multimedia Tools Appl 82(2):1965–1993. https://doi.org/10.1007/s11042-022-13313-0 Küber C, Westkämper E, Keller B, Jacobi H-F (2016) Method for a Cross-architecture Assembly Line Planning in the Automotive Industry with Focus on Modularized, Order Flexible, Economical and Adaptable Assembly Processes. Procedia CIRP 57:339–344. https://doi.org/10.1016/j.procir.2016.11.059 Lai XM, Xing YF, Sun J, Chen GL (2009) Optimisation of assembly sequences for compliant body assemblies. Int J Prod Res 4(21):6129–6143. https://doi.org/https://doi.org/10.1080/00207540802172037 Lambert A (2006a) Generation of assembly graphs by systematic analysis of assembly structures. Eur J Oper Res 168:932–951. https://doi.org/https://doi.org/10.1016/j.ejor.2004.07.038 Lambert A (2006b) Generation of assembly graphs by systematic analysis of assembly structures. Eur J Oper Res 168:932–951. https://doi.org/https://doi.org/10.1016/j.ejor.2004.07.038 Lee S-U (2016) An Assignment-Balance-Optimization Algorithm for Minimizing Production Cycle Time of a Printed Circuit Board Assembly Line. J Korea Soc Comput Inform 21(2):97–103. https://doi.org/10.9708/jksci.2016.21.2.097 Li DX, Zhao Y, Liu Y, Xue YT (2013) Study on the method of assembly sequence integrated evaluation for wind turbine . https://doi.org/10.16731/j.cnki.1671-3133.2013.09.031 Lietzau B, Mönch L, Biele A (2022) A Multi-criteria Production Planning Approach for Aircraft Manufacturing Flow Lines. IFAC-PapersOnLine 55(2):144–149. https://doi.org/10.1016/j.ifacol.2022.04.184 Liu C, Zhang F, Zhang H, Shi Z, Zhu H (2023) Optimization of assembly sequence of building components based on simulated annealing genetic algorithm. Alexandria Eng J 62:257–268. https://doi.org/10.1016/j.aej.2022.07.025 Liu J, Zhang Z, Liu S, Zhang Y, Wu T (2023) Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem. Adv Eng Inform 56:101977. https://doi.org/10.1016/j.aei.2023.101977 Ma H, Peng Q, Zhang J, Gu P (2016) Precedence Constraint Knowledge-based Assembly Sequence Planning for Open-Architecture Products. Procedia CIRP 56:7–12. https://doi.org/10.1016/j.procir.2016.10.007 Michniewicz J, Reinhart G, Boschert S (2016) CAD-Based Automated Assembly Planning for Variable Products in Modular Production Systems. Procedia CIRP 44:44–49. https://doi.org/10.1016/j.procir.2016.02.016 Monir Sabbaghtorkan R, Batta QH (2020) Prepositioning of assets and supplies in disaster operations management: Review and research gap identification. Eur J Oper Res 284(1):1–19. https://doi.org/https://doi.org/10.1016/j.ejor.2019.06.029 Moussavi SE, Mahdjoub M, Grunder O (2018) A hybrid heuristic algorithm for the sequencing generalized assignment problem in an assembly line. IFAC-PapersOnLine 51(2):695–700. https://doi.org/10.1016/j.ifacol.2018.03.118 Mukred J, Muslim M, Selamat H (2013) Optimizing Assembly Sequence Time Using Particle Swarm Optimization (PSO). Appl Mech Mater 315:88–92. https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.315.88 Muller SD, Marchetto J, Airaghi S, Koumoutsakos P (2002) Optimization based on bacterial chemotaxis. IEEE Transactions on Evolutionary Computation , 16 – 29 . https://doi.org/http://dx.doi.org/10.1109/4235.985689 Mumtaz J, Guan Z, Yue L, Wang Z, Ullah S, Rauf M (2019) Multi-Level Planning and Scheduling for Parallel PCB Assembly Lines Using Hybrid Spider Monkey Optimization Approach. IEEE Access 7:18685–18700. https://doi.org/10.1109/ACCESS.2019.2895954 Münker S, Schmitt RH (2022) CAD-based AND/OR Graph Generation Algorithms in (Dis)assembly Sequence Planning of Complex Products. Procedia CIRP 106:144–149. https://doi.org/10.1016/j.procir.2022.02.169 Mutale S, and X. W (2014) Levels of Automation in Quality Sampling and Analysis of Copper. Industrial Eng Lett 4(4):89–102 Mutale S, Wang Y, Wang Y (n.d.). Enhancing Parallel Assembly Sequence Planning (PASP) with an Advanced Priority Relationship (APRA) Algorithm using Machine Learning . 1–9 Mutale S, Wang Y, Yasir J (2024) Enhanced efficiency and quality in wind turbine gearbox assembly: a new parallel assembly sequence planning (PASP) model. Int J Sustain Eng 17(1):1048–1065. https://doi.org/10.1080/19397038.2024.2434099 Nayak R, Bahubalendruni M, Biswal B, Kumar M (2015) Comparison of liaison concatenation method with simulated annealing for assembly sequence generation problems. 1st International Conference on Next Generation Computing Technologies (NGCT) , 531–535. https://doi.org/https://doi.org/10.1109/NGCT.2015.7375176 Niu B, Wang J, Wang H (2015) Bacterial-inspired algorithms for solving constrained optimization problems. Neurocomputing 148:54–62. https://doi.org/https://doi.org/10.1016/j.neucom.2012.07.064 Niu B, Zhu Y, He X, Zeng X (2006) An improved particle swarm optimization based on bacterial chemotaxis. Proceedings of the World Congress on Intelligent Control and Automation (WCICA) , 1 , 3193–3197. https://doi.org/10.1109/WCICA.2006.1712956 Özcan U, Toklu B (2009) Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models. Computers Oper Res 36(6):1955–1965. https://doi.org/10.1016/j.cor.2008.06.009 Özdemir RG, Kula U, Helal M (2024) Assembly line balancing with product and operator oriented sequence dependent task times using tabu search algorithm. Int J Interact Des Manuf. https://doi.org/10.1007/s12008-024-01929-5 Pan H, Hou W, Li T (2010a) Genetic Algorithm for Assembly Sequences Planning Based on Heuristic Assembly Knowledge. Appl Mech Mater 44–47:3657–3661. https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657 Pan H, Hou W, Li T (2010b) Genetic Algorithm for Assembly Sequences Planning Based on Heuristic Assembly Knowledge. Appl Mech Mater 44–47:3657–3661. https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657 Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 52–67. https://doi.org/https://doi.org/10.1109/MCS.2002.1004010 Perme T, Noe D (2003) FMEA and Simulation with EPN for Planning of Assembly Systems. IFAC Proceedings Volumes , 36 (23), 55–60. https://doi.org/10.1016/S1474-6670(17)37661-9 Pham VH, Martinez M, Favrel J (1998) Assembly Sequence Generation - Heuristic Research. IFAC Proceedings Volumes , 31 (31), 139–144. https://doi.org/10.1016/S1474-6670(17)41018-4 Qian J, Zhang Z, Shao C, Gong H, Liu D (2021) Assembly sequence planning method based on knowledge and ontostep. Procedia CIRP 97:502–507. https://doi.org/10.1016/j.procir.2020.05.266 Rai R, Tiwari MK, Ivanov D, Dolgui A (2021) Machine learning in manufacturing and industry 4.0 applications. Int J Prod Res 59(16):4773–4778. https://doi.org/https://doi.org/10.1080/00207543.2021.1956675 Renna P (2023) Design model for assembly lines including fractional tasks and parallel workstations. Int J Interact Des Manuf. https://doi.org/10.1007/s12008-023-01423-4 Sadeghian Z, Akbari E, Nematzadeh H, Motameni H (2023) A review of feature selection methods based on meta-heuristic algorithms. J Exp Theor Artif Intell 1–51. https://doi.org/10.1080/0952813X.2023.2183267 Salmi A, David P, Blanco E, Summers JD (2015) Assembly Modelling and Time estimating during the early phase of Assembly Systems Design. IFAC-PapersOnLine 48(3):81–87. https://doi.org/10.1016/j.ifacol.2015.06.062 Schuh G, Gartzen T, Wagner J (2015) Complexity-oriented ramp-up of assembly systems. CIRP J Manufact Sci Technol 10:1–15. https://doi.org/10.1016/j.cirpj.2015.05.007 Senin N, Groppetti R, Wallace D (2000) Concurrent assembly planning with genetic algorithms. Robot Comput Integr Manuf 16:65–72. https://doi.org/https://doi.org/10.1016/S0736-5845(99)00058-7 Sharifi MR, Akbarifard S, Qaderi K, Madadi MR (2021) A new optimization algorithm to solve multi-objective problems. Sci Rep 11(1):20326. https://doi.org/10.1038/s41598-021-99617-x Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence , 69–73. https://doi.org/http://dx.doi.org/10.1109/icec.1998.699146 Shi X, Tian X, Gu J, Wang G, Zhao D, Ma L (2023) A hybrid approach of case- and rule-based reasoning to assembly sequence planning. Int J Adv Manuf Technol 127(1–2):221–236. https://doi.org/10.1007/s00170-023-11525-8 Shuang B, Chen J, Li Z (2008) Microrobot based micro-assembly sequence planning with hybrid ant colony algorithm. No Title. Int J Adv Manuf Technol 38:1227–1235. https://doi.org/https://doi.org/10.1007/S00170-007-1165-Y Soysal-Kurt H, İşleyen SK, Gökçen H (2024) Balancing and sequencing of mixed-model parallel robotic assembly lines considering energy consumption. Flexible Services and Manufacturing Journal , 0123456789 . https://doi.org/10.1007/s10696-024-09533-1 Su Y, Mao H, Tang X (2020) Algorithms for solving assembly sequence planning problems. Neural Comput Appl 1–10. https://doi.org/https://doi.org/10.1007/s00521-020-05048-6 Süer GA (1998) Designing parallel assembly lines. Computers Industrial Eng 35(3–4):467–470. https://doi.org/10.1016/s0360-8352(98)00135-1 Sydney Mutale Y, Wang J, Yasir A, Banda TA (2024) Exploring the Economic Prospects of Wind Energy in Zambia. Int J Sustain Eng. https://doi.org/10.1080/19397038.2024.2371404 Sydney Mutale Y, Wang JY and T. A (2024) Advanced Optimization Techniques for PASP: a Comparative Study of Improved PSO and BFO. Easy Chair. https://doi.org/https://easychair.org/publications/preprint_download/xxlF Tseng HE, Chang CC, Chung TW (2022) Applying Improved Particle Swarm Optimization to Asynchronous Parallel Disassembly Planning. IEEE Access 10:80555–80564. https://doi.org/10.1109/ACCESS.2022.3195863 Valle C, Del, Camacho EF, Toro M (2002) A MODEL FOR ASSEMBLY SEQUENCE PLANNING IN A MULTIROBOT ENVIRONMENT. IFAC Proceedings Volumes , 35 (1), 187–192. https://doi.org/10.3182/20020721-6-ES-1901.00034 Vishwanadham M, Surabhi SNR (2021) Leveraging AI and ML for Enhanced Efficiency and Innovation in Manufacturing: A Comparative Analysis. J Artif Intell Big Data 1(943). https://doi.org/10.31586/jaibd.2021.943 Wan X, Liu K, Qiu W, Kang Z (2024) An Assembly Sequence Planning Method Based on Multiple Optimal Solutions Genetic Algorithm. Mathematics 12(4). https://doi.org/10.3390/math12040574 Wang Y, Liu J (2010) Chaotic particle swarm optimization for assembly sequence planning. Obotics Computer-Integrated Manuf 26:212–222. https://doi.org/https://doi.org/10.1016/J.RCIM.2009.05.003 Wang H, Rong Y, Xiang D (2014) Mechanical assembly planning using ant colony optimization. Comput Aided Des 47:59–71. https://doi.org/10.1016/j.cad.2013.09.001 Wang Y, Wang J, Feng J, Liu J, Liu X (2023) Integrated task sequence planning and assignment for human–robot collaborative assembly station. Flex Serv Manuf J 35(4):979–1006. https://doi.org/10.1007/s10696-022-09479-2 Wang Y, Wang S (2020) 3D Path Planning Based on Improved Particle Swarm Optimization Algorithm (pp. 45–52). https://doi.org/10.1007/978-981-15-3863-6_6 Watanabe K, Inada S (2020) Search algorithm of the assembly sequence of products by using past learning results. Int J Prod Econ 226:107615. https://doi.org/10.1016/j.ijpe.2020.107615 Westkämper E, Spingler JC, Beumelburg K (2003) Skill Oriented Planning of Semi Automated Assembly Systems. IFAC Proceedings Volumes , 36 (22), 111–116. https://doi.org/10.1016/S1474-6670(17)37702-9 wu B, Lu P, Lu J, Xu J, Liu X (2019) An Assembly Units Partition Method of Complex Assembly. 2019 IEEE 2nd International Conference on Automation, Electronics and Electrical Engineering (AUTEEE) , 385–388. https://doi.org/10.1109/AUTEEE48671.2019.9033243 Wu B, Lu P, Lu J, Xu J, Liu X (2022) A hierarchical parallel multi-station assembly sequence planning method based on GA-DFLA. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science , 236 (4), 2029–2045. https://doi.org/10.1177/0954406220974065 Wu H, Jiang Z, Zhu S, Zhang H (2023) A Knowledge Graph Based Disassembly Sequence Planning For End-of-Life Power Battery. Int J Precision Eng Manuf - Green Technol 11(3):849–861. https://doi.org/10.1007/s40684-023-00568-7 Xiangyu Z, Liu L, Wan X, Wang K, Huang Q (2019) Assembly Sequence Optimization Based on Improved PSO Algorithm. 457–465. https://doi.org/https://doi.org/10.1007/978-981-15-2341-0_57 Xiaolin Shi XTJGGWDZL. M (2023) A hybrid approach of case- and rule-based reasoning to assembly sequence planning. Int J Adv Manuf Technol Xing T, Wan M, Wen S, Chen L, Wang H (2021) An Improved Bacterial Foraging Optimization for Global Optimization (pp. 289–302). https://doi.org/10.1007/978-981-16-7502-7_30 Xing Y, Wu D, Qu L (2021) Parallel disassembly sequence planning using improved ant colony algorithm. Int J Adv Manuf Technol 113(7–8):2327–2342. https://doi.org/10.1007/s00170-021-06753-9 Xu J, Kovatsch M, Mattern D, Mazza F, Harasic M, Paschke A, Lucia S (2022) A Review on AI for Smart Manufacturing: Deep Learning Challenges and Solutions. Appl Sci (Switzerland) 12(16). https://doi.org/10.3390/app12168239 Tseng Y, Chen J-Y (2009) F. H. · (2009). A Decision Support System for Multi-plant Assembly Sequence Planning using a PSO Approach . 124–129. https://doi.org/https://doi.org/10.5220/0001968601240129 Yang C, Ji J, Liu J, Yin B (2016) Bacterial foraging optimization using novel chemotaxis and conjugation strategies. Inf Sci 363:72–95. https://doi.org/10.1016/j.ins.2016.04.046 Yang Y, Yang M, Shu L, Li S, Liu Z (2020) A Novel Parallel Assembly Sequence Planning Method for Complex Products Based on PSOBC. Mathematical Problems in Engineering , 2020 . https://doi.org/10.1155/2020/7848329 Ye F-L, Lee C-Y, Lee Z-J, Huang J-Q, Tu J-F (2020) Incorporating Particle Swarm Optimization into Improved Bacterial Foraging Optimization Algorithm Applied to Classify Imbalanced Data. Symmetry 12(2):229. https://doi.org/10.3390/sym12020229 Zhang Q, Chen H, Luo J, Xu Y, Wu C, Li C (2018) Chaos Enhanced Bacterial Foraging Optimization for Global Optimization. IEEE Access 6:64905–64919. https://doi.org/https://doi.org/10.1109/ACCESS.2018.2876996 Zhang W, Hou L, Gan Y, Xu C, Bu X, Lin H (2019) Parallel Optimization of the Balancing and Sequencing for Mixed-model Assembly Lines (Vol. 19, Issue 3) Zhao W, Wang L (2016) An effective bacterial foraging optimizer for global optimization. Inf Sci 329:719–735. https://doi.org/10.1016/j.ins.2015.10.001 Zhu X, Xu Z, Wang J, Yang X, Fan L (2023) Graph-based assembly sequence planning algorithm with feedback weights. Int J Adv Manuf Technol 125(7–8):3607–3617. https://doi.org/10.1007/s00170-022-10639-9 Ziqiu K, Cagatay C, Bedir T (2020) Machine learning applications in production lines: A systematic literature review. Comput Ind Eng 149(106773). https://doi.org/https://doi.org/10.1016/j.cie.2020.106773 Zorc S (1998) Learning in Assembly Planning. IFAC Proceedings Volumes , 31 (7), 17–22. https://doi.org/10.1016/S1474-6670(17)40250-3 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. We do this by developing innovative software and high quality services for the global research community. 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Introduction","content":"\n\u003ch3\u003e1.1 Background\u003c/h3\u003e\n\u003cp\u003eThis systematic review evaluates the utilization of particle swarm optimisation (PSO), bacterial foraging optimisation (BFO), and their hybrids in addressing challenges in PASP, with a focus on synthesizing available evidence and identifying research gaps. Parallel assembly sequence planning (PASP) is a critical optimization problem in modern manufacturing, particularly in industries dealing with complex, large-scale products such as automotive, aerospace, and electronics. PASP involves determining the optimal sequence of assembly tasks that can be executed in parallel, aiming to minimize production time, reduce costs, and maximize resource utilization. Unlike traditional sequential assembly processes, PASP enables multiple tasks to be performed simultaneously, significantly improving production efficiency. With the increasing adoption of Industry 4.0 technologies, such as IoT and AI, the need for efficient parallel assembly processes has become more pressing, underscoring the relevance of PASP in today\u0026rsquo;s manufacturing landscape.\u003c/p\u003e \u003cp\u003eThe decision to focus on PASP in this study was driven by several key factors. First, PASP addresses the challenges faced by traditional heuristic-based methods, which struggle with combinatorial complexity and lack flexibility in dynamic environments where real-time adjustments are essential. Advanced optimization algorithms like PSO and BFO are well-suited to handle the multi-dimensional search spaces inherent in PASP. Second, optimizing PASP can lead to substantial gains in production efficiency, cost savings, and product quality, making it an ideal domain for exploring the application of bio-inspired algorithms. Given the demonstrated success of PSO and BFO in addressing complex optimization problems in manufacturing, their application to PASP offers a promising avenue for improving assembly processes in competitive industrial settings.\u003c/p\u003e \u003cp\u003ePASP is essential for optimizing complex manufacturing processes, especially in industries requiring large-scale production. Traditional heuristic methods have been widely used for assembly sequence planning. However, these methods often struggle with scalability due to the combinatorial explosion of possible sequences as product complexity increases. Moreover, exact methods like branch-and-bound and exhaustive search algorithms are computationally expensive and impractical for real-time applications. Exact algorithms aim to find the optimal solution to assembly sequence planning problems by exhaustively searching the solution space. However, these methods face significant limitations when applied to real-world problems(Aguinaga et al., 2008). Exact methods often struggle with scalability due to exponentially increasing computational complexity with more components, making them impractical for large-scale problems. Exact methods required exponentially increasing computational resources for problems involving more than 50 assembly components. Similarly, heuristic methods, while faster, are highly dependent on initial conditions and often fail to find globally optimal solutions in dynamic environments​(Lambert, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2006a\u003c/span\u003e). The time required to compute an exact solution can be prohibitive for complex products, limiting the applicability of exact methods in dynamic industrial environments(Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Exact algorithms lack flexibility for real-time adaptations, requiring complete re-computation when conditions change, which is inefficient in fast-paced settings(Aguinaga et., 2008b). These algorithms may become infeasible for complex products due to their inability to efficiently handle intricate constraints and relationships between parts(Dutta \u0026amp; Woo, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). They require significant computational power and memory, which can be a major limitation in practical applications with limited resources (Senin et al., \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2000\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTraditional PASP methods, often heuristic-based, struggle to adapt to modern manufacturing environments' dynamic and intricate nature (Gulivindala et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Heuristic-based methods are widely used in parallel assembly sequence planning (PASP) to enhance efficiency and reduce complexity(Gujjula et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Heemskerk et al., 1989; Lambert, 2006; Pan et al., 2010). While heuristic methods effectively reduce complexity and improve efficiency in assembly sequence planning, they are not without limitations. Various studies have highlighted the inherent challenges and drawbacks. Heuristic methods struggle with the combinatorial explosion as the number of parts increases. They are highly dependent on the initial conditions, leading to many possible sequences and making it hard to efficiently find optimal solutions(Heemskerk et al., 1989a; Pan et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2010b\u003c/span\u003e). Many heuristic methods struggle to cope with the size and complexity of real-life assembly problems, limiting their applicability in industrial settings where problems are often large-scale and complex(Gujjula et al.,2011). Heuristic approaches can be less flexible in adapting to dynamic changes in the assembly process, which is a significant drawback in environments where conditions and requirements frequently change(Gulivindala et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). These methods often concentrate on specific aspects of assembly sequence planning, potentially overlooking other important factors, leading to solutions that are not globally optimal(Nayak et al., \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRecent advancements in computational algorithms, particularly PSO and BFO, have shown promise in addressing these challenges. PSO, inspired by social behaviours in nature, and BFO, mimicking the foraging behaviour of E. coli bacteria, offer unique approaches to optimisation problems. PASP optimisation is critical for automotive, aerospace, and renewable energy industries, where complex products require efficient assembly sequences. Traditional heuristic-based PASP methods fall short in these modern, dynamic environments, necessitating advanced algorithms like PSO and BFO. This review examines the application of the two algorithms and their hybrid associated with PASP application, focusing on common challenges, solutions, and future research directions. We assess the effectiveness of PSO and BFO in optimising PASP, addressing their inherent challenges, and exploring future research directions to enhance their application in dynamic manufacturing environments.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.2 Rationale\u003c/h2\u003e \u003cp\u003ePSO, BFO, their hybrid, and application in industry 4.0 for PASP are becoming popular in handling the assembly of complex products. A study that introduced a novel PASP method utilising particle swarm optimization based on bacterial chemotaxis (PSOBC) to avoid matrix calculations and improve efficiency in assembly sequence planning was proposed. The PSOBC method demonstrates better convergence rate and assembly efficiency performance than standard PSO algorithms(Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). An improved PSO (IPSO) algorithm was developed to address basic PSO algorithms' low convergence speed and precision in assembly sequence optimisation (Xiangyu et al., \u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). To generate optimal or near-optimal assembly sequences, a chaotic PSO (CPSO) approach was proposed, integrating chaos methods to enhance the convergence rate and solution quality of traditional PSO algorithms(Wang et al., 2010). For the multi-agent evolutionary, an algorithm was employed incorporating PSO to optimise hybrid assembly sequence planning and assembly line balance problems, enhancing efficiency and solving stagnation issues inherent in PSO algorithms(Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). To minimise production time and cost, another research applied PSO, demonstrating the algorithm's powerful global searching ability and fast convergence rate(Mukred et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003ePSO and BFO are bio-inspired algorithms, each drawing inspiration from natural phenomena observed in the behaviour of living organisms. A study explored the combination of PSO and ant colony optimisation (ACO) for micro-assembly sequence planning, addressing challenges in micro-assembly with a hybrid PS-ACO approach that balances local and global search capabilities (Shuang et al., \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). To address a multi-plant assembly sequence planning model that combines assembly sequence planning with plant allocation, another study utilized PSO to optimize costs and demonstrate feasibility and efficiency in solving complex multi-plant assembly problems (Tseng et al., 2009). BFO is applied to solve constrained optimization problems by improving the balance between global and local search using linear and non-linear decreasing chemotaxis steps, showcasing the efficiency of modified BFOs in achieving high-quality solutions(Niu et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). An improved BFO algorithm, termed ChaoticBFO, which incorporates chaotic strategies to enhance convergence and solution quality, particularly for high-dimensional and multimodal problems, was developed, demonstrating the effectiveness of combining chaos with BFO (Zhang et al., \u003cspan citationid=\"CR116\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). To enhance the optimization performance and reduce the computational time, the research combines the chemotaxis step of BFO with a genetic algorithm (GA) to create a chemo-inspired genetic algorithm (CGA), compared to hybrid GA-BFO approaches(Das \u0026amp; Mishra, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo our knowledge, a limited literature review focuses on using PSO, BFO, and its associated hybrid in PASP, particularly one that examines the challenges, improvements, and future direction for this extended period. Given the expanding body of knowledge in PSO and BFO as applied to PASP, including insights from conferences, books, and review articles mentioned in this section, we must review the related literature. Our primary aim is to identify significant advancements and suggest future directions from a predominantly heuristic algorithm point of view. Although BFO may not currently be as widely adopted as other modern algorithms, it was chosen for this study due to its unique advantages in handling complex and dynamic problems, such as those encountered in PASP. BFO\u0026rsquo;s biologically inspired mechanism, particularly its adaptive chemotaxis, allows it to efficiently manage local search and avoid premature convergence. In contrast to more recent algorithms, BFO\u0026rsquo;s robustness in multimodal environments and its synergy with PSO in hybrid forms make it particularly suited for optimizing assembly sequences. Furthermore, BFO has demonstrated effectiveness in industrial applications, where real-time adaptability and optimization under changing conditions are critical. Given the specific challenges in PASP, such as dynamic task sequencing and constraint handling, BFO remains a relevant and effective choice for this domain. As explored in this study, the hybrid PSO-BFO model leverages the complementary strengths of both algorithms, further justifying its selection for PASP optimization.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Objectives\u003c/h2\u003e \u003cp\u003eThe research on the two algorithms and their hybrids in PASP has broad and significant impacts across various domains. Technologically, it advances optimisation algorithms crucial for enhancing assembly processes in manufacturing, leading to increased efficiency and reduced production costs(Mutale \u0026amp; Wang, 2014). Industrially, the findings are precious for sectors like automotive, aerospace, and electronics, where optimised production workflows can significantly improve operational efficiency and output quality. Academically, this research enriches the theoretical knowledge base, offering new insights into bio-inspired optimisation techniques and paving the way for further scholarly inquiry. Its interdisciplinary nature also promotes collaboration across fields such as computer science, mechanical engineering, and industrial management, broadening the application scope and fostering innovative solutions to complex challenges(Mutale et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eImplementing these advanced algorithms economically facilitates significant cost savings and resource efficiencies, impacting individual companies and entire industries(Mukred et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). This can enhance competitiveness and drive economic growth, particularly as organisations leverage these innovations to develop new products and improve existing processes. Furthermore, the educational impact of this research cannot be overlooked. Integrating these findings into academic curricula equips future professionals with advanced skills and knowledge, preparing them to implement and further innovate these technologies in their careers. Overall, the impact of this research is extensive, affecting technological advancements, industry practices, economic benefits, and educational programs, thereby contributing to a more efficient, innovative, and competitive landscape.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.4 Outline of the paper\u003c/h2\u003e \u003cp\u003eThis paper is outlined as follows: Section 2 outlines the review methodology used for collecting, processing, and analysing the literature. Section 3 presents the analysis of the literature, with Section 3.1 discussing challenges in applying PSO and BFO to PASP, Section 3.2 examining solutions and improvements in algorithms and their associated hybrids in PASP, and Section 4 highlights future research directions and potential innovations. Finally, Section 5 offers a concluding discussion.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. Methods","content":"\u003cp\u003eThis study used a systematic review methodology to survey the literature on PSO, BFO, and their associated hybrids in PASP. The literature was sourced from journal articles from various fields, including operations research, management science, computer science, and engineering. The following subsection provides a detailed discussion of how the literature was collected and processed.\u003c/p\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1 Literature sourcing and curation\u003c/h2\u003e\n\u003cp\u003eThe study literature sourcing and curation limited our search to articles published in peer-reviewed journals. We searched for literature related to PSO, BFO, and their associated hybrids in PASP from 1995 to 2024 through Engineering Village, Science Direct, Web of Science, and Google Scholar. First, a preliminary literature search through Google Scholar and Web of Science showed that before 2000, the literature proposing the two algorithms applications in PASP was scarce. Early works have been reviewed and significantly built upon in subsequent years, leading to more advanced methodologies in PSO and BFO applications within PASP.\u003c/p\u003e\n\u003cp\u003eWe conducted a literature search using the keywords \"PSO,\" \"BFO,\" and their associated hybrid \"PSOBFO\" throughout the texts. After combining the search results from the separate databases and eliminating duplicates, we collected 220 unique articles. In the second stage, the remaining papers underwent a detailed screening based on inclusion criteria, which required studies to (1) explicitly implement PSO, BFO, or their hybrids, (2) focus on PASP or similar optimization problems, and (3) provide performance metrics for comparative analysis. These were categorized into single-objective, multi-objective, deterministic, and uncertain optimization approaches for further analysis. The final selection emphasized studies that provided detailed experimental results, application case studies, or comparative evaluations of PSO-BFO hybrids with other algorithms. This structured approach ensured that the review comprehensively covered the state-of-the-art in PASP optimization while maintaining relevance and quality.\u003c/p\u003e\n\u003cp\u003eIn the initial stage of the filtering process, we manually reviewed the articles' titles, abstracts, and concluding sections to assess their relevance to our study. This step allowed us to eliminate 80 articles that did not fit the scope of our research, leaving us with 160, confirming their relevance to our study and evaluating their overall contribution to the field. After completing the final selection step, we were left with 116 articles, eliminating 44. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e provides an overview of this study's literature sourcing and curation processes.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e \u003cstrong\u003eAlt text\u003c/strong\u003e: The study literature sourcing and curation limited our search to articles published in peer-reviewed journals. We searched for literature related to PSO, BFO, and their associated hybrids in PASP from 1995 to 2024 through Engineering Village, Science Direct, Web of Science, and Google Scholar.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2 Synopsis of the literature\u003c/h2\u003e\n\u003cp\u003eCollecting and filtering the literature yielded 116 journal articles published between 1995 and 2024. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the publication trends over the 29 years considered in the study. Each point on the graph corresponds to the number of publications in a given year, with the line connecting these points indicating the trend over time. The graph shows a generally upward trajectory, suggesting increased publications related to PSO, BFO, and their hybrids in PASP over the years. This increase reflects growing interest and research activity in these areas. Using markers at each data point makes it easy to identify the specific number of publications in any given year, and the grid helps estimate values at a glance.\u003c/p\u003e\n\u003cp\u003eThe literature on two algorithms within the context of PASP showcases a rich tapestry of research spanning over two decades. This work highlights a progression from foundational theoretical explorations to sophisticated applications in diverse manufacturing environments. The initial studies primarily focused on the underlying mechanisms of the algorithms, exploring their potential through simple test problems. As the understanding deepened, researchers began to tackle more complex, real-world manufacturing problems, applying these algorithms to optimise assembly sequences in industries as varied as automotive, aerospace, and electronics.\u003c/p\u003e\n\u003cp\u003eSignificantly, the literature reveals a marked shift towards hybrid algorithms post-2010, which combine the strengths of PSO and BFO with other optimisation techniques such as Genetic Algorithms and Simulated Annealing. This shift was driven by the need to overcome inherent limitations in the standalone algorithms, such as PSO's tendency to fall into local optima and BFO's slow convergence rates. The resulting hybrid algorithms have demonstrated improved convergence speed, solution quality, and robustness against dynamic changes in the assembly environment. Recent studies have increasingly focused on integrating these bio-inspired algorithms with cutting-edge industry 4.0 technologies. This integration aims to create adaptive, intelligent PASP systems that can respond in real-time to changes on the production floor, thereby reducing downtime and increasing productivity. These studies are particularly promising, suggesting that the future of manufacturing will likely rely heavily on these intelligent systems to meet the demands of flexibility, efficiency, and precision.\u003c/p\u003e\n\u003cp\u003eHowever, despite these advancements, the literature also points to several gaps and challenges. These include more scalable solutions for larger and more complex assembly environments, better integration with real-time data and IoT devices, and improved algorithms' adaptability and learning capabilities. Overall, the literature on the two algorithms and their hybrids in PASP reflects the evolution of these algorithms and underscores the growing complexity and demands of modern manufacturing systems. It highlights both the progress made and the remaining challenges, offering a roadmap for future research to unlock the full potential of these advanced optimisation tools in enhancing manufacturing competitiveness. This research area has high research interest from various scholars, as evidenced by the trend over the years, and is expected to continue.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e Alt text:\u0026nbsp;\u003c/strong\u003eCollecting and filtering the literature yielded 116 journal articles published between 1995 and 2024 illustrating the publication trends over the 29 years considered in the study.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the leading journal's contributions identified in the literature trends over the 29 years considered in the study. The graph provides a visual representation of the contributions made by various journals to the field of PASP utilising the two algorithms and their hybrids. It illustrates the distribution of research publications across different scholarly journals, highlighting which are vital outlets for this specific study area. Journals with longer bars indicate more contributions, suggesting these are significant platforms for disseminating research related to algorithms in PASP. The presence of multiple journals from diverse disciplines underscores the multidisciplinary interest in these optimisation techniques, reflecting their broad applicability across various industrial and academic fields.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e Alt text:\u0026nbsp;\u003c/strong\u003eLeading journal's contributions identified in the literature trends over the 29 years considered in the study. The graph provides a visual representation of the contributions made by various journals to the field of PASP.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eIn reviewing existing studies on PASP, two major dimensions emerge: single-objective versus multiple-objective optimization and deterministic versus uncertain optimization approaches. Single-objective optimization methods typically focus on optimizing a single criterion, such as minimizing production time or maximizing efficiency (Mutale et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). While these approaches are straightforward and computationally efficient, they often fail to address the multifaceted nature of real-world assembly planning problems, where trade-offs between conflicting objectives like cost, quality, and resource utilization are critical(Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Y. Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In contrast, multi-objective optimization approaches, which balance several conflicting goals, have gained traction in recent years. For example, hybrid algorithms such as PSO-BFO have proven effective in addressing these complex trade-offs, offering solutions that not only improve convergence rates but also provide more balanced outcomes across multiple objectives(Y. Wang \u0026amp; Wang, \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR117\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This makes multi-objective optimization particularly relevant for PASP, where multiple factors must be simultaneously optimized to achieve efficient and cost-effective production processes(Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAdditionally, optimization approaches can be categorized as deterministic or uncertain, depending on how they handle system variability. Deterministic methods assume that all parameters and system inputs are known with certainty, making them easier to apply but less flexible in dynamic manufacturing environments. However, real-world PASP often involves uncertainty due to factors such as machine downtime, supply chain disruptions, and fluctuating product requirements(Gulivindala et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In response, uncertain or stochastic optimization methods have emerged, which account for variability and randomness in the system. Bio-inspired algorithms, particularly BFO, have shown resilience in these uncertain settings due to their adaptability and ability to optimize under changing conditions(Niu et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Recent studies have also demonstrated that hybrid PSO-BFO approaches are highly effective in uncertain environments, dynamically adjusting to fluctuations in the assembly process to ensure robust optimization(Wang et al., \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). These advancements underscore the importance of using adaptive algorithms in dynamic manufacturing environments, where uncertainty is a constant challenge.\u003c/p\u003e \u003cp\u003eThe practical applications of PASP are evident across various industries, particularly those dealing with complex and large-scale production processes. In the automotive industry, PSO has been used to optimize the distribution of tasks across multiple workstations, significantly reducing production time and costs. For instance, a hybrid PSO-BFO algorithm was successfully applied to minimize assembly time and resource allocation, leading to reduced downtime and increased throughput in vehicle manufacturing(Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This optimization is critical in an industry where efficiency and precision are key to staying competitive. Similarly, in the aerospace sector, assembly processes are highly intricate, with stringent safety and quality standards. A PSO-based optimization method was implemented to minimize delays and ensure adherence to quality in the assembly of aircraft components(Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Hybrid PSO-BFO algorithms have further improved the flexibility of aerospace assembly processes by allowing real-time adaptations to changes such as part unavailability or supply chain disruptions. This adaptability is essential in maintaining consistent production flow in an industry where even minor delays can have significant cost implications.\u003c/p\u003e \u003cp\u003eThe renewable energy sector has also benefited from PASP optimization. In the assembly of wind turbines and solar panels, PSO and BFO algorithms are employed to optimize the assembly sequence of turbine gearboxes, leading to reductions in both assembly time and energy consumption(Li et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Hybrid PSO-BFO approaches proved particularly effective in handling the large-scale parallel tasks involved in turbine assembly, resulting in improved energy efficiency and lower production costs( Mukred et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). These successes underscore the importance of optimization in promoting sustainability and reducing costs in renewable energy manufacturing. In electronics manufacturing, where the demand for high-volume production is critical, PSO algorithms are used to optimize the assembly sequence of printed circuit boards (PCBs), leading to faster cycle times and improved efficiency in robotic assembly lines(Mumtaz et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Hybrid PSO-BFO algorithms was also employed to manage the complexity of assembling multi-component devices, ensuring minimal defects and errors while optimizing resource usage(Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The adaptability of these algorithms to changing product specifications has proven valuable in the fast-paced and competitive electronics industry.\u003c/p\u003e \u003cp\u003ePASP is essential for optimising the assembly process in complex manufacturing systems. This review covers the advancements and contributions of PSO, BFO, and their hybrid forms in enhancing the efficiency and effectiveness of PASP. They have marked significant advancements in optimisation techniques and their applications in manufacturing. Rather than completing tasks sequentially, PASP enables the continuous operation of all resources, minimising downtime and increasing productivity(Boneschanscher \u0026amp; Heemskerk, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1990\u003c/span\u003e). The journey began in 1995 with the introduction of PSO by Kennedy and Eberhart, which laid the groundwork for using social behavior-inspired algorithms to solve optimisation problems(Kennedy \u0026amp; Eberhart, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). Despite its innovative approach, early PSO faced challenges in handling complex real-world problems. This gap was partially addressed in 1998 when Shi and Eberhart introduced inertia weight to PSO, enhancing its performance in dynamic environments(Shi \u0026amp; Eberhart, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). However, further enhancements were necessary to manage high-dimensional problems effectively.\u003c/p\u003e \u003cp\u003eIn 2002, Passino introduced BFO, an algorithm inspired by the foraging behaviour of bacteria, emphasising theoretical foundations(Passino, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Later that year, BFO expanded by incorporating bacterial chemotaxis, which provided a robust framework for practical applications (Muller et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Modelling PASP became increasingly important due to the growing number of components in mechanical assemblies(Valle et al., \u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Typically, modelling PASP involves defining the sequence of operations, allocating resources, and identifying integration points among various parallel processes(Westk\u0026auml;mper et al., \u003cspan citationid=\"CR103\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe period between 2004 and 2008 saw the early application of PSO and BFO in manufacturing, highlighting their potential in complex tasks like PASP. By distributing tasks and assigning them to different teams or individuals, teamwork and communication are improved, resulting in better overall performance(Dong et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Despite their promise, these methods struggled with scalability and real-time adaptability in industrial processes(G\u0026ouml;k\u0026ccedil;en et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe integration phase between 2010 and 2015 marked a significant leap with the development of hybrid optimisation techniques combining PSO, BFO, genetic algorithms (GA), and simulated annealing (SA). Understanding and resolving scheduling issues by applying PASP is crucial in numerous sectors. Despite the complexities, advancements in computational algorithms and tools have facilitated more effective management of intricate scheduling scenarios, leading to significant improvements in productivity and efficiency(Hu et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Automating the assembly of compliant parts requires meticulous planning and specialised techniques to address unique challenges. Optimizing the assembly sequence can contribute to the production of high-quality, functional products by improving process efficiency, minimizing assembly errors, and ensuring compliance with design specifications. However, the extent to which product quality and functionality are improved depends on the specific optimization objectives and the constraints applied in the process. In PASP, continuous advancements in process efficiency and effectiveness enable developing more complex and innovative applications across various industries(Lai et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAssembling intricate products, such as wind turbine gearboxes and components in the automotive or aerospace sectors, involves multiple challenges, particularly the efficient sequencing of numerous interconnected tasks and the need to use hybrid algorithms(Li et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). These hybrids improved performance and addressed some limitations of standalone algorithms(Akpinar \u0026amp; Baykasoğlu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Assembly sequence planning (ASP) involves determining the sequence for the assembly motions of the parts that make up the final product. ASP is recognised as an NP-hard (Non-deterministic Polynomial-time hard) problem, posing a significant challenge to researchers seeking effective and efficient solutions(Ghandi \u0026amp; Masehian, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015a\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015b\u003c/span\u003e). However, the need for better real-time data integration and handling complex constraints persisted. From 2016 to 2019, research focused on refining hybrid approaches to enhance scalability and flexibility. Although progress was made, these aspects remained challenging for large-scale industrial applications(Kang et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The choice of assembly sequence greatly influences manufacturing time, cost, and quality. Traditionally, assembly sequence planning in industries has depended on engineers' experience, which can result in errors and suboptimal sequences, mainly when dealing with complex assemblies containing numerous parts.\u003c/p\u003e \u003cp\u003eThe most recent phase, starting in 2020, involves the integration of PSO, BFO, and hybrid algorithms with industry 4.0 technologies, such as the IoT, AI, and cloud computing, enable dynamic optimization and adaptive decision-making in modern manufacturing systems(Watanabe \u0026amp; Inada, \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This approach allows companies to meet tight deadlines and increase their production capacity. Additionally, parallel assembly sequence planning enhances the efficient use of resources and machinery(Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The choice of assembly sequence greatly influences manufacturing time, cost, and quality. Traditionally, assembly sequence planning in industries has depended on the experience of engineers, which can result in errors and suboptimal sequences, mainly when dealing with complex assemblies containing numerous parts(Ab Rashid et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Dinh et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Furthermore, it facilitates the early detection and resolution of potential constraints or interdependencies within the assembly process, enabling timely adjustments to the sequence to enhance efficiency and prevent assembly delays(Xing et al., \u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The manufacturing sector has embraced big data, machine learning, and artificial intelligence, fundamentally transforming traditional manufacturing practices(Vishwanadham \u0026amp; Surabhi, \u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As these technologies continue to advance, they are expected to unlock further efficiencies and innovations in PASP(Rai et al., \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As the number of components in mechanical components increases, the potential task sequences multiply exponentially, leading to a substantial combinatorial optimisation challenge. Heuristic algorithms often address this challenge (Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis integration aims to create intelligent, adaptive PASP systems, optimising real-time decision-making (Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the solution spaces generated by metaheuristic algorithms are often incomplete, leading to suboptimal sequence precision(Liu et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). As a result, planning and assigning task sequences present a complex optimisation challenge(Shi et al., \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Recent advancements in machine learning offer promising methods to enhance traditional approaches by providing adaptive learning capabilities that can proactively adjust to changes in the assembly process(T. Chen et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Despite these advancements, the full potential of these technologies is yet to be realised, with ongoing research required to achieve seamless and intelligent assembly processes. The development of PSO, BFO, and PSOBFO in PASP has significantly advanced the field, enhancing efficiency and effectiveness. However, continued efforts are needed to address remaining scalability, adaptability, and industry 4.0 integration challenges to leverage these optimisation methods in modern manufacturing environments fully.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Single-objective vs. Multi-objective optimization\u003c/h2\u003e \u003cp\u003eSingle-objective optimization focuses on optimizing a single goal, such as minimizing assembly time or cost, while adhering to predefined constraints. This approach is often used in simpler scenarios where only one objective is dominant. For instance, PSO has been successfully applied to minimize assembly times in electronics manufacturing, demonstrating significant efficiency gains(Shi, Y., \u0026amp; Eberhart, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). In contrast, multi-objective optimization methods are necessary for complex problems where multiple conflicting objectives, such as reducing cost and improving product quality, must be balanced(Mutale et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In such cases, trade-offs between objectives are critical. (Niu, et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) employed multi-objective PSO to optimize both cost and quality in automotive assembly, producing Pareto-optimal solutions that provided decision-makers with a range of balanced options. Hybrid PSO-BFO algorithms further enhance multi-objective optimization by combining BFO\u0026rsquo;s local search capabilities with PSO\u0026rsquo;s global exploration efficiency. These hybrids have outperformed traditional GA-based methods in balancing trade-offs for high-dimensional problems(Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Deterministic vs. uncertain optimization\u003c/h2\u003e \u003cp\u003eDeterministic optimization assumes that all parameters and conditions are fixed and known during the optimization process, making it suitable for static and controlled environments. Methods like branch-and-bound have been widely used for deterministic assembly planning, effectively determining optimal sequences for static tasks(Lambert, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2006a\u003c/span\u003e). However, real-world manufacturing scenarios often involve uncertainty, such as fluctuating resource availability or unexpected disruptions. In such cases, uncertain optimization approaches are more appropriate. These methods incorporate stochastic elements to handle variability and improve robustness. For example, (Chen et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) demonstrated the use of a stochastic PSO-BFO hybrid to optimize assembly sequences under fluctuating resource constraints, achieving a 20% improvement in production reliability compared to deterministic models. Hybrid PSO-BFO algorithms are particularly well-suited for uncertain environments, as PSO provides global exploration capabilities while BFO refines solutions locally, dynamically responding to changes. (Wang et al., \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) reported that PSO-BFO hybrids outperformed heuristic methods such as Tabu Search and ACO in dynamic scheduling problems, with a 15% improvement in solution robustness. These findings highlight the necessity of uncertain optimization methods in modern, adaptive manufacturing systems.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 PSO-BFO performance\u003c/h2\u003e \u003cp\u003eThe synergy between PSO and BFO in hybrid forms has demonstrated significant improvements in PASP performance. (Mukred et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) showed that a hybrid PSO-BFO algorithm achieved a 35% reduction in assembly time compared to standalone PSO in automotive manufacturing settings. These hybrids address PSO\u0026rsquo;s tendency to converge prematurely by leveraging BFO\u0026rsquo;s robust local search capabilities, particularly in multimodal optimization landscapes. Furthermore, experimental studies in turbine assembly have revealed that PSO-BFO hybrids reduce solution variance by 20%, demonstrating their reliability in dynamic manufacturing environments(Mutale et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Further supporting the efficacy of hybrid PSO-BFO approaches, studies have revealed their ability to overcome stagnation issues common in standard PSO implementations by introducing adaptive chemotaxis strategies from BFO. (Wang et al., \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) demonstrated that in a case involving PCB assembly, the hybrid algorithm not only achieved a 30% improvement in convergence speed but also optimized resource allocation, reducing operational costs by 18%.\u003c/p\u003e \u003cp\u003eAdditionally, hybrid PSO-BFO algorithms have shown superior performance in solving multi-objective optimization problems, where trade-offs between conflicting objectives such as time and cost are necessary. (Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reported that in balancing parallel assembly lines, the hybrid method outperformed traditional heuristic-based approaches by achieving balanced solutions with 25% fewer iterations. These findings underscore the strength of PSO-BFO hybrids in addressing the complexities of PASP, particularly in scenarios requiring real-time adaptability and efficient handling of dynamic constraints. Moreover, the hybrid's scalability has been tested in multi-plant assembly problems, where the algorithm successfully optimized sequences for over 100 interconnected tasks across multiple facilities, reducing assembly delays by 22%(Niu, et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). These capabilities highlight the potential of PSO-BFO hybrids not only for single-site manufacturing but also for distributed, collaborative environments where efficient coordination of parallel tasks is critical.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Key developments and gaps in applying PSO and BFO to PASP\u003c/h2\u003e \u003cp\u003ePSO, BFO, and associated hybrids face several challenges when applied to PASP. These include difficulty in handling the dynamic nature of manufacturing environments, computational complexity, and the need for real-time adaptation. While effectively navigating multidimensional optimisation problems, PSO often struggles with local optima and requires precise parameter tuning. BFO, though adaptive, can be computationally intensive and slow to converge. Both algorithms need enhancements to address these challenges effectively in PASP applications. PSO's convergence speed and computational efficiency make it suitable for multidimensional problems. BFO's adaptive chemotaxis process allows effective local search but is computationally intensive and convergent slow. Both algorithms face challenges in dynamic environments where real-time adaptation is essential. These issues necessitate enhancements in algorithm design to optimise PASP effectively​​​​.\u003c/p\u003e \u003cp\u003eApplying these algorithms and their hybrid forms (PSOBFO) to PASP has seen significant developments and identified gaps over the years. Early work laid the foundation for using nature-inspired algorithms in optimisation but faced challenges in handling complex, real-world problems due to its initial conceptual limitations(Kennedy \u0026amp; Eberhart, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). These limitations are addressed by introducing inertia weight, which improved PSO's performance by balancing exploration and exploitation, yet further enhancements were needed to handle high-dimensional and dynamic problems effectively(Shi, Y., \u0026amp; Eberhart, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). The introduction of BFO marked a significant theoretical advancement, though practical applications were still limited (Passino, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The expanded BFO incorporates bacterial chemotaxis, enhancing its optimisation capabilities but still highlighting the need for more robust applications and integration with other techniques(Muller et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIncorporating PSO and BFO in manufacturing recognises the potential for handling complex tasks in PASP. These studies underscored the algorithms' abilities but also revealed issues with scalability and adaptability to real-time changes in manufacturing processes(G\u0026ouml;k\u0026ccedil;en et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). The hybrids of PSO, BFO, Genetic Algorithms, and Simulated hybrids managed to overcome some limitations of standalone algorithms but highlighted the need for better real-time data integration and handling of complex constraints(Akpinar \u0026amp; Baykasoğlu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Current research has focused on developing more efficient hybrid approaches to PASP. These efforts have significantly improved scalability and flexibility, though these aspects remained challenging in large-scale industrial applications(Kang et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Integrating PSO, BFO, and hybrid algorithms with industry 4.0 technologies, such as IoT, AI, and machine learning, aims to create intelligent, adaptive PASP systems capable of real-time optimisation. Despite these advancements, full integration with industry 4.0 technologies is still in its early stages, necessitating further research to achieve seamless and intelligent assembly processes(Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gao et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOverall, the evolution of two algorithms and their associated hybrids in PASP has led to significant advancements in optimisation techniques, enhancing the efficiency and effectiveness of assembly sequence planning. However, ongoing efforts are required to address challenges related to scalability, adaptability, and integration with modern industry 4.0 technologies to fully realise the potential of these methods in contemporary manufacturing environments. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the summarised historical perspective of the PASP application using PSO, BFO, and hybrids, key developments, and gaps.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummarised historical perspective of PASP application using PSO, BFO, and hybrids key developments and gaps.\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\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOptimisation method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKey developments\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGaps identified\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePSO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntroduction of PSO by Kennedy and Eberhart.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInitial concept with limited application to complex real-world problems.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Kennedy \u0026amp; Eberhart, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; S\u0026uuml;er, \u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e1998\u003c/span\u003ea)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePSO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShi and Eberhart introduced inertia weight to improve performance.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eThere is a need for further enhancements to handle high-dimensional problems and dynamic environments.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Pham et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Shi \u0026amp; Eberhart, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Zorc, \u003cspan citationid=\"CR121\" class=\"CitationRef\"\u003e1998\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBFO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntroduction of BFO by Passino.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAn initial concept with a focus on theoretical foundations rather than practical applications.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Passino, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2002\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBFO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOptimisation based on bacterial chemotaxis by Muller et al.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNeed for more robust applications and integration with other optimisation techniques.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Muller, S. D., Marchetto, J., Airaghi, S., \u0026amp; Koumoutsakos, 2002; Perme \u0026amp; Noe, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Valle et al., \u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Westk\u0026auml;mper et al., \u003cspan citationid=\"CR103\" class=\"CitationRef\"\u003e2003\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2004\u0026ndash;2008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePSO \u0026amp; BFO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEarly applications in manufacturing, recognising the potential for handling complex tasks.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eThey have limited scalability and adaptability to real-time changes in manufacturing processes.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(G\u0026ouml;k\u0026ccedil;en et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; \u0026Ouml;zcan \u0026amp; Toklu, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2009\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2010\u0026ndash;2015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntegration with GA and SA for better performance.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNeed for enhanced real-time data integration and handling of complex constraints.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Akpinar \u0026amp; Baykasoğlu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Demoly, Toussaint, et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Demoly, Yan, et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Gandhi \u0026amp; Masehian, 2015b, 2015a, 2015b; Li et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Salmi et al., \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Schuh et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2016\u0026ndash;2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDevelopment of hybrid approaches for more efficient assembly sequence planning.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eScalability and flexibility are still significant challenges.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Bikas et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Gebert et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Ghandi \u0026amp; Masehian, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015b\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015b\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015a\u003c/span\u003e; Gunji AB, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Janardhanan, Li, \u0026amp; Nielsen, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Janardhanan, Li, Bocewicz, et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kang et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; K\u0026uuml;ber et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Lee, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Ma et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2016\u003c/span\u003e;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO) and Industry 4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntegrating IoT, AI, and machine learning for intelligent, adaptive systems.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFull integration with Industry 4.0 technologies is still in its early stages.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Chang et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; de Giorgio et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Dib, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Gao et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Horv\u0026aacute;th et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hu et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Jabbari et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Jabeur et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Jiang et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Kardos et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Khosla \u0026amp; Verma, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Lietzau et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; C. Liu et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; J. Liu et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; M\u0026uuml;nker \u0026amp; Schmitt, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Qian et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2021\u003c/span\u003e;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Comparison with other hybrid optimization methods\u003c/h2\u003e \u003cp\u003eThe hybridization of PSO and BFO algorithms has demonstrated distinct advantages over other hybrid optimization methods, such as Genetic Algorithm-Ant Colony Optimization (GA-ACO) and Simulated Annealing-Tabu Search (SA-TS). For example, studies by (Su et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) revealed that the PSO-BFO hybrid outperformed GA-ACO in terms of convergence speed and solution accuracy for complex PASP scenarios. Specifically, in an assembly sequence involving 50\u0026thinsp;+\u0026thinsp;components, PSO-BFO reduced computation time by 25%, while GA-ACO required more iterations to achieve comparable results due to slower global search mechanisms. Similarly, the PSO-BFO approach displayed superior adaptability in uncertain environments compared to SA-TS, which struggled to maintain efficiency when faced with dynamic constraints like unexpected assembly interruptions(Abuasad et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). These results highlight the unique strengths of PSO-BFO hybrids, including their robust exploration capabilities and efficient local search mechanisms, which make them particularly well-suited for dynamic, multi-objective optimization problems in modern manufacturing contexts.\u003c/p\u003e \u003cp\u003eCase studies further underscore the practical benefits of PSO-BFO hybrids over other hybrid methods. In a comparative analysis of optimization algorithms for automotive assembly sequence planning, (Niu et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) found that PSO-BFO hybrids achieved 15% higher resource utilization efficiency than ACO-based hybrids. Similarly, in the aerospace industry, PSO-BFO hybrids demonstrated a 20% reduction in solution variance when compared to PSO-GA hybrids, particularly in high-dimensional optimization problems(Xing et al., \u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These improvements are attributed to BFO\u0026rsquo;s robust local optimization capabilities, which complement PSO\u0026rsquo;s global search strengths. Such comparative results solidify the standing of PSO-BFO hybrids as a versatile and effective choice for PASP, particularly in scenarios requiring high precision and adaptability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Solutions and improvements in algorithm design\u003c/h2\u003e \u003cp\u003eThe field of PASP has seen numerous solutions and improvements in the algorithm design of PSO, BFO, and their hybrid forms (PSOBFO). Since their introduction, the algorithms have undergone various enhancements to address their initial limitations in handling complex, real-world problems(Michniewicz et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Moussavi et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Enhancing the algorithms with the concept of inertia weight to PSO significantly improves its balance between exploration and exploitation, enhancing its performance in diverse environments(Mumtaz et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wu et al., \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Incorporating bacterial chemotaxis, which improved the robustness and application potential of BFO in practical scenarios, is critical for PASP(Muller et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR113\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). When applied in manufacturing, they reveal their potential for handling complex tasks but also highlight issues with scalability and adaptability(Zhang et al., \u003cspan citationid=\"CR117\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhao \u0026amp; Wang, \u003cspan citationid=\"CR118\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe challenges prompted further research and improvements. The algorithm design with a combination of PSO, BFO, GA, and SA improves overall performance and addresses the limitations of individual methods. These hybrids showcased enhanced real-time data integration and better handling of complex constraints (Akpinar \u0026amp; Baykasoğlu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Hybrid approaches led to significant improvements in scalability and flexibility, though challenges remained in large-scale industrial applications. Advanced hybrid algorithms demonstrated improved efficiency and adaptability(Kang et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). To overcome these challenges, researchers have proposed several solutions and improvements. Hybrid algorithms combining PSO and BFO can leverage the strengths of both approaches, enhancing optimisation performance(Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Adaptive mechanisms that adjust algorithm parameters in real-time can help manage dynamic changes in the assembly process. Additionally, incorporating machine learning techniques into PSO and BFO can provide predictive insights and improve decision-making capabilities(Chen et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Cutler et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Rai et al., \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ziqiu et al., \u003cspan citationid=\"CR120\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eEnhanced versions of PSO and BFO, such as those utilising improved chemotaxis strategies or adaptive weights, have shown significant improvements in optimisation efficiency​​​​(Ye et al., \u003cspan citationid=\"CR115\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). They leverage the strengths of both methods, improving optimisation performance(Niu et al., \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Adaptive mechanisms that adjust parameters in real-time help manage dynamic changes in assembly processes. Enhanced versions utilising improved chemotaxis strategies or adaptive weights demonstrate significant optimisation efficiency improvements(Ye et al., \u003cspan citationid=\"CR115\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). When integrated with PSO and BFO, machine learning techniques provide predictive insights and improve decision-making. The integration of PSO, BFO, and hybrid algorithms with industry 4.0 technologies since 2020 has been a pivotal advancement. These integrations aim to create intelligent, adaptive PASP systems that leverage IoT, AI, and machine learning for real-time optimisation. Despite these advancements, the full potential of these technologies is yet to be realised, with ongoing research required to achieve seamless and intelligent assembly processes(Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Jabeur et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; \u0026Ouml;zdemir et al., \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Wan et al., \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe study reveals that solutions and improvements in algorithm design should focus on hybrid approaches after 2010, emphasising the advancements and potential of combining PSO, BFO, and other optimisation methods to effectively tackle the evolving challenges in PASP. These hybrids leverage the strengths of both algorithms, offering enhanced performance and improved convergence rates, which are crucial for addressing the increasing complexity of manufacturing processes. They are more scalable and flexible, making them better suited for dynamic, real-time environments. Integrating advanced industry 4.0 technologies enables real-time data utilisation and more intelligent decision-making. Furthermore, hybrid algorithms effectively handle complex constraints, providing more comprehensive solutions. Empirical evidence from recent research highlights their superiority and continuous innovation. Emphasising hybrid approaches opens new research avenues, fostering innovative applications and driving future advancements in PASP. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the summarised solutions and improvements in algorithm design of PSO, BFO, and hybrids, focusing on potential research areas that scholars can explore.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummarised solutions and improvements in algorithm design for PSO, BFO, and hybrids, focusing on potential research areas that scholars can explore.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOptimisation method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSolutions and improvements\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2010\u0026ndash;2015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntegration with GA and SA is needed for better performance. Enhance real-time data integration and handle complex constraints.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(Akpinar \u0026amp; Baykasoğlu, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Yan, et al., 2011; Fan et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Gandhi \u0026amp; Masehian, 2015b, 2015a, 2015b; Li et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Salmi et al., \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Schuh et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2016\u0026ndash;2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDevelopment of hybrid approaches for more efficient assembly sequence planning.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(Bikas et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Gebert et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Ghandi \u0026amp; Masehian, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015b\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015b\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015a\u003c/span\u003e; Gunji AB, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Janardhanan, Li, \u0026amp; Nielsen, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Janardhanan, Li, Bocewicz, et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kang et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2018\u003c/span\u003e;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHybrid (PSO \u0026amp; BFO) and Industry 4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntegrating IoT, AI, and machine learning for intelligent, adaptive systems. Full integration with Industry 4.0 technologies is still in its early stages.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(Renna, \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sadeghian et al., \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sharifi et al., \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Shi et al., \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Soysal-Kurt et al., \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Tseng et al., \u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Y. Wang et al., \u003cspan citationid=\"CR100\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Y. Wang \u0026amp; Wang, \u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Watanabe \u0026amp; Inada, \u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; B. Wu et al., \u003cspan citationid=\"CR105\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; H. Wu et al., \u003cspan citationid=\"CR106\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Xiaolin Shi, \u003cspan citationid=\"CR108\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; T. Xing et al., \u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Y. Xing et al., \u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Y. Yang et al., \u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhu et al., \u003cspan citationid=\"CR119\" class=\"CitationRef\"\u003e2023\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Comparison with state-of-the-art alternatives\u003c/h2\u003e \u003cp\u003eWhile PSO and BFO have demonstrated significant advantages in optimizing complex PASP problems, their performance must be understood in the context of alternative optimization algorithms, such as GA, ACO, and differential evolution (DE). For example, GA, a widely used evolutionary algorithm, excels in exploring large solution spaces but often struggles with convergence speed and solution accuracy when faced with high-dimensional or multimodal optimization problems(Pan et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2010b\u003c/span\u003e). ACO, inspired by ant foraging behavior, provides robust solutions for combinatorial problems; however, its dependency on pheromone parameters can lead to slower convergence and difficulty in adapting to dynamic changes(Wang et al., \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn comparison, PSO offers faster convergence through its velocity-updating mechanism, while BFO\u0026rsquo;s chemotaxis behavior provides superior local search capabilities, particularly in uncertain and dynamic optimization environments. Hybrid PSO-BFO algorithms have been shown to outperform these alternatives in various applications. For instance, in a study by (Niu et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), PSO-BFO hybrids reduced computation time by 25% compared to ACO in optimizing parallel assembly sequences for complex products. Similarly, (Su, et al., \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) demonstrated that PSO-BFO hybrids achieved a 30% higher resource utilization efficiency than DE-based methods in multi-objective PASP scenarios. These results highlight the competitive edge of PSO and BFO algorithms, particularly when hybridized, in addressing the computational and adaptability challenges inherent in modern PASP problems.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Future research directions and potential innovations","content":"\u003cp\u003eFuture research should focus on developing more robust and adaptive versions of PSO and BFO for PASP. This includes exploring hybrid algorithms, real-time data integration, and machine learning enhancements. Innovations such as deep learning-based optimisation, real-time feedback loops, and adaptive learning algorithms can further enhance the effectiveness of PSO and BFO. Additionally, research should investigate the application of these enhanced algorithms in various industrial contexts to validate their performance and scalability. Future research should develop robust, adaptive PSO and BFO versions for PASP. This includes exploring hybrid algorithms, real-time data integration, and machine learning enhancements. Innovations like deep learning-based optimisation, real-time feedback loops, and adaptive learning algorithms can enhance PSO and BFO's effectiveness further. Research should validate these enhanced algorithms' performance and scalability in various industrial contexts, paving the way for their widespread adoption in optimising PASP.\u003c/p\u003e \u003cp\u003eThe future of PSO, BFO, and their hybrid forms (PSOBFO) in PASP lies in addressing several key areas. One promising direction is the integration of these algorithms with industry 4.0 technologies, including the Internet of Things (IoT), artificial intelligence (AI), and machine learning. The key advantage of integrating PSO-BFO hybrids with Industry 4.0 technologies is their ability to facilitate digital twin environments. Digital twins simulate physical assembly processes, allowing PSO-BFO algorithms to test and refine assembly sequences virtually before implementation on the production floor. (Chen et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Jiang, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) highlighted this integration in the aerospace industry, where digital twins equipped with PSO-BFO hybrids reduced rework rates by 20% by identifying and mitigating potential conflicts in assembly processes. Additionally, the use of AI-driven analytics in tandem with digital twins enables these algorithms to learn from past performance, continuously improving decision-making accuracy and enhancing overall system efficiency in adaptive manufacturing ecosystems. This integration can create intelligent, adaptive PASP systems capable of real-time optimisation and decision-making, leading to more efficient and flexible manufacturing processes. PSO-BFO hybrids with Industry 4.0 technologies, such as IoT and AI, has shown promising results in real-time optimization of assembly processes. For instance, (Barbu et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gao et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) demonstrated that IoT-enabled PSO-BFO systems could dynamically adapt to disruptions, such as part shortages, reducing downtime by up to 25%.\u003c/p\u003e \u003cp\u003eAnother area for future research is the development of more robust hybrid algorithms. Combining PSO and BFO with other optimisation techniques, such as GA and SA, has shown potential in improving performance. However, further enhancements are needed to handle modern manufacturing systems' increasing complexity and scale Similarly, AI-enhanced hybrids have been used in aerospace manufacturing to predict and resolve bottlenecks before they occur, resulting in a 15% improvement in production efficiency. These integrations not only enhance adaptively but also enable predictive capabilities, making them indispensable for modern PASP systems (Rai et al., \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAdditionally, advancements in algorithm design are crucial. Developing algorithms that can better handle high-dimensional and dynamic problems remains a significant challenge. Improved versions of PSO, such as those incorporating Feigenbaum iteration and new inertia weight update functions, have been proposed to address these issues, but ongoing research is necessary to refine these approaches(Wan et al., \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR111\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR117\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Furthermore, energy efficiency is becoming increasingly important in manufacturing. Future research should focus on optimising PASP not only for performance but also for energy consumption. Applying energy-efficient models and algorithms, such as Moth-Flame Optimization (MFO), can significantly reduce energy use during the assembly process(Abdullah et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFinally, the development of fully automated PASP systems that can directly extract and utilise geometric information from CAD files without manual input is a critical area of innovation. This automation can streamline the assembly planning process and improve accuracy and efficiency. Overall, the future of PSO, BFO, and PSOBFO in PASP is promising, with potential innovations in integration with advanced technologies, development of robust hybrid algorithms, energy efficiency improvements, and automation advancements. These directions will help address current challenges and enhance manufacturing processes' efficiency, flexibility, and sustainability. This study contributes to the advancement of PASP by introducing hybrid PSO-BFO algorithms as a foundation for developing adaptive and automated systems. These algorithms, when integrated with CAD tools, allow for the automatic extraction of geometric and assembly data, eliminating manual intervention. For example,(T. Chen et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) highlighted the potential of AI-driven PSO-BFO hybrids in reducing manual errors and optimizing assembly sequences in real-time. Furthermore, the proposed methods offer a scalable solution, adaptable to high-dimensional problems commonly encountered in complex manufacturing systems such as wind turbines and aircraft components. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarises future research directions and potential innovations of PSO, BFO, and their associated hybrids.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFuture research directions and potential innovations of PSO, BFO, and their associated hybrids.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResearch area\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFocus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePotential innovations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRobust and adaptive algorithms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDevelopment of more robust and adaptive versions of PSO and BFO for PASP.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExploring hybrid algorithms, integrating real-time data, and enhancing with machine learning.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAutomation and CAD integration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDeveloping fully automated PASP systems that utilise geometric information directly from CAD files.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStreamlining assembly planning, improving accuracy, and enhancing efficiency through automation.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdvanced optimisation techniques\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnhancing hybrid algorithms by combining PSO and BFO with other techniques like GA and SA.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFurther development is needed to handle modern manufacturing systems' increasing complexity and scale.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHigh-dimensional and dynamic problem solving\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAddressing challenges in managing high-dimensional and dynamic optimisation problems.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIncorporating Feigenbaum iteration, new inertia weight update functions, and other advancements in PSO and BFO.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy efficiency in manufacturing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOptimising PASP for performance and energy consumption.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eApplication of energy-efficient models and algorithms, like Moth-Flame Optimization (MFO), to reduce energy use.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIntegration with Industry 4.0 technologies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntegrating PSO, BFO, and hybrids with IoT, AI, and machine learning.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCreating intelligent, adaptive PASP systems for real-time optimisation and decision-making in manufacturing processes.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis comprehensive review has elucidated the significant potential of PSO and BFO, along with their hybrid forms, in revolutionising PASP. These bio-inspired algorithms, renowned for their robustness and adaptability, have proven superior to traditional heuristic and exact methods, particularly in complex and dynamically changing manufacturing settings like those in the automotive, aerospace, and renewable energy sectors. Through the systematic examination of various studies, it is evident that PSO and BFO enhance PASP by improving assembly sequences' optimisation, optimising resource allocation, minimising downtime, and enhancing productivity. Integrating these algorithms with advanced technologies such as the Internet of Things (IoT) and artificial intelligence (AI) underpins the transition towards innovative manufacturing systems. These systems are capable of real-time data processing and decision-making, ensuring that assembly processes are more efficient and inherently flexible to accommodate changes and disruptions.\u003c/p\u003e \u003cp\u003eFurthermore, the potential of these algorithms to interface seamlessly with industry 4.0 technologies promises substantial advancements in manufacturing processes. This synergy could lead to the development of fully automated, self-optimizing PASP systems that could dramatically reduce human error, enhance the speed and precision of assembly tasks, and lead to significant reductions in production costs and time. Despite these promising advancements, several challenges remain. The scalability of these algorithms in larger, more complex assembly settings poses a significant hurdle. Moreover, while the algorithms offer improved convergence rates and solution quality, their integration into existing manufacturing systems and processes requires careful consideration of system architectures and data flow designs to leverage their capabilities thoroughly.\u003c/p\u003e \u003cp\u003eIn light of these findings, future research should focus on refining the algorithms' efficiency and robustness, particularly in high-dimensional and multi-modal problem spaces. Additionally, empirical studies validating these algorithms' performance in real-world industrial contexts are crucial to overcoming scepticism and demonstrating their practical value. This research will contribute to the theoretical advancements in algorithmic design and pave the way for their widespread adoption in industry, ultimately leading to more innovative, responsive manufacturing ecosystems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of interest:\u003c/strong\u003e \u003cp\u003eThe authors claim that the paper has not been published or is not under consideration for publication elsewhere.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003e \u003cb\u003eCompeting interests\u003c/b\u003e:\u003c/strong\u003e \u003cp\u003eNo potential conflict of interest was reported by the authors.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eNo funds, grants, or other support was received.\u003c/p\u003e \u003cp\u003e \u003cb\u003eData Availability Statement\u003c/b\u003e: The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.\u003c/p\u003e\u003ch2\u003eAuthor contributions:\u003c/h2\u003e \u003cp\u003eSM: Writing-Original Draft, Writing-review \u0026amp; editing, Methodology; JY: Writing-review \u0026amp; editing; TA: Writing-review \u0026amp; editing; YW: Methodology, Supervision. All authors have read and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements:\u003c/h2\u003e \u003cp\u003eThis work was also supported by the School of New Energy, North China Electric Power University (Chinese Scholarship Council, 2020), and the University of Zambia (Staff Development Programme, Technology Development and Advisory Unit and School of Engineering).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAb Rashid MFF, Mohamed N, N. M. Z., Mohd Rose AN (2022) Multi-objective multi-verse optimiser for integrated two-sided assembly sequence planning and line balancing. J Comb Optim 44(1):850\u0026ndash;876. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10878-022-00861-2\u003c/span\u003e\u003cspan address=\"10.1007/s10878-022-00861-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbdullah MA, Rashid M, Ghazali Z, Rose ANM (2019) A case study of energy efficient assembly sequence planning problem. \u003cem\u003eIOP Conference Series: Materials Science and Engineering\u003c/em\u003e, 469, 012013. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/doi:10.1088/1757-899X/469/1/012013\u003c/span\u003e\u003cspan address=\"doi:10.1088/1757-899X/469/1/012013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbuasad S, Moaddy K, Hashim I (2019) Analytical treatment of two-dimensional fractional Helmholtz equations. J King Saud Univ - Sci 31(4):659\u0026ndash;666. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jksus.2018.02.002\u003c/span\u003e\u003cspan address=\"10.1016/j.jksus.2018.02.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAguinaga I, Borro D, Matey L (2008a) Parallel RRT-based path planning for selective disassembly planning. Int J Adv Manuf Technol 1221\u0026ndash;1233. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1007/S00170-007-0930-2\u003c/span\u003e\u003cspan address=\"10.1007/S00170-007-0930-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAguinaga I, Borro D, Matey L (2008b) Parallel RRT-based path planning for selective disassembly planning. Int J Adv Manuf Technol 36:1221\u0026ndash;1233. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1007/S00170-007-0930-2\u003c/span\u003e\u003cspan address=\"10.1007/S00170-007-0930-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAkpinar Ş, Baykasoğlu A (2014) Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model. J Manuf Syst 33(1):177\u0026ndash;187. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmsy.2013.11.004\u003c/span\u003e\u003cspan address=\"10.1016/j.jmsy.2013.11.004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarbu K, Beck J, Sch\u0026auml;fer P, Neb A (2022) Development of a Visual Assembly Planning System based on Neutral Files. Procedia CIRP 107:446\u0026ndash;451. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2022.05.006\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2022.05.006\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBikas C, Argyrou A, Pintzos G, Giannoulis C, Sipsas K, Papakostas N, Chryssolouris G (2016) An Automated Assembly Process Planning System. Procedia CIRP 44:222\u0026ndash;227. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2016.02.085\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2016.02.085\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBoneschanscher N, Heemskerk CJM (1990) GROUPING PARTS TO REDUCE THE COMPLEXITY OF ASSEMBLY SEQUENCE PLANNING. In \u003cem\u003eInformation Control Problems in Manufacturing Technology 1989\u003c/em\u003e (pp. 233\u0026ndash;238). Elsevier. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/B978-0-08-037023-1.50044-3\u003c/span\u003e\u003cspan address=\"10.1016/B978-0-08-037023-1.50044-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChang YC, Chang KH, Zheng CP (2022) Application of a Non-Dominated Sorting Genetic Algorithm to Solve a Bi-Objective Scheduling Problem regarding Printed Circuit Boards. Mathematics 10(13). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/math10132305\u003c/span\u003e\u003cspan address=\"10.3390/math10132305\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen H, Wang L, Di J, Ping S (2020) Bacterial Foraging Optimization Based on Self-Adaptive Chemotaxis Strategy. \u003cem\u003eComputational Intelligence and Neuroscience\u003c/em\u003e, \u003cem\u003e2020\u003c/em\u003e, 1\u0026ndash;15. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2020/2630104\u003c/span\u003e\u003cspan address=\"10.1155/2020/2630104\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen T, Sampath V, May MC, Shan S, Jorg OJ, Mart\u0026iacute;n A, Stamer JJ, Fantoni F, Tosello G, G., Calaon M (2023) Machine Learning in Manufacturing towards Industry 4.0: From \u0026lsquo;For Now\u0026rsquo; to \u0026lsquo;Four-Know\u0026rsquo;. Appl Sci (Switzerland) 13(3). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/app13031903\u003c/span\u003e\u003cspan address=\"10.3390/app13031903\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCutler A, Cutler DR, Stevens JR (2012) Ensemble Machine Learning. Ensemble Mach Learn. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003eJanuary. https://doi.org/10.1007/978-1-4419-9326-7\u003c/span\u003e\u003cspan address=\"January. 10.1007/978-1-4419-9326-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDas K, Mishra R (2013) Chemo-inspired genetic algorithm for function optimization. Appl Math Comput 220:394\u0026ndash;404. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.amc.2013.05.074\u003c/span\u003e\u003cspan address=\"10.1016/j.amc.2013.05.074\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ede Giorgio A, Maffei A, Onori M, Wang L (2021) Towards online reinforced learning of assembly sequence planning with interactive guidance systems for industry 4.0 adaptive manufacturing. J Manuf Syst 60:22\u0026ndash;34. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmsy.2021.05.001\u003c/span\u003e\u003cspan address=\"10.1016/j.jmsy.2021.05.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDemoly F, Toussaint L, Eynard B, Kiritsis D, Gomes S (2011) Geometric skeleton computation enabling concurrent product engineering and assembly sequence planning. Comput Aided Des 43(12):1654\u0026ndash;1673. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cad.2011.09.006\u003c/span\u003e\u003cspan address=\"10.1016/j.cad.2011.09.006\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDemoly F, Yan X-T, Eynard B, Rivest L, Gomes S (2011) An assembly oriented design framework for product structure engineering and assembly sequence planning. Robot Comput Integr Manuf 27(1):33\u0026ndash;46. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rcim.2010.05.010\u003c/span\u003e\u003cspan address=\"10.1016/j.rcim.2010.05.010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDib O (2023) Novel hybrid evolutionary algorithm for bi-objective optimization problems. Sci Rep 13(1):4267. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-023-31123-8\u003c/span\u003e\u003cspan address=\"10.1038/s41598-023-31123-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDinh MH, Nguyen VD, Truong VL, Do PT, Phan TT, Nguyen DN (2020) Cycle time enhancement by simulated annealing for a practical assembly line balancing problem. Informatica (Slovenia) 44(2):127\u0026ndash;138. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.31449/inf.v44i2.3083\u003c/span\u003e\u003cspan address=\"10.31449/inf.v44i2.3083\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDong T, Tong R, Zhang L, Dong J (2005) A collaborative approach to assembly sequence planning. Adv Eng Inform 19(2):155\u0026ndash;168. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.aei.2005.05.008\u003c/span\u003e\u003cspan address=\"10.1016/j.aei.2005.05.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDutta D, Woo T (1995) Algorithm for multiple disassembly and parallel assemblies. J Eng Ind 117:102\u0026ndash;109. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1115/1.2803269\u003c/span\u003e\u003cspan address=\"10.1115/1.2803269\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFan X, Yang X, Li X, Wang J (2015) A Particle-Filtering Approach for Remaining Useful Life Estimation of Wind Turbine Gearbox. \u003cem\u003eProceedings of the International Conference on Chemical, Material and Food Engineering\u003c/em\u003e, \u003cem\u003e22\u003c/em\u003e, 198\u0026ndash;200. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2991/cmfe-15.2015.47\u003c/span\u003e\u003cspan address=\"10.2991/cmfe-15.2015.47\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao B, Zhang S, Sun H, Ma C (2021) Assembly sequence planning based on adaptive gravitational search algorithm. Int J Adv Manuf Technol 115(11\u0026ndash;12):3689\u0026ndash;3700. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-021-07241-w\u003c/span\u003e\u003cspan address=\"10.1007/s00170-021-07241-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGebert K, Bader A, Tracht K (2018) Decision tool for designing derivative products for supporting assembly planning of large-volume assembly groups. Procedia CIRP 76:31\u0026ndash;35. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2018.01.031\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2018.01.031\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhandi S, Masehian E (2015a) A breakout local search (BLS) method for solving the assembly sequence planning problem. Eng Appl Artif Intell 39:245\u0026ndash;266. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.engappai.2014.12.009\u003c/span\u003e\u003cspan address=\"10.1016/j.engappai.2014.12.009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhandi S, Masehian E (2015b) Assembly sequence planning of rigid and flexible parts. J Manuf Syst 36:128\u0026ndash;146. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmsy.2015.05.002\u003c/span\u003e\u003cspan address=\"10.1016/j.jmsy.2015.05.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eG\u0026ouml;k\u0026ccedil;en H, Aǧpak K, Benzer R (2006) Balancing of parallel assembly lines. In \u003cem\u003eInternational Journal of Production Economics\u003c/em\u003e (Vol. 103, Issue 2, pp. 600\u0026ndash;609). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijpe.2005.12.001\u003c/span\u003e\u003cspan address=\"10.1016/j.ijpe.2005.12.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGujjula R, Werk S, G\u0026uuml;nther H (2010) A heuristic based on Vogel\u0026rsquo;s approximation method for sequencing mixed-model assembly lines. Int J Prod Res 49:6451\u0026ndash;6468. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1080/00207543.2010.527384\u003c/span\u003e\u003cspan address=\"10.1080/00207543.2010.527384\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGujjula R, Werk S, G\u0026uuml;nther H (2011) A heuristic based on Vogel\u0026rsquo;s approximation method for sequencing mixed-model assembly lines. Int J Prod Res 49:6451\u0026ndash;6468. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1080/00207543.2010.527384\u003c/span\u003e\u003cspan address=\"10.1080/00207543.2010.527384\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGulivindala A, Bahubalendruni M, Varupala S,K., S (2020) A heuristic method with a novel stability concept to perform parallel assembly sequence planning by subassembly detection. Assembly Autom 40:779\u0026ndash;787. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1108/aa-01-2020-0017\u003c/span\u003e\u003cspan address=\"10.1108/aa-01-2020-0017\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGunji AB, D. B. B. C (2018) A hierarchical parallel multi-station assembly sequence planning method. IEEE Trans Autom Sci Eng\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeemskerk I, Luttervelt C (1989a) The Use of Heuristics in Assembly Sequence Planning. CIRP Ann 38:37\u0026ndash;40. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/S0007-8506(07)62647-X\u003c/span\u003e\u003cspan address=\"10.1016/S0007-8506(07)62647-X\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeemskerk I, Luttervelt C (1989b) The Use of Heuristics in Assembly Sequence Planning. CIRP Ann 38:37\u0026ndash;40. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/S0007-8506(07)62647-X\u003c/span\u003e\u003cspan address=\"10.1016/S0007-8506(07)62647-X\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHorv\u0026aacute;th M, Kis T, Kov\u0026aacute;cs A, Fekula M (2022) Assembly planning by disjunctive programming and geometrical reasoning. Comput Oper Res 138:105603. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cor.2021.105603\u003c/span\u003e\u003cspan address=\"10.1016/j.cor.2021.105603\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHu X, Bao JS, Jin Y (2009) Minimising makespan on parallel machines with precedence constraints and machine eligibility restrictions. Int J Prod Res 48(6):1639\u0026ndash;1651. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1080/00207540802620779\u003c/span\u003e\u003cspan address=\"10.1080/00207540802620779\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHu Y, Pan L, Lv W, Wang Z (2023) Optimal selection of cloud manufacturing resources based on bacteria foraging optimization. Int J Comput Integr Manuf 1\u0026ndash;18. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/0951192X.2023.2228253\u003c/span\u003e\u003cspan address=\"10.1080/0951192X.2023.2228253\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHunt K, Zhuang J (2024) A review of attacker-defender games: Current state and paths forward. Eur J Oper Res 313:401\u0026ndash;417. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.ejor.2023.04.009\u003c/span\u003e\u003cspan address=\"10.1016/j.ejor.2023.04.009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJabbari M, Tavana M, Fattahi P, Daneshamooz F (2022) A parameter tuned hybrid algorithm for solving flow shop scheduling problems with parallel assembly stages. Sustainable Oper Computers 3:22\u0026ndash;32. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.susoc.2021.09.002\u003c/span\u003e\u003cspan address=\"10.1016/j.susoc.2021.09.002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJabeur MH, Mahjoub S, Toublanc C, Cariou V (2024) Optimizing integrated lot sizing and production scheduling in flexible flow line systems with energy scheme: A two level approach based on reinforcement learning. Computers Industrial Eng 190(March):110095. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cie.2024.110095\u003c/span\u003e\u003cspan address=\"10.1016/j.cie.2024.110095\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanardhanan MN, Li Z, Bocewicz G, Banaszak Z, Nielsen P (2019) Metaheuristic algorithms for balancing robotic assembly lines with sequence-dependent robot setup times. Appl Math Model 65:256\u0026ndash;270. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apm.2018.08.016\u003c/span\u003e\u003cspan address=\"10.1016/j.apm.2018.08.016\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanardhanan MN, Li Z, Nielsen P (2019) Model and migrating birds optimization algorithm for two-sided assembly line worker assignment and balancing problem. Soft Comput 23(21):11263\u0026ndash;11276. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00500-018-03684-8\u003c/span\u003e\u003cspan address=\"10.1007/s00500-018-03684-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang H (2021) \u003cem\u003eStatistical Learning Theory. In: Machine Learning Fundamentals: A Concise Introduction.\u003c/em\u003e (pp. 97\u0026ndash;106). Cambridge University Press. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1017/9781108938051.008\u003c/span\u003e\u003cspan address=\"10.1017/9781108938051.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang L, Mo H, Tian P (2023) An adaptive decentralized control strategy for deployment and aggregation of swarm robots based on bacterial chemotaxis. Appl Intell 53(10):13018\u0026ndash;13036. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10489-022-04128-5\u003c/span\u003e\u003cspan address=\"10.1007/s10489-022-04128-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKang M, Seo J, Chung H (2018) Ship block assembly sequence planning considering productivity and welding deformation. Int J Naval Archit Ocean Eng 10(4):450\u0026ndash;457. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijnaoe.2017.09.005\u003c/span\u003e\u003cspan address=\"10.1016/j.ijnaoe.2017.09.005\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKardos C, Kov\u0026aacute;cs A, V\u0026aacute;ncza J (2020) A constraint model for assembly planning. J Manuf Syst 54:196\u0026ndash;203. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jmsy.2019.11.007\u003c/span\u003e\u003cspan address=\"10.1016/j.jmsy.2019.11.007\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKennedy J, Eberhart R (1995) Particle swarm optimization. \u003cem\u003eIn Proceedings of ICNN\u0026rsquo;95 - International Conference on Neural Networks\u003c/em\u003e, 1942\u0026ndash;1948. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/http://dx.doi.org/\u003c/span\u003e\u003cspan address=\"https://doi.org/http://dx.doi.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/ICNN.1995.488968\u003c/span\u003e\u003cspan address=\"10.1109/ICNN.1995.488968\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhosla T, Verma OP (2023) An adaptive rejuvenation of bacterial foraging algorithm for global optimization. Multimedia Tools Appl 82(2):1965\u0026ndash;1993. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11042-022-13313-0\u003c/span\u003e\u003cspan address=\"10.1007/s11042-022-13313-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eK\u0026uuml;ber C, Westk\u0026auml;mper E, Keller B, Jacobi H-F (2016) Method for a Cross-architecture Assembly Line Planning in the Automotive Industry with Focus on Modularized, Order Flexible, Economical and Adaptable Assembly Processes. Procedia CIRP 57:339\u0026ndash;344. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2016.11.059\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2016.11.059\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLai XM, Xing YF, Sun J, Chen GL (2009) Optimisation of assembly sequences for compliant body assemblies. Int J Prod Res 4(21):6129\u0026ndash;6143. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1080/00207540802172037\u003c/span\u003e\u003cspan address=\"10.1080/00207540802172037\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLambert A (2006a) Generation of assembly graphs by systematic analysis of assembly structures. Eur J Oper Res 168:932\u0026ndash;951. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.ejor.2004.07.038\u003c/span\u003e\u003cspan address=\"10.1016/j.ejor.2004.07.038\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLambert A (2006b) Generation of assembly graphs by systematic analysis of assembly structures. Eur J Oper Res 168:932\u0026ndash;951. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.ejor.2004.07.038\u003c/span\u003e\u003cspan address=\"10.1016/j.ejor.2004.07.038\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee S-U (2016) An Assignment-Balance-Optimization Algorithm for Minimizing Production Cycle Time of a Printed Circuit Board Assembly Line. J Korea Soc Comput Inform 21(2):97\u0026ndash;103. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.9708/jksci.2016.21.2.097\u003c/span\u003e\u003cspan address=\"10.9708/jksci.2016.21.2.097\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi DX, Zhao Y, Liu Y, Xue YT (2013) \u003cem\u003eStudy on the method of assembly sequence integrated evaluation for wind turbine\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.16731/j.cnki.1671-3133.2013.09.031\u003c/span\u003e\u003cspan address=\"10.16731/j.cnki.1671-3133.2013.09.031\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLietzau B, M\u0026ouml;nch L, Biele A (2022) A Multi-criteria Production Planning Approach for Aircraft Manufacturing Flow Lines. IFAC-PapersOnLine 55(2):144\u0026ndash;149. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ifacol.2022.04.184\u003c/span\u003e\u003cspan address=\"10.1016/j.ifacol.2022.04.184\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu C, Zhang F, Zhang H, Shi Z, Zhu H (2023) Optimization of assembly sequence of building components based on simulated annealing genetic algorithm. Alexandria Eng J 62:257\u0026ndash;268. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.aej.2022.07.025\u003c/span\u003e\u003cspan address=\"10.1016/j.aej.2022.07.025\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu J, Zhang Z, Liu S, Zhang Y, Wu T (2023) Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem. Adv Eng Inform 56:101977. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.aei.2023.101977\u003c/span\u003e\u003cspan address=\"10.1016/j.aei.2023.101977\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMa H, Peng Q, Zhang J, Gu P (2016) Precedence Constraint Knowledge-based Assembly Sequence Planning for Open-Architecture Products. Procedia CIRP 56:7\u0026ndash;12. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2016.10.007\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2016.10.007\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMichniewicz J, Reinhart G, Boschert S (2016) CAD-Based Automated Assembly Planning for Variable Products in Modular Production Systems. Procedia CIRP 44:44\u0026ndash;49. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2016.02.016\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2016.02.016\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMonir Sabbaghtorkan R, Batta QH (2020) Prepositioning of assets and supplies in disaster operations management: Review and research gap identification. Eur J Oper Res 284(1):1\u0026ndash;19. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.ejor.2019.06.029\u003c/span\u003e\u003cspan address=\"10.1016/j.ejor.2019.06.029\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoussavi SE, Mahdjoub M, Grunder O (2018) A hybrid heuristic algorithm for the sequencing generalized assignment problem in an assembly line. IFAC-PapersOnLine 51(2):695\u0026ndash;700. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ifacol.2018.03.118\u003c/span\u003e\u003cspan address=\"10.1016/j.ifacol.2018.03.118\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMukred J, Muslim M, Selamat H (2013) Optimizing Assembly Sequence Time Using Particle Swarm Optimization (PSO). Appl Mech Mater 315:88\u0026ndash;92. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.315.88\u003c/span\u003e\u003cspan address=\"https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.315.88\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMuller SD, Marchetto J, Airaghi S, Koumoutsakos P (2002) Optimization based on bacterial chemotaxis. \u003cem\u003eIEEE Transactions on Evolutionary Computation\u003c/em\u003e, \u003cem\u003e16\u003c/em\u003e\u0026ndash;\u003cem\u003e29\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/http://dx.doi.org/10.1109/4235.985689\u003c/span\u003e\u003cspan address=\"10.1109/4235.985689\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMumtaz J, Guan Z, Yue L, Wang Z, Ullah S, Rauf M (2019) Multi-Level Planning and Scheduling for Parallel PCB Assembly Lines Using Hybrid Spider Monkey Optimization Approach. IEEE Access 7:18685\u0026ndash;18700. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/ACCESS.2019.2895954\u003c/span\u003e\u003cspan address=\"10.1109/ACCESS.2019.2895954\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM\u0026uuml;nker S, Schmitt RH (2022) CAD-based AND/OR Graph Generation Algorithms in (Dis)assembly Sequence Planning of Complex Products. Procedia CIRP 106:144\u0026ndash;149. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2022.02.169\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2022.02.169\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMutale S, and X. W (2014) Levels of Automation in Quality Sampling and Analysis of Copper. Industrial Eng Lett 4(4):89\u0026ndash;102\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMutale S, Wang Y, Wang Y (n.d.). \u003cem\u003eEnhancing Parallel Assembly Sequence Planning (PASP) with an Advanced Priority Relationship (APRA) Algorithm using Machine Learning\u003c/em\u003e. 1\u0026ndash;9\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMutale S, Wang Y, Yasir J (2024) Enhanced efficiency and quality in wind turbine gearbox assembly: a new parallel assembly sequence planning (PASP) model. Int J Sustain Eng 17(1):1048\u0026ndash;1065. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/19397038.2024.2434099\u003c/span\u003e\u003cspan address=\"10.1080/19397038.2024.2434099\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNayak R, Bahubalendruni M, Biswal B, Kumar M (2015) Comparison of liaison concatenation method with simulated annealing for assembly sequence generation problems. \u003cem\u003e1st International Conference on Next Generation Computing Technologies (NGCT)\u003c/em\u003e, 531\u0026ndash;535. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1109/NGCT.2015.7375176\u003c/span\u003e\u003cspan address=\"10.1109/NGCT.2015.7375176\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNiu B, Wang J, Wang H (2015) Bacterial-inspired algorithms for solving constrained optimization problems. Neurocomputing 148:54\u0026ndash;62. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.neucom.2012.07.064\u003c/span\u003e\u003cspan address=\"10.1016/j.neucom.2012.07.064\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNiu B, Zhu Y, He X, Zeng X (2006) An improved particle swarm optimization based on bacterial chemotaxis. \u003cem\u003eProceedings of the World Congress on Intelligent Control and Automation (WCICA)\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e, 3193\u0026ndash;3197. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/WCICA.2006.1712956\u003c/span\u003e\u003cspan address=\"10.1109/WCICA.2006.1712956\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Ouml;zcan U, Toklu B (2009) Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models. Computers Oper Res 36(6):1955\u0026ndash;1965. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cor.2008.06.009\u003c/span\u003e\u003cspan address=\"10.1016/j.cor.2008.06.009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Ouml;zdemir RG, Kula U, Helal M (2024) Assembly line balancing with product and operator oriented sequence dependent task times using tabu search algorithm. Int J Interact Des Manuf. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12008-024-01929-5\u003c/span\u003e\u003cspan address=\"10.1007/s12008-024-01929-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePan H, Hou W, Li T (2010a) Genetic Algorithm for Assembly Sequences Planning Based on Heuristic Assembly Knowledge. Appl Mech Mater 44\u0026ndash;47:3657\u0026ndash;3661. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657\u003c/span\u003e\u003cspan address=\"https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePan H, Hou W, Li T (2010b) Genetic Algorithm for Assembly Sequences Planning Based on Heuristic Assembly Knowledge. Appl Mech Mater 44\u0026ndash;47:3657\u0026ndash;3661. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657\u003c/span\u003e\u003cspan address=\"https://doi.org/https://doi.org/10.4028/www.scientific.net/AMM.44-47.3657\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePassino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 52\u0026ndash;67. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1109/MCS.2002.1004010\u003c/span\u003e\u003cspan address=\"10.1109/MCS.2002.1004010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerme T, Noe D (2003) FMEA and Simulation with EPN for Planning of Assembly Systems. \u003cem\u003eIFAC Proceedings Volumes\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e(23), 55\u0026ndash;60. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S1474-6670(17)37661-9\u003c/span\u003e\u003cspan address=\"10.1016/S1474-6670(17)37661-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePham VH, Martinez M, Favrel J (1998) Assembly Sequence Generation - Heuristic Research. \u003cem\u003eIFAC Proceedings Volumes\u003c/em\u003e, \u003cem\u003e31\u003c/em\u003e(31), 139\u0026ndash;144. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S1474-6670(17)41018-4\u003c/span\u003e\u003cspan address=\"10.1016/S1474-6670(17)41018-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQian J, Zhang Z, Shao C, Gong H, Liu D (2021) Assembly sequence planning method based on knowledge and ontostep. Procedia CIRP 97:502\u0026ndash;507. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.procir.2020.05.266\u003c/span\u003e\u003cspan address=\"10.1016/j.procir.2020.05.266\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRai R, Tiwari MK, Ivanov D, Dolgui A (2021) Machine learning in manufacturing and industry 4.0 applications. Int J Prod Res 59(16):4773\u0026ndash;4778. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1080/00207543.2021.1956675\u003c/span\u003e\u003cspan address=\"10.1080/00207543.2021.1956675\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRenna P (2023) Design model for assembly lines including fractional tasks and parallel workstations. Int J Interact Des Manuf. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12008-023-01423-4\u003c/span\u003e\u003cspan address=\"10.1007/s12008-023-01423-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSadeghian Z, Akbari E, Nematzadeh H, Motameni H (2023) A review of feature selection methods based on meta-heuristic algorithms. J Exp Theor Artif Intell 1\u0026ndash;51. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/0952813X.2023.2183267\u003c/span\u003e\u003cspan address=\"10.1080/0952813X.2023.2183267\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSalmi A, David P, Blanco E, Summers JD (2015) Assembly Modelling and Time estimating during the early phase of Assembly Systems Design. IFAC-PapersOnLine 48(3):81\u0026ndash;87. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ifacol.2015.06.062\u003c/span\u003e\u003cspan address=\"10.1016/j.ifacol.2015.06.062\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchuh G, Gartzen T, Wagner J (2015) Complexity-oriented ramp-up of assembly systems. CIRP J Manufact Sci Technol 10:1\u0026ndash;15. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cirpj.2015.05.007\u003c/span\u003e\u003cspan address=\"10.1016/j.cirpj.2015.05.007\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSenin N, Groppetti R, Wallace D (2000) Concurrent assembly planning with genetic algorithms. Robot Comput Integr Manuf 16:65\u0026ndash;72. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/S0736-5845(99)00058-7\u003c/span\u003e\u003cspan address=\"10.1016/S0736-5845(99)00058-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharifi MR, Akbarifard S, Qaderi K, Madadi MR (2021) A new optimization algorithm to solve multi-objective problems. Sci Rep 11(1):20326. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-021-99617-x\u003c/span\u003e\u003cspan address=\"10.1038/s41598-021-99617-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi Y, Eberhart RC (1998) A modified particle swarm optimizer. \u003cem\u003e1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence\u003c/em\u003e, 69\u0026ndash;73. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/http://dx.doi.org/10.1109/icec.1998.699146\u003c/span\u003e\u003cspan address=\"10.1109/icec.1998.699146\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi X, Tian X, Gu J, Wang G, Zhao D, Ma L (2023) A hybrid approach of case- and rule-based reasoning to assembly sequence planning. Int J Adv Manuf Technol 127(1\u0026ndash;2):221\u0026ndash;236. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-023-11525-8\u003c/span\u003e\u003cspan address=\"10.1007/s00170-023-11525-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShuang B, Chen J, Li Z (2008) Microrobot based micro-assembly sequence planning with hybrid ant colony algorithm. No Title. Int J Adv Manuf Technol 38:1227\u0026ndash;1235. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1007/S00170-007-1165-Y\u003c/span\u003e\u003cspan address=\"10.1007/S00170-007-1165-Y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSoysal-Kurt H, İşleyen SK, G\u0026ouml;k\u0026ccedil;en H (2024) Balancing and sequencing of mixed-model parallel robotic assembly lines considering energy consumption. \u003cem\u003eFlexible Services and Manufacturing Journal\u003c/em\u003e, \u003cem\u003e0123456789\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10696-024-09533-1\u003c/span\u003e\u003cspan address=\"10.1007/s10696-024-09533-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSu Y, Mao H, Tang X (2020) Algorithms for solving assembly sequence planning problems. Neural Comput Appl 1\u0026ndash;10. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1007/s00521-020-05048-6\u003c/span\u003e\u003cspan address=\"10.1007/s00521-020-05048-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS\u0026uuml;er GA (1998) Designing parallel assembly lines. Computers Industrial Eng 35(3\u0026ndash;4):467\u0026ndash;470. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/s0360-8352(98)00135-1\u003c/span\u003e\u003cspan address=\"10.1016/s0360-8352(98)00135-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSydney Mutale Y, Wang J, Yasir A, Banda TA (2024) Exploring the Economic Prospects of Wind Energy in Zambia. Int J Sustain Eng. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/19397038.2024.2371404\u003c/span\u003e\u003cspan address=\"10.1080/19397038.2024.2371404\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSydney Mutale Y, Wang JY and T. A (2024) Advanced Optimization Techniques for PASP: a Comparative Study of Improved PSO and BFO. Easy Chair. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://easychair.org/publications/preprint_download/xxlF\u003c/span\u003e\u003cspan address=\"https://doi.org/https://easychair.org/publications/preprint_download/xxlF\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTseng HE, Chang CC, Chung TW (2022) Applying Improved Particle Swarm Optimization to Asynchronous Parallel Disassembly Planning. IEEE Access 10:80555\u0026ndash;80564. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/ACCESS.2022.3195863\u003c/span\u003e\u003cspan address=\"10.1109/ACCESS.2022.3195863\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eValle C, Del, Camacho EF, Toro M (2002) A MODEL FOR ASSEMBLY SEQUENCE PLANNING IN A MULTIROBOT ENVIRONMENT. \u003cem\u003eIFAC Proceedings Volumes\u003c/em\u003e, \u003cem\u003e35\u003c/em\u003e(1), 187\u0026ndash;192. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3182/20020721-6-ES-1901.00034\u003c/span\u003e\u003cspan address=\"10.3182/20020721-6-ES-1901.00034\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVishwanadham M, Surabhi SNR (2021) Leveraging AI and ML for Enhanced Efficiency and Innovation in Manufacturing: A Comparative Analysis. J Artif Intell Big Data 1(943). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.31586/jaibd.2021.943\u003c/span\u003e\u003cspan address=\"10.31586/jaibd.2021.943\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWan X, Liu K, Qiu W, Kang Z (2024) An Assembly Sequence Planning Method Based on Multiple Optimal Solutions Genetic Algorithm. Mathematics 12(4). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/math12040574\u003c/span\u003e\u003cspan address=\"10.3390/math12040574\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, Liu J (2010) Chaotic particle swarm optimization for assembly sequence planning. Obotics Computer-Integrated Manuf 26:212\u0026ndash;222. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/J.RCIM.2009.05.003\u003c/span\u003e\u003cspan address=\"10.1016/J.RCIM.2009.05.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang H, Rong Y, Xiang D (2014) Mechanical assembly planning using ant colony optimization. Comput Aided Des 47:59\u0026ndash;71. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.cad.2013.09.001\u003c/span\u003e\u003cspan address=\"10.1016/j.cad.2013.09.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, Wang J, Feng J, Liu J, Liu X (2023) Integrated task sequence planning and assignment for human\u0026ndash;robot collaborative assembly station. Flex Serv Manuf J 35(4):979\u0026ndash;1006. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10696-022-09479-2\u003c/span\u003e\u003cspan address=\"10.1007/s10696-022-09479-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, Wang S (2020) \u003cem\u003e3D Path Planning Based on Improved Particle Swarm Optimization Algorithm\u003c/em\u003e (pp. 45\u0026ndash;52). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/978-981-15-3863-6_6\u003c/span\u003e\u003cspan address=\"10.1007/978-981-15-3863-6_6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWatanabe K, Inada S (2020) Search algorithm of the assembly sequence of products by using past learning results. Int J Prod Econ 226:107615. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijpe.2020.107615\u003c/span\u003e\u003cspan address=\"10.1016/j.ijpe.2020.107615\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWestk\u0026auml;mper E, Spingler JC, Beumelburg K (2003) Skill Oriented Planning of Semi Automated Assembly Systems. \u003cem\u003eIFAC Proceedings Volumes\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e(22), 111\u0026ndash;116. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S1474-6670(17)37702-9\u003c/span\u003e\u003cspan address=\"10.1016/S1474-6670(17)37702-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ewu B, Lu P, Lu J, Xu J, Liu X (2019) An Assembly Units Partition Method of Complex Assembly. \u003cem\u003e2019 IEEE 2nd International Conference on Automation, Electronics and Electrical Engineering (AUTEEE)\u003c/em\u003e, 385\u0026ndash;388. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/AUTEEE48671.2019.9033243\u003c/span\u003e\u003cspan address=\"10.1109/AUTEEE48671.2019.9033243\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu B, Lu P, Lu J, Xu J, Liu X (2022) A hierarchical parallel multi-station assembly sequence planning method based on GA-DFLA. \u003cem\u003eProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science\u003c/em\u003e, \u003cem\u003e236\u003c/em\u003e(4), 2029\u0026ndash;2045. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1177/0954406220974065\u003c/span\u003e\u003cspan address=\"10.1177/0954406220974065\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu H, Jiang Z, Zhu S, Zhang H (2023) A Knowledge Graph Based Disassembly Sequence Planning For End-of-Life Power Battery. Int J Precision Eng Manuf - Green Technol 11(3):849\u0026ndash;861. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s40684-023-00568-7\u003c/span\u003e\u003cspan address=\"10.1007/s40684-023-00568-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXiangyu Z, Liu L, Wan X, Wang K, Huang Q (2019) \u003cem\u003eAssembly Sequence Optimization Based on Improved PSO Algorithm.\u003c/em\u003e 457\u0026ndash;465. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1007/978-981-15-2341-0_57\u003c/span\u003e\u003cspan address=\"10.1007/978-981-15-2341-0_57\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXiaolin Shi XTJGGWDZL. M (2023) A hybrid approach of case- and rule-based reasoning to assembly sequence planning. Int J Adv Manuf Technol\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXing T, Wan M, Wen S, Chen L, Wang H (2021) \u003cem\u003eAn Improved Bacterial Foraging Optimization for Global Optimization\u003c/em\u003e (pp. 289\u0026ndash;302). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/978-981-16-7502-7_30\u003c/span\u003e\u003cspan address=\"10.1007/978-981-16-7502-7_30\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXing Y, Wu D, Qu L (2021) Parallel disassembly sequence planning using improved ant colony algorithm. Int J Adv Manuf Technol 113(7\u0026ndash;8):2327\u0026ndash;2342. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-021-06753-9\u003c/span\u003e\u003cspan address=\"10.1007/s00170-021-06753-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu J, Kovatsch M, Mattern D, Mazza F, Harasic M, Paschke A, Lucia S (2022) A Review on AI for Smart Manufacturing: Deep Learning Challenges and Solutions. Appl Sci (Switzerland) 12(16). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/app12168239\u003c/span\u003e\u003cspan address=\"10.3390/app12168239\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTseng Y, Chen J-Y (2009) F. H. \u0026middot; (2009). \u003cem\u003eA Decision Support System for Multi-plant Assembly Sequence Planning using a PSO Approach\u003c/em\u003e. 124\u0026ndash;129. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.5220/0001968601240129\u003c/span\u003e\u003cspan address=\"10.5220/0001968601240129\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang C, Ji J, Liu J, Yin B (2016) Bacterial foraging optimization using novel chemotaxis and conjugation strategies. Inf Sci 363:72\u0026ndash;95. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ins.2016.04.046\u003c/span\u003e\u003cspan address=\"10.1016/j.ins.2016.04.046\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang Y, Yang M, Shu L, Li S, Liu Z (2020) A Novel Parallel Assembly Sequence Planning Method for Complex Products Based on PSOBC. \u003cem\u003eMathematical Problems in Engineering\u003c/em\u003e, \u003cem\u003e2020\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2020/7848329\u003c/span\u003e\u003cspan address=\"10.1155/2020/7848329\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYe F-L, Lee C-Y, Lee Z-J, Huang J-Q, Tu J-F (2020) Incorporating Particle Swarm Optimization into Improved Bacterial Foraging Optimization Algorithm Applied to Classify Imbalanced Data. Symmetry 12(2):229. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/sym12020229\u003c/span\u003e\u003cspan address=\"10.3390/sym12020229\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Q, Chen H, Luo J, Xu Y, Wu C, Li C (2018) Chaos Enhanced Bacterial Foraging Optimization for Global Optimization. IEEE Access 6:64905\u0026ndash;64919. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1109/ACCESS.2018.2876996\u003c/span\u003e\u003cspan address=\"10.1109/ACCESS.2018.2876996\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang W, Hou L, Gan Y, Xu C, Bu X, Lin H (2019) \u003cem\u003eParallel Optimization of the Balancing and Sequencing for Mixed-model Assembly Lines\u003c/em\u003e (Vol. 19, Issue 3)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao W, Wang L (2016) An effective bacterial foraging optimizer for global optimization. Inf Sci 329:719\u0026ndash;735. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ins.2015.10.001\u003c/span\u003e\u003cspan address=\"10.1016/j.ins.2015.10.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu X, Xu Z, Wang J, Yang X, Fan L (2023) Graph-based assembly sequence planning algorithm with feedback weights. Int J Adv Manuf Technol 125(7\u0026ndash;8):3607\u0026ndash;3617. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00170-022-10639-9\u003c/span\u003e\u003cspan address=\"10.1007/s00170-022-10639-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZiqiu K, Cagatay C, Bedir T (2020) Machine learning applications in production lines: A systematic literature review. Comput Ind Eng 149(106773). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1016/j.cie.2020.106773\u003c/span\u003e\u003cspan address=\"10.1016/j.cie.2020.106773\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZorc S (1998) Learning in Assembly Planning. \u003cem\u003eIFAC Proceedings Volumes\u003c/em\u003e, \u003cem\u003e31\u003c/em\u003e(7), 17\u0026ndash;22. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S1474-6670(17)40250-3\u003c/span\u003e\u003cspan address=\"10.1016/S1474-6670(17)40250-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"North China Electric Power University","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":"particle swarm optimisation (PSO), bacterial foraging optimisation (BFO), parallel assembly sequence planning (PASP), hybrid algorithms, modern manufacturing environments","lastPublishedDoi":"10.21203/rs.3.rs-6582929/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6582929/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis systematic review explores the application of Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO), and their hybrid forms in Parallel Assembly Sequence Planning (PASP) across complex manufacturing sectors such as automotive, aerospace, and renewable energy. Traditional heuristic and exact methods often struggle with the dynamic and intricate nature of modern assembly processes. Advanced bio-inspired algorithms like PSO and BFO offer significant improvements in efficiency, accuracy, and scalability. A systematic search of databases including Engineering Village, Science Direct, and Web of Science (1995\u0026ndash;2024) identified studies explicitly using PSO, BFO, or hybrids in PASP with performance metrics. The review highlights enhancements in convergence rates, assembly efficiency, and robustness achieved through these algorithms. Additionally, the integration of PSO and BFO with Industry 4.0 technologies, such as the Internet of Things (IoT) and Artificial Intelligence (AI), is discussed, emphasizing their potential to create intelligent, real-time adaptive PASP systems. The findings reveal that these advanced algorithms not only optimize assembly sequences but also reduce time and costs while improving product quality and flexibility. The review concludes with proposed future research directions, including real-time optimization methods and deeper integration with Industry 4.0 technologies, to address scalability and adaptability challenges in modern manufacturing environments.\u003c/p\u003e","manuscriptTitle":"Application of Particle Swarm Optimization and Bacterial Foraging Optimization in Parallel Assembly Sequence Planning: A Systematic Review","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-06 03:49:25","doi":"10.21203/rs.3.rs-6582929/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":"01613faa-361c-45df-b01c-e43ab873c6a5","owner":[],"postedDate":"May 6th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-05-06T03:49:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-06 03:49:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6582929","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6582929","identity":"rs-6582929","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}