{"paper_id":"4db87bf2-3e3b-422c-9adf-f38386bf4ef5","body_text":"Nature inspired Meta-heuristic optimization integrated with ensemble machine learning for PM2.5 modeling: a potential approach for sustainable eco-friendly health risk management | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nature inspired Meta-heuristic optimization integrated with ensemble machine learning for PM2.5 modeling: a potential approach for sustainable eco-friendly health risk management Abdullahi G. Usman, Sagiru Mati, Sujay Raghavendra Naganna, Jamilu Usman, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4663193/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Particulate Matter 2.5 (PM 2.5) is a major air pollutant that can deeply penetrate the respiratory system and enter the bloodstream when inhaled. Therefore, it is significant to monitor and model PM 2.5, which is also considered as a key indicator of overall air quality. The current study employs the use of both Nature inspired Meta-heuristic optimization algorithms and Ensemble Machine learning (ML) techniques for the prediction of PM 2.5 using Sulfur dioxide (SO 2 ), Nitrogen Dioxide (NO 2 ), Respiratory suspended particulate matter (RSPM). Prior to dwelling into the modelling step, various pre-analysis techniques were conducted for data clean up and to understand the behaviour of the data. The quantitative performance results obtained from the Metaheuristic algorithms indicates that ANN-PSO outperformed all the other techniques including; SVR-BO, ENN-GA and LR. Furthermore, the quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively. More also, recent visualizations such as Fan plot and Bump chart were used in ranking the performance results obtained in PM 2.5 prediction. Moreover, Neural network ensemble (NNE) technique equally showed superior potentials over Simple average (SA) ensemble technique. To conclude, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms indicates their importance in modelling and mitigation of PM 2.5 pollution, which requires concerted efforts at the local, and international levels to mitigate its effects and improve air quality on a global scale. Air quality pollution PM 2.5 Ensemble ML Meta-heuristic optimization algorithms Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1.0 Introduction Particulate matter (PM) is a complex and multidimensional aspect of atmospheric chemistry that is represented by a variety of small solid and liquid droplets suspended in the atmosphere. These minuscule particles come in a variety of sizes and compositions, with dimensions ranging from a few nanometers to a few tens of micrometers. The causes of PM are closely linked to the environment on Earth, resulting from a complicated interaction between natural and human-caused factors (Ogrizek et al., 2022 ). A thorough investigation of the chemical components and generation mechanisms of PM is necessary to comprehend its complex character. PM originates from a variety of sources, including particles produced by the Earth’s natural processes (Rai, 2016 ). These include mineral dust particles created by the erosion of rocks and soil, as well as biological elements like pollen and spores from plants and microbes (Aarnink et al., 2010 ). Sea salt aerosols are produced by the breaking waves in the ocean and add to the natural PM concentration. These naturally occurring particulates are crucial to the functioning of Earth’s ecosystems because they help in transferring nutrients, generate clouds, and serve as the building blocks for the creation of raindrops (Ubaid et al., 2019 ). Human activity significantly contributes to the atmospheric PM, releasing a variety of particles from combustion, construction, and industrial processes. These sources often contain heavy metals and organic chemicals, resulting in a dynamic and ever-changing composition (Chen et al., 2015 ). The increase in PM pollution poses an increasing threat to the environment. These microscopic particles can have profound and far-reaching effects on human health, ecosystems, and the environment. Owing to the fact that PM can enter the respiratory system deeply and cause a variety of respiratory and cardiovascular disorders, it poses a serious risk to human health (Hamanaka & Mutlu, 2018 ). In addition, PM harms the environment due to its participation in the production of smog, decreased visibility, and deposition of natural ecosystems, which lowers the quality of the soil and water (Kim et al., 2016 ). Therefore, the need for effective addressing of PM pollution necessitates the use of intricate and advanced models to comprehend its origins, distribution, and ecological impacts (G et al., 2013 ). Before the advancement of advanced machine learning (ML) and artificial intelligence (AI) techniques, managing the intricate issues related to particulate matter pollution was difficult. Policymakers and environmental scientists mainly used manual data analysis and simple equations in their older models (Liu et al., 2018 ). The complex dynamics of PM sources and dispersion patterns were difficult for these older methods to capture. Furthermore, they could not properly utilize the potential of the enormous datasets that are already accessible (Luo et al., 2019 ). Consequently, the shortcomings of these conventional approaches limited the ability to minimize the harmful impacts of PM pollution and optimize environmental management (Wu et al., 2018 ). For decades classical methods of managing air pollution have been associated with several uncertainties and approximations owing to their complex and nonlinear nature(Costache et al., 2019 ; Mohammadi et al., 2020 ; Pham et al., 2019 ; Sammen et al., 2021 ). It is well known based on the developed traditional techniques of controlling PM 2.5 that utilizing AI models for PM 2.5 prediction offers substantial advantages by significantly enhancing the accuracy and efficiency of air quality forecasting. Artificial intelligence (AI) algorithms improve the overall understanding of PM 2.5 modelling, enabling them to adapt to complex environmental data and ensuring real-time, globally applicable insights. This approach not only accelerates computational processes but also supports informed decision-making for effective and sustainable air quality management. However, coupling nature-inspired meta-heuristic optimization algorithms and ensemble machine learning (ML) presents a novel approach to modelling particulate matter (PM 2.5) concentrations, which are critical to air quality management. By mimicking evolutionary processes, these algorithms can efficiently navigate complex search spaces to calibrate ensemble ML models, thereby enhancing their predictive accuracy(Baig et al., 2023 ). This serves as the fundamental in creating sustainable, eco-friendly strategies for air quality control, leveraging the inherent adaptability of nature-inspired algorithms to optimize the weights and hyperparameters of ML models (Uniyal et al., 2022 ). Recently, PM 2.5 modelling using advanced AI and spatial mapping attracted a huge researcher’s attention. For instance, Tai et al. (Tai et al., 2010 ) explored correlation-based and ML models for the prediction of PM 2.5 using metrological parameters over 11 years of US data and showed that weather conditions explain about 50% of PM2.5 variations. In 2012, Tai et al. (Tai et al., 2012 ) employed several models to predict PM 2.5 using metrological variables for the Impact of 2000–2050 climate change. In 2018, Polezar et al. (Polezer et al., 2018 ) employed nonlinear artificial neural network (ANN), Multilayer Perceptron (MLP), Extreme Learning Machines (ELM) and Echo State Networks (ESN) to evaluate the impact of PM 2.5 on human health. The outcomes indicated that ANN is a more reliable method for a smaller amount of data. In addition, Wei et al. (Wei et al., 2020 ) in 2020 utilize computational randomized trees to estimate PM 2.5 across China based on 1km resolution. A more recent study in 2023 was conducted by Gokul et al. (Gokul et al., 2023 ) in Hyderabad city India in which PM 2.5 was predicted using spatial method, single and deep learning approaches. The outcomes indicated the prediction skills of LSTM (Long Short-Term Memory) over XGBoost. The other that attempt to predict PM 2.5 in several region across the globe include (Hu et al., 2014 ; Lary et al., 2016 ; Liang et al., 2018 ; Lin et al., 2015 ; Meng et al., 2021 ; Pandya et al., 2023 ; Prunicki et al., 2018 ; Xue et al., 2019 ; Zhang et al., 2021 ). It can be seen that PM 2.5 received significant attention using single AI model, however it is very crucial to optimize the standalone model using optimization techniques(Moayedi et al., 2023 ; Simon, 2008 ; Yaseen et al., 2018 ). Optimization is essential in prediction as it enhances model accuracy, ensures computational efficiency, and improves generalization capabilities, which are crucial for effective and cost-efficient decision-making, particularly in environmental monitoring like PM 2.5 assessment. Moreover, the application of these advanced techniques to PM 2.5 modelling is a testament to the potential of AI in environmental science. By harnessing the stochastic yet structured search mechanisms of meta-heuristic algorithms, such as Ant Colony Optimization (ACO) or Simulated Annealing (SA), the ensemble models can simulate and predict PM 2.5 variations with high precision. This allows for real-time monitoring and proactive policymaking, mapping a course towards a sustainable future with cleaner air, thus implementing both environmental and public health imperatives(Nabipour et al., 2020 ). Similarly, the motivation for the study is to improve the monitoring and modelling of PM 2.5, a significant air pollutant with serious health implications, due to its capacity to access deep into the respiratory system. The study aims to enhance the accuracy of PM 2.5 predictions, which are vital for developing effective air quality management strategies to protect public health and ensure a sustainable environment. It is worth mentioning based on the above literature that the gap identified in the study is the need for more efficient and accurate prediction models for PM 2.5 concentrations. Existing models may not fully capture the complexity of air quality data or might not be optimized for the best performance. To address this, the study integrates nature-inspired meta-heuristic optimization algorithms with ensemble machine learning techniques to improve the prediction models. The use of specific algorithms like ANN-PSO (Artificial Neural Network with Particle Swarm Optimization) is highlighted as particularly effective, outperforming other techniques in both calibration and validation phases. The research also explores the potential of the Neural Network Ensemble (NNE) over simpler averaging (SA) ensemble methods, indicating a methodological improvement in the field of air quality modelling. 2.0 Materials and Methods 2.1 The Proposed Methodology Ever since the advent of industrialization, there has been a growing worry regarding the impact of environmental pollution. According to the World Health Organization’s findings, air pollution is responsible for a staggering annual toll of 7 million premature deaths, making it the most significant environmental hazard globally (Lynch, 2020 ). The dataset used in the current study contained 435,742 instances were utilized each for both the input variables inform of Sulfur dioxide (SO 2 ), Nitrogen Dioxide (NO 2 ) and Respiratory suspended particulate matter (RSPM) as well as the output variable inform of Particulate Matter 2.5 (PM 2.5). The unclean dataset can be found in the following open source link https://www.kaggle.com/datasets/shrutibhargava94/india-air-quality-data . In the proposed methodology we commence with the collection and pre-processing of PM 2.5 and relevant environmental data, followed by dimensionality reduction using techniques like PCA to select significant features. We then develop an array of individual predictive models, including ANN, Emotional NN, SVR, and LR, which are optimized using meta-heuristic algorithms such as PSO, GA and BO for hyperparameter tuning. These models are subsequently integrated into an ensemble framework, to improve prediction accuracy at certain instances. Both the metaheuristic algorithms and ensemble’s performance are rigorously evaluated using metrics like R-squared (R 2 ), Pearson Correlation Coefficient (PCC), Mean Squared Error (MSE) and Mean Absolute Error (MAE), and upon successful validation, the model is deployed for real-world application. Continuous performance monitoring and a feedback loop for incorporating actual measurements ensure dynamic model recalibration and sustainability in managing air quality. 2.2 The study location India is located in South Asia and is bordered by several countries; Pakistan to the northwest, China to the northeast, Nepal to the north, Bhutan to the north, Bangladesh to the east, Myanmar to the east, and Sri Lanka to the south though separated by the Palk Strait. Furthermore, this country has an approximate Latitude of 20.5937 degrees north and an approximate Longitude of 78.9629 degrees East (Duraisamy et al., 2019 ). The Republic of India is a large, diversified nation that has many opportunities for all kinds of research and study. India is a great place to study since it has a rich history, culture, and educational institutions. India is confronted with environmental issues such as deforestation, air and water pollution, and climate change. Studying environmental science and sustainability initiatives is made possible by this exceptional opportunity (Marghade et al., 2020 ). Furthermore, Fig. 1 demonstrates the map of the study location indicating the major pollutant sources. 2.3 The machine learning and metaheuristic algorithms 2.3.1 Artificial Neural Network (ANN) Artificial neural networks (ANNs) are computationally analytically-based systems that mimic how human brains utilize data. (Abba et al., 2017 , 2020 ; Jibril, Zayyan, et al., 2023 ). As processing units, they are made up of several neurons coupled by movable weights and biases. An input, hidden, and output layer comprise an ANN’s single or multi-layered system (Tayyebi et al., 2019 ). The feed-forward network with backpropagation algorithms (FFNN-BP) is used in this study. The literature claims that artificial neural networks, which feature a fundamental unit called a neuron (node), are information processing instruments that are modeled after the biological nervous system of the brain. Owing to their promising capabilities, ANNs with FFNN-BP have shown themselves to be useful instruments in various scientific and technical domains for surmounting extremely non-linear processes (Elkiran et al., 2019 ; Jibril, Malami, et al., 2023 ; Khalid & Usman, 2021 ). Furthermore, FFNN-BP entails training the network using trained input data that is processed within the network and then sent to the output layer, where errors may occur and then spread throughout the system until the desired output is obtained(Usman, Işik, & Abba, 2021b ). The main idea behind FFNN-BP is that in order for the network to comprehend the training data and predict the real value, it must reduce the created mistakes (Elkiran et al., 2018 ). Throughout its operation, the inputs are multiplied by the initial weights, after which the value advances to the second layer and ultimately to the output layer. It is seen in Eq. 1 (Gaya et al., 2013 ). $${z}_{i}= \\sum _{j=1}^{m}{w}_{ij}{x}_{ij}$$ 1 where zi denotes the final total of the ith node’s outputs, 𝒘𝒊𝒋 represents the input, and 𝒘𝒊𝒋 represents the weight shifted from the jth input to the ith node. Consequently, by computing the difference between the goal value and the projected values, backpropagation is utilized to ascertain the inaccuracy. Usually, it is carried out backwards, beginning at the output layer and working backwards to the input layer. The error node j in layer l is indicated by this difference, δ(l)j. The mathematical expression of the error term for a training set (xj, yj) is given by Eq. 2 : $${e}_{p }= {y}_{d}- {y}_{a}$$ 2 where y_a is the real output of the training model and y_d is the neuron p’s output. However, a large number of neurons in the buried layer may affect the neural network’s capacity and generalization ability, which adds to the computational cost because lower neurons cannot deliver the desired prediction accuracy (Gaya et al., 2013 ). The biases and connection weights are continuously modified during the learning process in order to achieve the desired output. This technique is known as continuous learning. This might be an unsupervised or supervised process. Generally speaking, supervised learning is utilized to reduce the discrepancies between the computed and desired values. (Hamed et al., 2004 ). The learning rate is crucial in defining the network’s intelligence by bringing the network system together and so minimizing the problems associated with a local minimum. The trial-and-error method makes use of both the learning rate and the architecture, or the quantity of layers, transfer function, and neurons. The input and hidden layers employ sigmoid activation, whereas the output layer uses the linear activation function. Every neuron has an activation function, which is a mathematical function that transforms a linear function into a non-linear function (Yetilmezsoy et al., 2011 ) (see Eq. 3 ). $$F\\left(x\\right)= \\frac{1}{1+{e}^{(-x)}}$$ 3 2.3.2 Support Vector Regression (SVR) In 1995, Vatnik developed the idea of learning within the SVM framework, which designed the ideal idea for resolving problems pertaining to regression, pattern recognition, classification, and prediction models. The SVM is composed of a data-driven model and is based on the concept of machine learning (Hong et al., 2008 ). The two primary purposes of SVM are statistical learning theory and structural risk minimization. This gives information that sets it apart from ANN in terms of its ability to lower error, redundancy in data, and complexity while simultaneously enhancing system performance. There are two varieties of support vector regression (SVR): non-linear and linear (USMAN et al., 2020 ). This gives an insight that sets it apart from ANN in terms of its capacity to lower error, redundancy in data, and complexity while simultaneously enhancing system performance (Usman, Işik, & Abba, 2021a ). Furthermore, SVR is a machine learning technique that is used for regression tasks. Kernel Support Vector Regression (Kernel-SVR) is a version of SVR. When dealing with nonlinear interactions between the input variables and the target variable, kernel-SVR is especially useful (Abba, Benaafi, et al., 2022a ). By applying kernel functions to convert the input variables into a higher-dimensional feature space, kernel-SVR improves upon the fundamental SVR. Nonlinear interactions between the variables and the target variable can be captured by Kernel-SVR by translating the input variables into a higher-dimensional space (Bonakdari et al., 2019 ). 2.3.3 Genetic algorithm (GA) Charles Darwin’s idea of natural selection served as the foundation for John Holland’s metaheuristic search and optimization method, known as the GA [3]. The main focus of GA is its capacity to manage complex systems and parallelism. To solve complex problems, GA searches a wide range of parameter spaces and provides an approximate optimal solution (regardless of whether the fitness function is stationary, nonstationary, linear, nonlinear, continuous, discontinuous, or contains random noise) (Abba, Abdulkadir, et al., 2022 ). It is the outcome of the many progenies of the population functioning as independent actors. These individuals investigate the search space in multiple directions at the same time. The three primary GA operators are crossover, mutation, and selection. In selection operators, chromosomes are selected for subsequent replication (e.g., via roulette wheel selection) (Termeh et al., 2019 ). 2.3.4 Particle swarm optimization (PSO) algorithm Particle Swarm Optimization (PSO), a newly developed metaheuristic for optimizing population-based algorithms, was proposed by Eberhart and Kennedy. This algorithm is a nature-inspired method based on fish schools and avian foraging (Malik et al., 2021 ). PSO is regarded as an optimizer that affects both local and global swarm locations to revolve around the problem space. Generally, different random values are assigned for the particle location in each PSO. Next, iteration, the global cost of the optimal swarm positioning, and the cost of the best swarm are kept. Equations X and Y could be used to modernize each particle’s position and velocity (Malik et al., 2021 ). $${v}_{i}^{t+1}=w{v}_{i}^{t}+{C}_{c1}\\times randN\\times \\left({Pbest}_{i}-{x}_{i}^{t}\\right)+{S}_{f1}\\times randNO\\times \\left(Gbest-{x}_{i}^{t}\\right)$$ 4 $${d}_{i}^{t+1}={d}_{i}^{t}+{v}_{i}^{t+1}$$ 5 where w denotes inertial weight and governs the PSO algorithm’s stability. C_c1 displays the cognitive coefficient, which regulates the impact of each person’s memory. S_f1, or social factor, is utilized to boost PSO performance; randNO, on the other hand, displays a random number between 0 and 1, giving PSO greater capacity for randomized search. While Gbest displays the best solutions for the entire swarm, Pbest displays the greatest solutions for a single person (Nabipour et al., 2020 ). 2.3.5 Emotional Neural Network (ENN) Scientists are becoming interested in the incorporation of emotions into ANN to create ENNs. From a biological perspective, an animal’s emotions are reflected in the activity of its hormone glands, which governs the neurophysiological response of the animal to a given task under varying conditions (Biswas et al., 2019 ). By connecting the neurological and hormonal systems in the ENN so that each node is impacted by the other, a feedback loop enhances the model’s capacity for learning. The ENN’s mathematical development and application are still in their early phases (Lotfi & Akbarzadeh-T., 2014). Emotional backpropagation algorithms (EmBP), limbic-based artificial emotional neural network (LiAENN), and brain emotional learning (BEL) are a few ENN training algorithms that have been developed in recent years for modeling complex engineering problems. Each of these algorithms has unique features and benefits (Khashman, 2008 ; Lotfi & Akbarzadeh-T., 2014; Lotfi & Akbarzadeh-T, 2013). Furthermore, ENN models are the next generation of FFNN models that incorporate an artificial emotion system that emits hormones to adjust the performance of every node in the network. The values in the input and response nodes are used to modify the hormone weights in the feedback loop (Khashman, 2008 ). 2.3.6 Bayesian Optimization (BO) The sequential model-based optimization (SMBO) method known as Bayesian optimization is used to determine the best solution for a difficult and costly objective function. It is especially useful when there is no known analytical expression for the goal function, it is noisy, or the evaluation costs are high (Frazier, 2018 ). Gaussian Processes (GPs) are a common probabilistic model used to represent the unknown objective function. In addition to uncertainty estimates at various points in the search space, GPs offer a probabilistic estimate of the behavior of the function. Optimization is an iterative process. Using the GP model, it begins with an initial set of observations (often random or predicated on previous knowledge) and predicts the next optimal point to be assessed. Bayesian optimization uses acquisition functions, including Expected Improvement (EI), Probability of Improvement (PI), or Upper Confidence Bound (UCB), to determine the next evaluation point (Snoek et al., n.d.). To direct the search, these functions strike a balance between sampling in unpromising areas (exploration) and places that seem promising (exploitation). The new data point is appended to the preexisting observations following the evaluation of the objective function at the designated point. The GP model is then updated to improve its estimates and consider this fresh data. The ultimate outcome is the location in the search space where the probabilistic model estimates the goal function to be optimal, and this location relates to the solved problem (Shahriari et al., 2016 ). 2.3.7 Linear Regression The primary distinction between the logistic and reg approaches is in the fact that the latter are intended for modeling binary categorical outcomes, such cancer vs no cancer, etc. Many of the theories and assumptions that underpin both logistic and linear regression (Nguyen et al., 2022 ). Despite the fact that it is useful in many ways, there is one minor problem with the outcome. Due to the binary nature of the outcome, predicting unit change is either pointless or meaningless (Ghali et al., 2020 ; Khademi et al., 2016 ; Su et al., 2019 ). Rather than forecasting the outcome’s value, logistic regression focuses on the relative likelihood (odds) of achieving a particular result category. It turns out that most of the time, the natural logarithm of the odds is linear, thus we can keep applying many of the methods developed for linear models. For additional information on LR, see (Okeke et al., 2022 ). 2.3.8 Simple Averaging Ensemble (SA) The ANN-PSO, SVR-BO, ENN-GA and LR stand-alone models are first trained and evaluated independently for the suggested ensemble approach Simple Averaging Ensemble (SA). Then, the average of the ANN-PSO, SVR-BO, ENN-GA and LR outputs is compared and tested against the observed values. The general formula for SA is provided as follows. $${P}_{\\left(t\\right)}= \\frac{1}{N}\\sum _{i=1}^{N}{p}_{i}\\left(t\\right)$$ 6 N (in this case, N = 4) indicates the number of learners, while pi (i.e., ANN-PSO, SVR-BO, ENN-GA and LR) indicates the output of a single model at time t . 2.3.9 Neural network ensemble (NNE) Non-linear averaging in the neural ensemble approach (NNE) is achieved by training a second neural network. The outputs of the individual models, each of which is allocated to a single neuron in the input layer, feed the input layer of the neural ensemble model (Jimoh et al., 2022 ; Usman, Işik, Abba, et al., 2021). Similar to a basic ANN, the neural ensemble approach uses the tangent sigmoid as the activation function for the hidden and output layers (Khan & Chai, 2017 ). The network was trained using back propagation algorithms, which allow trial and error to determine the optimal structure and epoch number for the ensemble network. 2.4 The performance objective functions In the context of using nature-inspired meta-heuristic optimization algorithms alongside with Ensemble ML for PM 2.5 modeling, the evaluation criteria; R², PCC, MSE, MAE, and MAPE will provide a multifaceted assessment of model performance (Abba, Benaafi, et al., 2022b ). R² indicates the proportion of variance in PM 2.5 concentrations captured by the model, reflecting its explanatory power, while PCC measures the strength of the linear relationship between predicted and actual PM2.5 values, ensuring the model’s responsiveness to changes in input variables. MSE is critical for emphasizing the cost of large prediction errors, pertinent for capturing extreme pollution events, whereas MAE offers a straightforward, outlier-insensitive average error metric, useful for consistent performance across varying pollution levels. Lastly, MAPE provides an intuitive percentage-based accuracy measure, invaluable for stakeholders in eco-friendly air quality management to evaluate predictive performance on a relatable scale, facilitating informed decision-making and resource allocation. Together, these criteria deliver a comprehensive picture of the model’s accuracy, reliability, and practical utility in sustainable air quality management. The evaluation criteria were computed using Eq. 7 – 11 below: More information on objective functions can be found in (Abba et al., 2023 ; Ahmad et al., 2021 ; Bala et al., 2023 ; Benaafi et al., 2022 ; Ismail et al., 2022 ). $${R}^{2}=1-\\frac{\\sum _{i=1}^{N}{({Q}_{PM 2.5 \\left(o\\right)}- {Q}_{PM 2.5 \\left(p\\right)})}^{2}}{\\sum _{i=1}^{N}{({QPM 2.5 }_{ \\left(o\\right)}- {Q{\\prime }}_{PM 2.5 \\left(p\\right)})}^{2}}$$ 7 $$PCC=\\frac{\\sum _{i=1}^{N}\\left[{PM 2.5 }_{\\left(t\\right),i}-\\overline{{PM 2.5 }_{\\left(t\\right)}}\\right]\\left[{\\widehat{PM 2.5 }}_{\\left(t\\right),i}-{\\stackrel{\\sim}{PM 2.5 }}_{\\left(t\\right)}\\right]}{\\sqrt{\\sum _{i=1}^{N}{\\left[{QPM 2.5 }_{ \\left(t\\right),i}-{PM 2.5 }_{\\left(t\\right)}\\right]}^{2}{\\left[{\\widehat{PM 2.5 }}_{\\left(t\\right),i}-{\\stackrel{\\sim}{PM 2.5 }}_{\\left(t\\right)}\\right]}^{2}}}$$ 8 $$MSE=\\frac{1}{N}\\sum _{i=1}^{N}{({PM 2.5 }_{\\left(p\\right)}-{PM 2.5 }_{\\left(o\\right)})}^{2}$$ 9 $$MAE=\\frac{\\sum _{i=1}^{N}\\left|{PM 2.5 }_{\\left(p\\right)}-{PM 2.5 }_{\\left(o\\right)}\\right|}{N}$$ 10 $$MAPE=\\frac{100}{n}\\sum _{i=1}^{N}\\left|\\frac{{PM 2.5 }_{\\left(o\\right)}-{PM 2.5 }_{\\left(p\\right)}}{{PM 2.5 }_{\\left(o\\right)}}\\right|$$ 11 Where; \\({PM 2.5 }_{\\left(p\\right)}\\) , \\({PM 2.5 }_{\\left(o\\right)} and\\) N is defined as the predicted, observe and number of PM 2.5 instances respectively. 3.0 Results and discussions Understanding the behaviour and nature of the data involve in any data-driven approach is of paramount importance, owing to the fact that it helps researchers make informed decisions about which analytical techniques and models to use. Additionally, it establishes the groundwork for efficient modeling and data analysis, allowing you to get valuable insights and make defensible choices. Moreover, this is also similar in the case of air quality management modelling, which consists of various attributes such as emission sources, emission inventories, meteorological data (including; atmospheric stability, wind speed and direction, temperature as well as other weather-related attributes), topographical information and emission concentration (e.g SO 2 , NO 2 , NOX, CO, O 3 , PM 2.5, PM 2.10 etc). Therefore, two basic pre-analysis inform of descriptive statistics and correlation analysis were conducted to understand the nature of the air pollution data (see Table 1 and Fig. 2 ). Table 1 Descriptive statistics of the air pollutants SO 2 (µg/m³) NO 2 (µg/m³) RSPM (µg/m³) PM 2.5 (µg/m³) Mean 14.132 19.914 87.257 30.784 Median 14.000 20.000 88.000 30.000 Mode 14.000 21.000 94.000 31.000 SD 2.033 2.381 11.546 5.915 Kurtosis 1.584 0.582 -0.389 0.861 Skewness 0.808 -0.564 -0.054 0.530 Minimum 10.000 12.000 54.000 10.000 Maximum 23.000 26.000 120.000 55.000 Table 1 presents the basic descriptive statistics of the air pollutants involve in the current work, which demonstrates that SO 2 (µg/m³), NO 2 (µg/m³), RSPM (µg/m³), PM 2.5 (µg/m³) presents a concentration range of 13 µg/m³, 14 µg/m³, 66 µg/m³ and 45 µg/m³ respectively. Furthermore, considering PM 2.5 as a deadly respiratory air pollutant the primary 24-hour standard is 35 µg/m³, and the secondary 24-hour standard is also 35 µg/m³ (Holder et al., 2023 ; Pratiwi et al., 2023 ). These standards are designed to protect public health, and this indicates the average PM 2.5 (45 µg/m³) is higher than the standard level, hence there is concern for health issues (Holder et al., 2023 ). More also, since PM 2.5 consists of wide range of chemical compositions that are suspended in the air particulate, there is need for understanding its relationship with other environmentally hazardous air pollutants such as NO 2 and SO 2 as well as with RSPM in order to develop protocols for its mitigation to prevents its dangerous effects on human and the environment. Furthermore, the health effects of PM 2.5 exposure can also depend on the chemical composition and size distribution of these particles. Therefore, regulatory agencies and environmental researchers monitor PM2.5 concentrations and composition to assess air quality and its impact on public health. Furthermore, Fig. 2 presents the correlation matrix chart embedded with histogram, which depicts the relationship between the air pollutants (with more emphasizes to the relationship of the independent variables with PM 2.5 as the target variable). The correlation matrix chart illustrated in Figure a depicts a strong correlation between RSPM with PM 2.5 (R = 0.6), this is not surprising owing to the fact that RSPM refers to a class of airborne particles that can be inhaled into the respiratory system of a human. RSPM typically contains particles of a diameter of 10 micrometers (PM10) or less, frequently focusing on those with sizes of 10 micrometers or less, notwithstanding considerable variation in the precise size range that different areas or standards are utilize. Compared to PM 2.5, RSPM covers a wider range of particle sizes. More also, the target showed an average correlation with SO 2 and a weak correlation with NO 2 with R-values equal to 0.42 and 0.25 respectively. Based on this relationship we can understand that precursor gases like NO 2 and SO 2 can react chemically in the environment to create secondary particulate matter like PM 2.5. Through different chemical processes, gaseous contaminants are transformed into particle form throughout this process. For instance, the generation of sulfate and nitrate aerosols, both of which can contribute to PM 2 .5, that can result from the oxidation of SO 2 and NO 2 . In general, PM 2.5, NO 2 , and SO 2 are interrelated in the atmosphere due to their common emission sources, chemical interactions, and shared health implications. The specific nature of their relationship can depend on local factors, emission sources, and meteorological conditions. Monitoring and managing these pollutants are critical for air quality management and public health protection. Prior to the modelling step, a trial by error simulation was done in order to select input combinations for prediction of the PM 2.5 as the target variable. The outcomes indicate that utilizing the three input variables provides significant performance than the other way around. This is in line with recent studies conducted in the literature (Gbadamosi et al., 2023 ; Nourani et al., 2019 ; Rajaee et al., 2019 ). Therefore, the current study employed the three (RSPM, SO 2 and NO 2 ) variables in a single schema in modelling the target (PM 2.5). 3.1 Modelling results of the hybrid metaheuristic algorithms Hyperparameter tuning by trial and error and experimentation are common methods for determining a good tuning parameter range. The modelling step conducted in the current research was done on Mat Lab 2019b. For ANN-PSO the best performance was achieved based on the following optimized architecture with Iteration = 1000, Best Cost = 16.0956, learning rate (0.001–0.1), number of populations = 100 and Activation Function = Sigmoid. For ENN-GA 30 to 60 range of number for the hidden units was used, learning rate (0.001–0.1) as well as Activation Function = Sigmoid also. For SVR-BO the optimizable hyperparameters are; Box constraint = 5.121, epsilon = 0.196, Kernel function = quadratic and standardize data = true. Moreover, it is significant to note that optimal hyperparameters can vary depending on the dataset used. Moreover, one can find the ideal mixture of hyperparameters that results in strong prediction performance by performing a search in a logarithmic or exponential space and observing model performance using strategies like cross-validation or leave-one-out validation. Furthermore, the quantitative performance of the metaheuristic approach was presented in Table 2 . The objective metrics (R 2 , PCC, MSE, MAE and MAPE) are employed to checked the models’ performances. Table 2 equally indicates the robust capability of ANN-PSO over the other two metaheuristic algorithms; ENN-GA and SVR-BO as well as the classical technique inform of LR. The quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively. The MAPE values ranges between 0.00–41.00% in the training and 0.00–32.20% in the validation phases respectively. ANN-PSO illustrates the lowest MAPE values in both the training and validation stages, while SVR-BO showed highest MAPE values in the training phase and ENN-GA depicts the highest MAPE values in the validation stage. Correspondingly, the MAE results range between 0.000 to 0.450 and 0.000 to 0.376 in the calibration and validation phases respectively. Similarly, the MSE values range between 0.000 to 32.453 and 0.000 to 7.361 in the calibration and validation phases respectively. Table 2 Results of the hybrid metaheuristic algorithms Calibration R2 PCC MSE MAE MAPE ANN-PSO 1.000 1.000 0.000 0.000 0.000 ENN-GA 0.196 0.442 32.453 0.027 0.027 SVR-BO 0.435 0.659 22.811 0.450 0.450 LR 0.439 0.662 22.647 0.080 0.080 Validation ANN-PSO 1.000 1.000 0.000 0.000 0.000 ENN-GA 0.268 0.518 7.361 0.376 0.376 SVR-BO 0.337 0.581 6.665 0.042 0.042 LR 0.345 0.587 6.589 0.080 0.080 Therefore, the performance of the models can also be demonstrated graphically using various visualizations. In order to understand and analyze the data used in the training and evaluation of AI models, visualizations are essential. They make it easier to see trends, outliers, and linkages in the data. Additionally, when an AI model is not performing as expected, visualizations can be used to pinpoint where and why errors are occurring. Also, Visualizations can offer immediate feedback on the effectiveness of an AI model while it is being trained. This may contain learning curves that demonstrate how a model’s performance increases over time and feature maps that display the model’s learning at various layer depths. Consequently, visualizations can help in explaining AI model predictions to stakeholders who may not have a deep understanding of machine learning, which can serve as a step crucial for building trust and transparency in AI systems. For instance, the bump plot presented in Fig. 3 , which was also known as a rank chart or a slope graph, is a type of data visualization that is often used to display the ranking of items or categories over time or across different conditions. It’s particularly useful for visualizing changes in rank order and comparing the relative positions of items or categories. More also, Figure b demonstrates the comparative performance of the hybrid metaheuristic algorithms (ANN-PSO, ENN-GA and SVR-BO) as well as the classical LR technique using five different performance metrics; MSE, MAPE, MAE, PCC and R 2 . The bump plot demonstrates that ANN-PSO showed the lowest ranking for the error metrics; MSE, MAE and MAPE and highest ranking for PCC and R2. This indicates that ANN-PSO has outperformed other approaches (ENN-GA and SVR-BO) used in the current study in both the calibration and validation stages respectively. Also, the performance presented by the bump plot is in line with the quantitative performance results depicted in Table 2 . Furthermore, the modelling performance can equally be visualized using the Fan plot (see Fig. 4 ). The distribution of data over many categories, features or metrics is shown using a fan plot, sometimes it is referred to as a wind rose chart or polar bar chart. Moreover, data with both directional and frequency components are frequently represented using it. Therefore, the Fan plot was utilized in the current study to depict the comaparative performance of an individual metric used in the current study such as the MSE, MAE, PCC and R 2 . For example, the plot indicates that ANN-PSO depicts lower error performance based on MSE and MAE values and higher performance fitness for PCC and R 2 . Furthermore, the plot indicates that for MAE values the models; ANN-PSO, ENN-GA, SVR-BO and LR depicts the following results 0.000, 0.027, 0.450, 0.080 in training and 0.000, 0.376, 0.042, 0.080 in validation phases respectively. Hence, the performance of the techniques can be depicted in the following order Hence, the performance of the techniques can be depicted in the following order ANN-PSO > ENN-GA > LR > SVR-BO in the training and ANN-PSO > SVR-BO > LR > ENN-GA in the validation stage respectively. Furthermore, the classical visulizations techniques inform of scatter plot and response plot were equally used to compare the performance of the metaheuristics techniques used in the current study for modelling the air quality based on PM 2.5 as the target variable (see Fig. 5 ). A scatter plot is a type of graph that uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables. For the current study the scatter plot illustrates the simulated PM 2.5 using various techniques in the y-axis and the observe PM 2.5 in the x-axis and hence presents the relationship between the two using dots. Figure 5 demosntrates close relation between ANN-PSO PM 2.5 simulated values and the observe PM 2.5 values over ENN-GA, SVR-BO and LR simulated PM 2.5 values. Furthermore, the response plot is a data visualization that displays data points in sequential order, typically at equally spaced time intervals. Response plots are used to visualize how data changes over time, making them valuable for identifying trends, patterns, and anomalies in temporal data. Therefore, the current study utilizes the response plot to show the trend between the actual and simulated values and the best method will show similar or closely related trend with the actual PM 2.5 values. Figure e illustrates that ANN-PSO showed closely related trend with the observe PM 2.5 than ENN-GA, SVR-BO and LR (see Fig. 6 ). 3.2 Modelling results of the Ensemble techniques The utilization of single approach has gain remarkable attention over the years, even though, in various instances, it was found to provide lower accuracies owing to different reasons. Therefore, ensemble techniques were proposed to boost the performance of the models at certain instances as well to compare their performance with the metaheuristic algorithms for PM 2.5 modelling. Table c presents the performance of the ensemble paradigms for modelling PM 2.5 using both linear ensemble paradigm informs of SA and non-linear ensemble technique using NNE. Even though, the SA technique doesn’t provide robust performance as expected in the calibration and validation phases but was able to provide higher performance than SVR-BO and ENN-GA, though, considered as a linear approach. Moreover, SA as a linear ensemble paradigm was able to boost the prediction performance of the LR classical technique up to 19.2% in the calibration and 23.8% in the validation phases respectively based on their PCC performance metrics values. Therefore, this illustrates the importance of the ensemble paradigms over the classical techniques. Furthermore, the non-linear NNE technique demonstrates outstanding performance, which has the ability of improving the performance of both the classical LR linear technique, SA and SVR-BO and ENN-GA metaheuristic approaches. Furthermore, NNE depicts relatively lower performance than ANN-PSO especially considering their MSE, MAE and MAPE performance metrics differences. Nevertheless, NNE depicts an outstanding performance for PM 2.5 modelling than SA linear technique (see Table 3 ). Table 3 Results of the Ensemble techniques Calibration R 2 PCC MSE MAE MAPE NNE 0.999 1.000 0.032 0.005 0.004 SA 0.730 0.854 2.714 0.084 0.055 Validation NNE 0.999 0.999 0.010 0.004 0.003 SA 0.681 0.825 12.852 0.126 0.108 Moreover, the performance of the two ensemble paradigms can be graphically compared using the bar chart based on their respective MSE and MAE error performance metrics (see Fig. 7 ). Based on Fig. 8 SA presents higher MSE and MAE values than NNE in both the calibration and validation phases. Also, we are aware the lower the error performance the better the performance of the technique and vice-versa. Also, the performance of the techniques can be visualized using the time series plot. As mentioned earlier this plot shows data points gathered at progressively longer intervals of time. The time is represented by the x-axis in a time series diagram, while the variable being measured is represented by the y-axis. Figure 9 demonstrates both the actual and simulated values generated over a period of time. For the simulation values to be accepted, it should follow the same trend as the actual values. Hence, NNE showed more affinity to following same trend with the actual PM 2.5 than SA ensemble paradigm. Moreover, the scatter plot just like the time series plot presents the fitness between the simulated and actual values (see Fig. 9 ). Whereby, the model that illustrates higher agreement between the values is considered the best and vice-versa. For Fig. 9 , NNE simulated values showed higher affinity to the actual PM 2.5 values than SA. Therefore, NNE technique is considered as more robust technique than SA in modelling PM 2.5. Additionally, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms can be presented in the following order for modelling PM 2.5 using various air quality attributes; ANN-PSO > NNE > SA > ENN-GA > LR > SVR-BO in the training and ANN-PSO > NNE > SA > SVR-BO > LR > ENN-GA in the validation stage respectively. Furthermore, the performance obtained by the current study for modelling PM 2.5 as a potential approach for sustainable eco-friendly air quality management step can be compared with recent studies published in the technical literature. For example, Yu et al., (Yu et al., 2022 ) reported the prediction of PM 2.5 concentration using deep ensemble machine learning framework (DEML) using three different stages. The performance results obtained from the three stages composed of R 2 = 0. 87 and RMSE = 5.38. Therefore, the to compare our results and theirs, in our results the best performing techniques consists of ANN-PSO and NNE with R 2 = 1. 00, MSE = 0.00 and R 2 = 0. 99, MSE = 0.01 in the testing phase respectively. Hence, this indicates the robust ability of our results over theirs. Also, Sihag et al., (Sihag, 2019 ) presented the use of various soft computing techniques for modelling PM 2.5. Whereby, random forest (RF) emerges as the best performing model with PCC-values = 0.8312, MAE = 30.7757 and R 2 = 0.6909. Therefore, the performance depicted by the best technique is lower than the performance presented in the current study by both NNE and ANN-PSO in the prediction of PM 2.5. Additionally, Gokul et al., (Gokul et al., 2023 ) recently employed various AI-based techniques for modelling PM 2.5 in Hyderabad city. XGBoost regression and LSTM deep learning emerged as the best performing models having R 2 = 0.82, MAE = 7.01 and R 2 = 0.89, MAE = 5.78 respectively. A fair comparison with the best models in our study indicates that NNE with R 2 = 1. 00, MAE = 0.00 and R 2 = 0. 99, MAE = 0.004 in the testing phase has outperformed their models. Therefore, it is worthy of note to mention that based on various studies reported in the recent published technical article for prediction and modelling PM 2.5 using various models including soft computing techniques, deep learning, metaheuristic algorithms, ensemble ML, hybrid models etc, the performance depicted by NNE and ANN-PSO is outstanding, reliable and robust over other techniques. Hence, can be used as a reliable potential approach for sustainable eco-friendly air quality management for modelling PM 2.5 concentration. Conclusion Sustainable eco-friendly air quality management is a comprehensive approach to improving air quality that minimizes environmental and social impacts. It involves a combination of strategies, including; minimizing emissions from stationary and mobile sources, educating and empowering the public to act to improve air quality, Protecting and enhancing natural air quality filters (this includes planting trees, restoring wetlands, and protecting forests) etc. Sustainable eco-friendly air quality management is essential for protecting human health and the environment. It can also create economic opportunities and improve quality of life. Therefore, this work reported the use of both Metaheuristic algorithms and Ensemble techniques for modelling PM 2.5 as potential approach for improving air quality management. Furthermore, various pre-analysis techniques were conducted for data clean up and for understanding the behaviour of the variables prior to dwelling into modelling step such as through handling missing data by imputing values, Exploratory Data Analysis (EDA) using the distribution plot to understand data distributions, relationships, and patterns using histograms, descriptive statistics and correlation analysis. Hence, the obtained results of the study can be summarized as follows; The correlation matrix results indicate that RSPM (0.60) showed the highest correlation with the target PM 2.5 then followed by NO 2 (0.42) and SO 2 (0.25), The quantitative performance results obtained from the Metaheuristic algorithms indicates that ANN-PSO outperformed all the other techniques including; SVR-BO, ENN-GA and LR. The quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively based on their R 2 -values. Also, recent and novel visualizations such as Fan plot and Bump chart were used to rank the performance results obtained in PM 2.5 prediction. Moreover, NNE equally showed superior potentials over SA ensemble technique for modelling PM 2.5. Moreover, SA as a linear ensemble paradigm was able to boost the prediction performance of the LR classical technique up to 19.2% in the calibration and 23.8% in the validation phases respectively based on their PCC performance metrics values. Therefore, this illustrates the importance of the ensemble paradigms over the classical techniques. To conclude, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms can be presented in the following order for modelling PM 2.5 using various air quality attributes; ANN-PSO > NNE > SA > ENN-GA > LR > SVR-BO in the training and ANN-PSO > NNE > SA > SVR-BO > LR > ENN-GA in the validation stage respectively. Finally, the study recommends that other Metaheuristic algorithms such as HHO, BBO can be used in boosting the performance of the models for PM 2.5 prediction. Declarations Ethical Approval: Not applicable. Consent to Participate: Not applicable. Consent to Publish: Not applicable. Competing Interests: The authors declare no competing interests. Funding: Not applicable. Author Contribution Author's Contributions: AGU, SIA, SM, JU and SRN write the initial manuscript draft and AI experimental analysis. MA, AA, and SD analyzed and interpreted the data, and contributed to editing the manuscript. 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Environment International, 123 , 345–357. https://doi.org/https://doi.org/10.1016/j.envint.2018.11.075 Yaseen, Z. M., Ehteram, M., Sharafati, A., Shahid, S., Al-Ansari, N., & El-Shafie, A. (2018). The integration of nature-inspired algorithms with Least Square Support Vector regression models: Application to modeling river dissolved oxygen concentration. Water (Switzerland), 10 (9). https://doi.org/10.3390/w10091124 Yetilmezsoy, K., Ozkaya, B., & Cakmakci, M. (2011). Artificial Intelligence-Based Prediction Models. Neural Network World, 193–218. Yu, W., Li, S., Ye, T., Xu, R., Song, J., & Guo, Y. (2022). Deep Ensemble Machine Learning Framework for the Estimation of PM 2: 5 . 130 (March), 1–11. Zhang, L., Liu, P., Zhao, L., Wang, G., Zhang, W., & Liu, J. (2021). Air quality predictions with a semi-supervised bidirectional LSTM neural network. Atmospheric Pollution Research, 12 (1), 328–339. https://doi.org/https://doi.org/10.1016/j.apr.2020.09.003 Additional Declarations No competing interests reported. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4663193\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":331363401,\"identity\":\"5c5c76c6-229d-4277-86a7-7ba1ca0e15e0\",\"order_by\":0,\"name\":\"Abdullahi G. 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modelling\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4663193/v1/681579f1a66da8d9f1e5119a.png\"},{\"id\":61315775,\"identity\":\"8ae24839-8817-487f-bbb1-5e3a048881c5\",\"added_by\":\"auto\",\"created_at\":\"2024-07-29 11:59:02\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":53263,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eScatter plot of the ensemble techniques for pm 2.5 modelling\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"9.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4663193/v1/39f9824fde46932494ee5fc2.png\"},{\"id\":61753191,\"identity\":\"087f64d4-4b80-48b2-8c59-2175e5be9c45\",\"added_by\":\"auto\",\"created_at\":\"2024-08-05 08:07:28\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1586032,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4663193/v1/9b07c9e4-063c-47fc-9ebc-dbd71a209162.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Nature inspired Meta-heuristic optimization integrated with ensemble machine learning for PM2.5 modeling: a potential approach for sustainable eco-friendly health risk management\",\"fulltext\":[{\"header\":\"1.0 Introduction\",\"content\":\"\\u003cp\\u003eParticulate matter (PM) is a complex and multidimensional aspect of atmospheric chemistry that is represented by a variety of small solid and liquid droplets suspended in the atmosphere. These minuscule particles come in a variety of sizes and compositions, with dimensions ranging from a few nanometers to a few tens of micrometers. The causes of PM are closely linked to the environment on Earth, resulting from a complicated interaction between natural and human-caused factors (Ogrizek et al., \\u003cspan citationid=\\\"CR55\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). A thorough investigation of the chemical components and generation mechanisms of PM is necessary to comprehend its complex character. PM originates from a variety of sources, including particles produced by the Earth\\u0026rsquo;s natural processes (Rai, \\u003cspan citationid=\\\"CR62\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e). These include mineral dust particles created by the erosion of rocks and soil, as well as biological elements like pollen and spores from plants and microbes (Aarnink et al., \\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e). Sea salt aerosols are produced by the breaking waves in the ocean and add to the natural PM concentration. These naturally occurring particulates are crucial to the functioning of Earth\\u0026rsquo;s ecosystems because they help in transferring nutrients, generate clouds, and serve as the building blocks for the creation of raindrops (Ubaid et al., \\u003cspan citationid=\\\"CR74\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). Human activity significantly contributes to the atmospheric PM, releasing a variety of particles from combustion, construction, and industrial processes. These sources often contain heavy metals and organic chemicals, resulting in a dynamic and ever-changing composition (Chen et al., \\u003cspan citationid=\\\"CR14\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe increase in PM pollution poses an increasing threat to the environment. These microscopic particles can have profound and far-reaching effects on human health, ecosystems, and the environment. Owing to the fact that PM can enter the respiratory system deeply and cause a variety of respiratory and cardiovascular disorders, it poses a serious risk to human health (Hamanaka \\u0026amp; Mutlu, \\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). In addition, PM harms the environment due to its participation in the production of smog, decreased visibility, and deposition of natural ecosystems, which lowers the quality of the soil and water (Kim et al., \\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e). Therefore, the need for effective addressing of PM pollution necessitates the use of intricate and advanced models to comprehend its origins, distribution, and ecological impacts (G et al., \\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eBefore the advancement of advanced machine learning (ML) and artificial intelligence (AI) techniques, managing the intricate issues related to particulate matter pollution was difficult. Policymakers and environmental scientists mainly used manual data analysis and simple equations in their older models (Liu et al., \\u003cspan citationid=\\\"CR42\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). The complex dynamics of PM sources and dispersion patterns were difficult for these older methods to capture. Furthermore, they could not properly utilize the potential of the enormous datasets that are already accessible (Luo et al., \\u003cspan citationid=\\\"CR45\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). Consequently, the shortcomings of these conventional approaches limited the ability to minimize the harmful impacts of PM pollution and optimize environmental management (Wu et al., \\u003cspan citationid=\\\"CR81\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eFor decades classical methods of managing air pollution have been associated with several uncertainties and approximations owing to their complex and nonlinear nature(Costache et al., \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Mohammadi et al., \\u003cspan citationid=\\\"CR51\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e; Pham et al., \\u003cspan citationid=\\\"CR58\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Sammen et al., \\u003cspan citationid=\\\"CR64\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e). It is well known based on the developed traditional techniques of controlling PM 2.5 that utilizing AI models for PM 2.5 prediction offers substantial advantages by significantly enhancing the accuracy and efficiency of air quality forecasting. Artificial intelligence (AI) algorithms improve the overall understanding of PM 2.5 modelling, enabling them to adapt to complex environmental data and ensuring real-time, globally applicable insights. This approach not only accelerates computational processes but also supports informed decision-making for effective and sustainable air quality management. However, coupling nature-inspired meta-heuristic optimization algorithms and ensemble machine learning (ML) presents a novel approach to modelling particulate matter (PM 2.5) concentrations, which are critical to air quality management. By mimicking evolutionary processes, these algorithms can efficiently navigate complex search spaces to calibrate ensemble ML models, thereby enhancing their predictive accuracy(Baig et al., \\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). This serves as the fundamental in creating sustainable, eco-friendly strategies for air quality control, leveraging the inherent adaptability of nature-inspired algorithms to optimize the weights and hyperparameters of ML models (Uniyal et al., \\u003cspan citationid=\\\"CR75\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eRecently, PM 2.5 modelling using advanced AI and spatial mapping attracted a huge researcher\\u0026rsquo;s attention. For instance, Tai et al. (Tai et al., \\u003cspan citationid=\\\"CR70\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e) explored correlation-based and ML models for the prediction of PM 2.5 using metrological parameters over 11 years of US data and showed that weather conditions explain about 50% of PM2.5 variations. In 2012, Tai et al. (Tai et al., \\u003cspan citationid=\\\"CR71\\\" class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e) employed several models to predict PM 2.5 using metrological variables for the Impact of 2000\\u0026ndash;2050 climate change. In 2018, Polezar et al. (Polezer et al., \\u003cspan citationid=\\\"CR59\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e) employed nonlinear artificial neural network (ANN), Multilayer Perceptron (MLP), Extreme Learning Machines (ELM) and Echo State Networks (ESN) to evaluate the impact of PM 2.5 on human health. The outcomes indicated that ANN is a more reliable method for a smaller amount of data. In addition, Wei et al. (Wei et al., \\u003cspan citationid=\\\"CR80\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e) in 2020 utilize computational randomized trees to estimate PM 2.5 across China based on 1km resolution. A more recent study in 2023 was conducted by Gokul et al. (Gokul et al., \\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) in Hyderabad city India in which PM 2.5 was predicted using spatial method, single and deep learning approaches. The outcomes indicated the prediction skills of LSTM (Long Short-Term Memory) over XGBoost. The other that attempt to predict PM 2.5 in several region across the globe include (Hu et al., \\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e2014\\u003c/span\\u003e; Lary et al., \\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e; Liang et al., \\u003cspan citationid=\\\"CR40\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e; Lin et al., \\u003cspan citationid=\\\"CR41\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e; Meng et al., \\u003cspan citationid=\\\"CR49\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; Pandya et al., \\u003cspan citationid=\\\"CR57\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Prunicki et al., \\u003cspan citationid=\\\"CR61\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e; Xue et al., \\u003cspan citationid=\\\"CR82\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Zhang et al., \\u003cspan citationid=\\\"CR86\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eIt can be seen that PM 2.5 received significant attention using single AI model, however it is very crucial to optimize the standalone model using optimization techniques(Moayedi et al., \\u003cspan citationid=\\\"CR50\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Simon, \\u003cspan citationid=\\\"CR67\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e; Yaseen et al., \\u003cspan citationid=\\\"CR83\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). Optimization is essential in prediction as it enhances model accuracy, ensures computational efficiency, and improves generalization capabilities, which are crucial for effective and cost-efficient decision-making, particularly in environmental monitoring like PM 2.5 assessment. Moreover, the application of these advanced techniques to PM 2.5 modelling is a testament to the potential of AI in environmental science. By harnessing the stochastic yet structured search mechanisms of meta-heuristic algorithms, such as Ant Colony Optimization (ACO) or Simulated Annealing (SA), the ensemble models can simulate and predict PM 2.5 variations with high precision. This allows for real-time monitoring and proactive policymaking, mapping a course towards a sustainable future with cleaner air, thus implementing both environmental and public health imperatives(Nabipour et al., \\u003cspan citationid=\\\"CR52\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eSimilarly, the motivation for the study is to improve the monitoring and modelling of PM 2.5, a significant air pollutant with serious health implications, due to its capacity to access deep into the respiratory system. The study aims to enhance the accuracy of PM 2.5 predictions, which are vital for developing effective air quality management strategies to protect public health and ensure a sustainable environment. It is worth mentioning based on the above literature that the gap identified in the study is the need for more efficient and accurate prediction models for PM 2.5 concentrations. Existing models may not fully capture the complexity of air quality data or might not be optimized for the best performance. To address this, the study integrates nature-inspired meta-heuristic optimization algorithms with ensemble machine learning techniques to improve the prediction models. The use of specific algorithms like ANN-PSO (Artificial Neural Network with Particle Swarm Optimization) is highlighted as particularly effective, outperforming other techniques in both calibration and validation phases. The research also explores the potential of the Neural Network Ensemble (NNE) over simpler averaging (SA) ensemble methods, indicating a methodological improvement in the field of air quality modelling.\\u003c/p\\u003e\"},{\"header\":\"2.0 Materials and Methods\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.1 The Proposed Methodology\\u003c/h2\\u003e \\u003cp\\u003eEver since the advent of industrialization, there has been a growing worry regarding the impact of environmental pollution. According to the World Health Organization\\u0026rsquo;s findings, air pollution is responsible for a staggering annual toll of 7\\u0026nbsp;million premature deaths, making it the most significant environmental hazard globally (Lynch, \\u003cspan citationid=\\\"CR46\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). The dataset used in the current study contained 435,742 instances were utilized each for both the input variables inform of Sulfur dioxide (SO\\u003csub\\u003e2\\u003c/sub\\u003e), Nitrogen Dioxide (NO\\u003csub\\u003e2\\u003c/sub\\u003e) and Respiratory suspended particulate matter (RSPM) as well as the output variable inform of Particulate Matter 2.5 (PM 2.5). The unclean dataset can be found in the following open source link \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://www.kaggle.com/datasets/shrutibhargava94/india-air-quality-data\\u003c/span\\u003e\\u003cspan address=\\\"https://www.kaggle.com/datasets/shrutibhargava94/india-air-quality-data\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003eIn the proposed methodology we commence with the collection and pre-processing of PM 2.5 and relevant environmental data, followed by dimensionality reduction using techniques like PCA to select significant features. We then develop an array of individual predictive models, including ANN, Emotional NN, SVR, and LR, which are optimized using meta-heuristic algorithms such as PSO, GA and BO for hyperparameter tuning. These models are subsequently integrated into an ensemble framework, to improve prediction accuracy at certain instances. Both the metaheuristic algorithms and ensemble\\u0026rsquo;s performance are rigorously evaluated using metrics like R-squared (R\\u003csup\\u003e2\\u003c/sup\\u003e), Pearson Correlation Coefficient (PCC), Mean Squared Error (MSE) and Mean Absolute Error (MAE), and upon successful validation, the model is deployed for real-world application. Continuous performance monitoring and a feedback loop for incorporating actual measurements ensure dynamic model recalibration and sustainability in managing air quality.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.2 The study location\\u003c/h2\\u003e \\u003cp\\u003eIndia is located in South Asia and is bordered by several countries; Pakistan to the northwest, China to the northeast, Nepal to the north, Bhutan to the north, Bangladesh to the east, Myanmar to the east, and Sri Lanka to the south though separated by the Palk Strait. Furthermore, this country has an approximate Latitude of 20.5937 degrees north and an approximate Longitude of 78.9629 degrees East (Duraisamy et al., \\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). The Republic of India is a large, diversified nation that has many opportunities for all kinds of research and study. India is a great place to study since it has a rich history, culture, and educational institutions. India is confronted with environmental issues such as deforestation, air and water pollution, and climate change. Studying environmental science and sustainability initiatives is made possible by this exceptional opportunity (Marghade et al., \\u003cspan citationid=\\\"CR48\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). Furthermore, Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e demonstrates the map of the study location indicating the major pollutant sources.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.3 The machine learning and metaheuristic algorithms\\u003c/h2\\u003e \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.1 Artificial Neural Network (ANN)\\u003c/h2\\u003e \\u003cp\\u003eArtificial neural networks (ANNs) are computationally analytically-based systems that mimic how human brains utilize data. (Abba et al., \\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e, \\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e; Jibril, Zayyan, et al., \\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). As processing units, they are made up of several neurons coupled by movable weights and biases. An input, hidden, and output layer comprise an ANN\\u0026rsquo;s single or multi-layered system (Tayyebi et al., \\u003cspan citationid=\\\"CR72\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). The feed-forward network with backpropagation algorithms (FFNN-BP) is used in this study. The literature claims that artificial neural networks, which feature a fundamental unit called a neuron (node), are information processing instruments that are modeled after the biological nervous system of the brain. Owing to their promising capabilities, ANNs with FFNN-BP have shown themselves to be useful instruments in various scientific and technical domains for surmounting extremely non-linear processes (Elkiran et al., \\u003cspan citationid=\\\"CR17\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Jibril, Malami, et al., \\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Khalid \\u0026amp; Usman, \\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e). Furthermore, FFNN-BP entails training the network using trained input data that is processed within the network and then sent to the output layer, where errors may occur and then spread throughout the system until the desired output is obtained(Usman, Işik, \\u0026amp; Abba, \\u003cspan citationid=\\\"CR77\\\" class=\\\"CitationRef\\\"\\u003e2021b\\u003c/span\\u003e). The main idea behind FFNN-BP is that in order for the network to comprehend the training data and predict the real value, it must reduce the created mistakes (Elkiran et al., \\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). Throughout its operation, the inputs are multiplied by the initial weights, after which the value advances to the second layer and ultimately to the output layer. It is seen in Eq.\\u0026nbsp;\\u003cspan refid=\\\"Equ1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e (Gaya et al., \\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e).\\u003cdiv id=\\\"Equ1\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ1\\\" name=\\\"EquationSource\\\"\\u003e\\n$${z}_{i}= \\\\sum _{j=1}^{m}{w}_{ij}{x}_{ij}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e1\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere zi denotes the final total of the ith node\\u0026rsquo;s outputs, \\u0026#119960;\\u0026#119946;\\u0026#119947; represents the input, and \\u0026#119960;\\u0026#119946;\\u0026#119947; represents the weight shifted from the jth input to the ith node. Consequently, by computing the difference between the goal value and the projected values, backpropagation is utilized to ascertain the inaccuracy. Usually, it is carried out backwards, beginning at the output layer and working backwards to the input layer. The error node j in layer l is indicated by this difference, δ(l)j. The mathematical expression of the error term for a training set (xj, yj) is given by Eq.\\u0026nbsp;\\u003cspan refid=\\\"Equ2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e:\\u003cdiv id=\\\"Equ2\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ2\\\" name=\\\"EquationSource\\\"\\u003e\\n$${e}_{p }= {y}_{d}- {y}_{a}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e2\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere y_a is the real output of the training model and y_d is the neuron p\\u0026rsquo;s output.\\u003c/p\\u003e \\u003cp\\u003eHowever, a large number of neurons in the buried layer may affect the neural network\\u0026rsquo;s capacity and generalization ability, which adds to the computational cost because lower neurons cannot deliver the desired prediction accuracy (Gaya et al., \\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e). The biases and connection weights are continuously modified during the learning process in order to achieve the desired output. This technique is known as continuous learning. This might be an unsupervised or supervised process. Generally speaking, supervised learning is utilized to reduce the discrepancies between the computed and desired values. (Hamed et al., \\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2004\\u003c/span\\u003e). The learning rate is crucial in defining the network\\u0026rsquo;s intelligence by bringing the network system together and so minimizing the problems associated with a local minimum. The trial-and-error method makes use of both the learning rate and the architecture, or the quantity of layers, transfer function, and neurons. The input and hidden layers employ sigmoid activation, whereas the output layer uses the linear activation function. Every neuron has an activation function, which is a mathematical function that transforms a linear function into a non-linear function (Yetilmezsoy et al., \\u003cspan citationid=\\\"CR84\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e) (see Eq.\\u0026nbsp;\\u003cspan refid=\\\"Equ3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e).\\u003cdiv id=\\\"Equ3\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ3\\\" name=\\\"EquationSource\\\"\\u003e\\n$$F\\\\left(x\\\\right)= \\\\frac{1}{1+{e}^{(-x)}}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e3\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec7\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.2 Support Vector Regression (SVR)\\u003c/h2\\u003e \\u003cp\\u003eIn 1995, Vatnik developed the idea of learning within the SVM framework, which designed the ideal idea for resolving problems pertaining to regression, pattern recognition, classification, and prediction models. The SVM is composed of a data-driven model and is based on the concept of machine learning (Hong et al., \\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e). The two primary purposes of SVM are statistical learning theory and structural risk minimization. This gives information that sets it apart from ANN in terms of its ability to lower error, redundancy in data, and complexity while simultaneously enhancing system performance. There are two varieties of support vector regression (SVR): non-linear and linear (USMAN et al., \\u003cspan citationid=\\\"CR79\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). This gives an insight that sets it apart from ANN in terms of its capacity to lower error, redundancy in data, and complexity while simultaneously enhancing system performance (Usman, Işik, \\u0026amp; Abba, \\u003cspan citationid=\\\"CR76\\\" class=\\\"CitationRef\\\"\\u003e2021a\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eFurthermore, SVR is a machine learning technique that is used for regression tasks. Kernel Support Vector Regression (Kernel-SVR) is a version of SVR. When dealing with nonlinear interactions between the input variables and the target variable, kernel-SVR is especially useful (Abba, Benaafi, et al., \\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e2022a\\u003c/span\\u003e). By applying kernel functions to convert the input variables into a higher-dimensional feature space, kernel-SVR improves upon the fundamental SVR. Nonlinear interactions between the variables and the target variable can be captured by Kernel-SVR by translating the input variables into a higher-dimensional space (Bonakdari et al., \\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec8\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.3 Genetic algorithm (GA)\\u003c/h2\\u003e \\u003cp\\u003eCharles Darwin\\u0026rsquo;s idea of natural selection served as the foundation for John Holland\\u0026rsquo;s metaheuristic search and optimization method, known as the GA [3]. The main focus of GA is its capacity to manage complex systems and parallelism. To solve complex problems, GA searches a wide range of parameter spaces and provides an approximate optimal solution (regardless of whether the fitness function is stationary, nonstationary, linear, nonlinear, continuous, discontinuous, or contains random noise) (Abba, Abdulkadir, et al., \\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). It is the outcome of the many progenies of the population functioning as independent actors. These individuals investigate the search space in multiple directions at the same time. The three primary GA operators are crossover, mutation, and selection. In selection operators, chromosomes are selected for subsequent replication (e.g., via roulette wheel selection) (Termeh et al., \\u003cspan citationid=\\\"CR73\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec9\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.4 Particle swarm optimization (PSO) algorithm\\u003c/h2\\u003e \\u003cp\\u003eParticle Swarm Optimization (PSO), a newly developed metaheuristic for optimizing population-based algorithms, was proposed by Eberhart and Kennedy. This algorithm is a nature-inspired method based on fish schools and avian foraging (Malik et al., \\u003cspan citationid=\\\"CR47\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e). PSO is regarded as an optimizer that affects both local and global swarm locations to revolve around the problem space. Generally, different random values are assigned for the particle location in each PSO. Next, iteration, the global cost of the optimal swarm positioning, and the cost of the best swarm are kept. Equations X and Y could be used to modernize each particle\\u0026rsquo;s position and velocity (Malik et al., \\u003cspan citationid=\\\"CR47\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e).\\u003cdiv id=\\\"Equ4\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ4\\\" name=\\\"EquationSource\\\"\\u003e\\n$${v}_{i}^{t+1}=w{v}_{i}^{t}+{C}_{c1}\\\\times randN\\\\times \\\\left({Pbest}_{i}-{x}_{i}^{t}\\\\right)+{S}_{f1}\\\\times randNO\\\\times \\\\left(Gbest-{x}_{i}^{t}\\\\right)$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e4\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ5\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ5\\\" name=\\\"EquationSource\\\"\\u003e\\n$${d}_{i}^{t+1}={d}_{i}^{t}+{v}_{i}^{t+1}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e5\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere w denotes inertial weight and governs the PSO algorithm\\u0026rsquo;s stability. C_c1 displays the cognitive coefficient, which regulates the impact of each person\\u0026rsquo;s memory. S_f1, or social factor, is utilized to boost PSO performance; randNO, on the other hand, displays a random number between 0 and 1, giving PSO greater capacity for randomized search. While Gbest displays the best solutions for the entire swarm, Pbest displays the greatest solutions for a single person (Nabipour et al., \\u003cspan citationid=\\\"CR52\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec10\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.5 Emotional Neural Network (ENN)\\u003c/h2\\u003e \\u003cp\\u003eScientists are becoming interested in the incorporation of emotions into ANN to create ENNs. From a biological perspective, an animal\\u0026rsquo;s emotions are reflected in the activity of its hormone glands, which governs the neurophysiological response of the animal to a given task under varying conditions (Biswas et al., \\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). By connecting the neurological and hormonal systems in the ENN so that each node is impacted by the other, a feedback loop enhances the model\\u0026rsquo;s capacity for learning. The ENN\\u0026rsquo;s mathematical development and application are still in their early phases (Lotfi \\u0026amp; Akbarzadeh-T., 2014). Emotional backpropagation algorithms (EmBP), limbic-based artificial emotional neural network (LiAENN), and brain emotional learning (BEL) are a few ENN training algorithms that have been developed in recent years for modeling complex engineering problems. Each of these algorithms has unique features and benefits (Khashman, \\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e; Lotfi \\u0026amp; Akbarzadeh-T., 2014; Lotfi \\u0026amp; Akbarzadeh-T, 2013). Furthermore, ENN models are the next generation of FFNN models that incorporate an artificial emotion system that emits hormones to adjust the performance of every node in the network. The values in the input and response nodes are used to modify the hormone weights in the feedback loop (Khashman, \\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec11\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.6 Bayesian Optimization (BO)\\u003c/h2\\u003e \\u003cp\\u003eThe sequential model-based optimization (SMBO) method known as Bayesian optimization is used to determine the best solution for a difficult and costly objective function. It is especially useful when there is no known analytical expression for the goal function, it is noisy, or the evaluation costs are high (Frazier, \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). Gaussian Processes (GPs) are a common probabilistic model used to represent the unknown objective function. In addition to uncertainty estimates at various points in the search space, GPs offer a probabilistic estimate of the behavior of the function. Optimization is an iterative process. Using the GP model, it begins with an initial set of observations (often random or predicated on previous knowledge) and predicts the next optimal point to be assessed. Bayesian optimization uses acquisition functions, including Expected Improvement (EI), Probability of Improvement (PI), or Upper Confidence Bound (UCB), to determine the next evaluation point (Snoek et al., n.d.). To direct the search, these functions strike a balance between sampling in unpromising areas (exploration) and places that seem promising (exploitation). The new data point is appended to the preexisting observations following the evaluation of the objective function at the designated point. The GP model is then updated to improve its estimates and consider this fresh data. The ultimate outcome is the location in the search space where the probabilistic model estimates the goal function to be optimal, and this location relates to the solved problem (Shahriari et al., \\u003cspan citationid=\\\"CR65\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec12\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.7 Linear Regression\\u003c/h2\\u003e \\u003cp\\u003eThe primary distinction between the logistic and reg approaches is in the fact that the latter are intended for modeling binary categorical outcomes, such cancer vs no cancer, etc. Many of the theories and assumptions that underpin both logistic and linear regression (Nguyen et al., \\u003cspan citationid=\\\"CR53\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). Despite the fact that it is useful in many ways, there is one minor problem with the outcome. Due to the binary nature of the outcome, predicting unit change is either pointless or meaningless (Ghali et al., \\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e; Khademi et al., \\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e; Su et al., \\u003cspan citationid=\\\"CR69\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). Rather than forecasting the outcome\\u0026rsquo;s value, logistic regression focuses on the relative likelihood (odds) of achieving a particular result category. It turns out that most of the time, the natural logarithm of the odds is linear, thus we can keep applying many of the methods developed for linear models. For additional information on LR, see (Okeke et al., \\u003cspan citationid=\\\"CR56\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec13\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.8 Simple Averaging Ensemble (SA)\\u003c/h2\\u003e \\u003cp\\u003eThe ANN-PSO, SVR-BO, ENN-GA and LR stand-alone models are first trained and evaluated independently for the suggested ensemble approach Simple Averaging Ensemble (SA). Then, the average of the ANN-PSO, SVR-BO, ENN-GA and LR outputs is compared and tested against the observed values. The general formula for SA is provided as follows.\\u003cdiv id=\\\"Equ6\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ6\\\" name=\\\"EquationSource\\\"\\u003e\\n$${P}_{\\\\left(t\\\\right)}= \\\\frac{1}{N}\\\\sum _{i=1}^{N}{p}_{i}\\\\left(t\\\\right)$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e6\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003eN (in this case, N\\u0026thinsp;=\\u0026thinsp;4) indicates the number of learners, while pi (i.e., ANN-PSO, SVR-BO, ENN-GA and LR) indicates the output of a single model at time \\u003cem\\u003et\\u003c/em\\u003e.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec14\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.9 Neural network ensemble (NNE)\\u003c/h2\\u003e \\u003cp\\u003eNon-linear averaging in the neural ensemble approach (NNE) is achieved by training a second neural network. The outputs of the individual models, each of which is allocated to a single neuron in the input layer, feed the input layer of the neural ensemble model (Jimoh et al., \\u003cspan citationid=\\\"CR33\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e; Usman, Işik, Abba, et al., 2021). Similar to a basic ANN, the neural ensemble approach uses the tangent sigmoid as the activation function for the hidden and output layers (Khan \\u0026amp; Chai, \\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e). The network was trained using back propagation algorithms, which allow trial and error to determine the optimal structure and epoch number for the ensemble network.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.4 The performance objective functions\\u003c/h2\\u003e \\u003cp\\u003eIn the context of using nature-inspired meta-heuristic optimization algorithms alongside with Ensemble ML for PM 2.5 modeling, the evaluation criteria; R\\u0026sup2;, PCC, MSE, MAE, and MAPE will provide a multifaceted assessment of model performance (Abba, Benaafi, et al., \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2022b\\u003c/span\\u003e). R\\u0026sup2; indicates the proportion of variance in PM 2.5 concentrations captured by the model, reflecting its explanatory power, while PCC measures the strength of the linear relationship between predicted and actual PM2.5 values, ensuring the model\\u0026rsquo;s responsiveness to changes in input variables. MSE is critical for emphasizing the cost of large prediction errors, pertinent for capturing extreme pollution events, whereas MAE offers a straightforward, outlier-insensitive average error metric, useful for consistent performance across varying pollution levels. Lastly, MAPE provides an intuitive percentage-based accuracy measure, invaluable for stakeholders in eco-friendly air quality management to evaluate predictive performance on a relatable scale, facilitating informed decision-making and resource allocation. Together, these criteria deliver a comprehensive picture of the model\\u0026rsquo;s accuracy, reliability, and practical utility in sustainable air quality management. The evaluation criteria were computed using Eq.\\u0026nbsp;\\u003cspan refid=\\\"Equ7\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e\\u0026ndash;\\u003cspan refid=\\\"Equ11\\\" class=\\\"InternalRef\\\"\\u003e11\\u003c/span\\u003e below:\\u003c/p\\u003e \\u003cp\\u003eMore information on objective functions can be found in (Abba et al., \\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Ahmad et al., \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; Bala et al., \\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Benaafi et al., \\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e; Ismail et al., \\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e).\\u003cdiv id=\\\"Equ7\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ7\\\" name=\\\"EquationSource\\\"\\u003e\\n$${R}^{2}=1-\\\\frac{\\\\sum _{i=1}^{N}{({Q}_{PM 2.5 \\\\left(o\\\\right)}- {Q}_{PM 2.5 \\\\left(p\\\\right)})}^{2}}{\\\\sum _{i=1}^{N}{({QPM 2.5 }_{ \\\\left(o\\\\right)}- {Q{\\\\prime }}_{PM 2.5 \\\\left(p\\\\right)})}^{2}}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e7\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ8\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ8\\\" name=\\\"EquationSource\\\"\\u003e\\n$$PCC=\\\\frac{\\\\sum _{i=1}^{N}\\\\left[{PM 2.5 }_{\\\\left(t\\\\right),i}-\\\\overline{{PM 2.5 }_{\\\\left(t\\\\right)}}\\\\right]\\\\left[{\\\\widehat{PM 2.5 }}_{\\\\left(t\\\\right),i}-{\\\\stackrel{\\\\sim}{PM 2.5 }}_{\\\\left(t\\\\right)}\\\\right]}{\\\\sqrt{\\\\sum _{i=1}^{N}{\\\\left[{QPM 2.5 }_{ \\\\left(t\\\\right),i}-{PM 2.5 }_{\\\\left(t\\\\right)}\\\\right]}^{2}{\\\\left[{\\\\widehat{PM 2.5 }}_{\\\\left(t\\\\right),i}-{\\\\stackrel{\\\\sim}{PM 2.5 }}_{\\\\left(t\\\\right)}\\\\right]}^{2}}}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e8\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ9\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ9\\\" name=\\\"EquationSource\\\"\\u003e\\n$$MSE=\\\\frac{1}{N}\\\\sum _{i=1}^{N}{({PM 2.5 }_{\\\\left(p\\\\right)}-{PM 2.5 }_{\\\\left(o\\\\right)})}^{2}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e9\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ10\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ10\\\" name=\\\"EquationSource\\\"\\u003e\\n$$MAE=\\\\frac{\\\\sum _{i=1}^{N}\\\\left|{PM 2.5 }_{\\\\left(p\\\\right)}-{PM 2.5 }_{\\\\left(o\\\\right)}\\\\right|}{N}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e10\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ11\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ11\\\" name=\\\"EquationSource\\\"\\u003e\\n$$MAPE=\\\\frac{100}{n}\\\\sum _{i=1}^{N}\\\\left|\\\\frac{{PM 2.5 }_{\\\\left(o\\\\right)}-{PM 2.5 }_{\\\\left(p\\\\right)}}{{PM 2.5 }_{\\\\left(o\\\\right)}}\\\\right|$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e11\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003eWhere; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({PM 2.5 }_{\\\\left(p\\\\right)}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({PM 2.5 }_{\\\\left(o\\\\right)} and\\\\)\\u003c/span\\u003e\\u003c/span\\u003eN is defined as the predicted, observe and number of PM 2.5 instances respectively.\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"3.0 Results and discussions\",\"content\":\"\\u003cp\\u003eUnderstanding the behaviour and nature of the data involve in any data-driven approach is of paramount importance, owing to the fact that it helps researchers make informed decisions about which analytical techniques and models to use. Additionally, it establishes the groundwork for efficient modeling and data analysis, allowing you to get valuable insights and make defensible choices. Moreover, this is also similar in the case of air quality management modelling, which consists of various attributes such as emission sources, emission inventories, meteorological data (including; atmospheric stability, wind speed and direction, temperature as well as other weather-related attributes), topographical information and emission concentration (e.g SO\\u003csub\\u003e2\\u003c/sub\\u003e, NO\\u003csub\\u003e2\\u003c/sub\\u003e, NOX, CO, O\\u003csub\\u003e3\\u003c/sub\\u003e, PM 2.5, PM 2.10 etc). Therefore, two basic pre-analysis inform of descriptive statistics and correlation analysis were conducted to understand the nature of the air pollution data (see Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e and Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\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\\u003eDescriptive statistics of the air pollutants\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e\\u003ccolgroup cols=\\\"5\\\"\\u003e\\u003c/colgroup\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eSO\\u003csub\\u003e2\\u003c/sub\\u003e (µg/m³)\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eNO\\u003csub\\u003e2\\u003c/sub\\u003e (µg/m³)\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eRSPM (µg/m³)\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003ePM 2.5 (µg/m³)\\u003c/p\\u003e \\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eMean\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e14.132\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e19.914\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e87.257\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e30.784\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eMedian\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e14.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e20.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e88.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e30.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eMode\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e14.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e21.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e94.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e31.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSD\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e2.033\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2.381\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e11.546\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5.915\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eKurtosis\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1.584\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.582\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e-0.389\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.861\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSkewness\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.808\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e-0.564\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e-0.054\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.530\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eMinimum\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e10.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e12.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e54.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e10.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eMaximum\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e23.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e26.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e120.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e55.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/table\\u003e\\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eTable\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e presents the basic descriptive statistics of the air pollutants involve in the current work, which demonstrates that SO\\u003csub\\u003e2\\u003c/sub\\u003e (µg/m³), NO\\u003csub\\u003e2\\u003c/sub\\u003e (µg/m³), RSPM (µg/m³), PM 2.5 (µg/m³) presents a concentration range of 13 µg/m³, 14 µg/m³, 66 µg/m³ and 45 µg/m³ respectively. Furthermore, considering PM 2.5 as a deadly respiratory air pollutant the primary 24-hour standard is 35 µg/m³, and the secondary 24-hour standard is also 35 µg/m³ (Holder et al., \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Pratiwi et al., \\u003cspan citationid=\\\"CR60\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). These standards are designed to protect public health, and this indicates the average PM 2.5 (45 µg/m³) is higher than the standard level, hence there is concern for health issues (Holder et al., \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). More also, since PM 2.5 consists of wide range of chemical compositions that are suspended in the air particulate, there is need for understanding its relationship with other environmentally hazardous air pollutants such as NO\\u003csub\\u003e2\\u003c/sub\\u003e and SO\\u003csub\\u003e2\\u003c/sub\\u003e as well as with RSPM in order to develop protocols for its mitigation to prevents its dangerous effects on human and the environment. Furthermore, the health effects of PM 2.5 exposure can also depend on the chemical composition and size distribution of these particles. Therefore, regulatory agencies and environmental researchers monitor PM2.5 concentrations and composition to assess air quality and its impact on public health. Furthermore, Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e presents the correlation matrix chart embedded with histogram, which depicts the relationship between the air pollutants (with more emphasizes to the relationship of the independent variables with PM 2.5 as the target variable).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eThe correlation matrix chart illustrated in Figure a depicts a strong correlation between RSPM with PM 2.5 (R = 0.6), this is not surprising owing to the fact that RSPM refers to a class of airborne particles that can be inhaled into the respiratory system of a human. RSPM typically contains particles of a diameter of 10 micrometers (PM10) or less, frequently focusing on those with sizes of 10 micrometers or less, notwithstanding considerable variation in the precise size range that different areas or standards are utilize. Compared to PM 2.5, RSPM covers a wider range of particle sizes. More also, the target showed an average correlation with SO\\u003csub\\u003e2\\u003c/sub\\u003e and a weak correlation with NO\\u003csub\\u003e2\\u003c/sub\\u003e with R-values equal to 0.42 and 0.25 respectively. Based on this relationship we can understand that precursor gases like NO\\u003csub\\u003e2\\u003c/sub\\u003e and SO\\u003csub\\u003e2\\u003c/sub\\u003e can react chemically in the environment to create secondary particulate matter like PM 2.5. Through different chemical processes, gaseous contaminants are transformed into particle form throughout this process. For instance, the generation of sulfate and nitrate aerosols, both of which can contribute to PM 2 .5, that can result from the oxidation of SO\\u003csub\\u003e2\\u003c/sub\\u003e and NO\\u003csub\\u003e2\\u003c/sub\\u003e. In general, PM 2.5, NO\\u003csub\\u003e2\\u003c/sub\\u003e, and SO\\u003csub\\u003e2\\u003c/sub\\u003e are interrelated in the atmosphere due to their common emission sources, chemical interactions, and shared health implications. The specific nature of their relationship can depend on local factors, emission sources, and meteorological conditions. Monitoring and managing these pollutants are critical for air quality management and public health protection. Prior to the modelling step, a trial by error simulation was done in order to select input combinations for prediction of the PM 2.5 as the target variable. The outcomes indicate that utilizing the three input variables provides significant performance than the other way around. This is in line with recent studies conducted in the literature (Gbadamosi et al., \\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Nourani et al., \\u003cspan citationid=\\\"CR54\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Rajaee et al., \\u003cspan citationid=\\\"CR63\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). Therefore, the current study employed the three (RSPM, SO\\u003csub\\u003e2\\u003c/sub\\u003e and NO\\u003csub\\u003e2\\u003c/sub\\u003e) variables in a single schema in modelling the target (PM 2.5).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cdiv id=\\\"Sec17\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.1 Modelling results of the hybrid metaheuristic algorithms\\u003c/h2\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eHyperparameter tuning by trial and error and experimentation are common methods for determining a good tuning parameter range. The modelling step conducted in the current research was done on Mat Lab 2019b. For ANN-PSO the best performance was achieved based on the following optimized architecture with Iteration = 1000, Best Cost = 16.0956, learning rate (0.001–0.1), number of populations = 100 and Activation Function = Sigmoid. For ENN-GA 30 to 60 range of number for the hidden units was used, learning rate (0.001–0.1) as well as Activation Function = Sigmoid also. For SVR-BO the optimizable hyperparameters are; Box constraint = 5.121, epsilon = 0.196, Kernel function = quadratic and standardize data = true. Moreover, it is significant to note that optimal hyperparameters can vary depending on the dataset used. Moreover, one can find the ideal mixture of hyperparameters that results in strong prediction performance by performing a search in a logarithmic or exponential space and observing model performance using strategies like cross-validation or leave-one-out validation. Furthermore, the quantitative performance of the metaheuristic approach was presented in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e. The objective metrics (R\\u003csup\\u003e2\\u003c/sup\\u003e, PCC, MSE, MAE and MAPE) are employed to checked the models’ performances. Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e equally indicates the robust capability of ANN-PSO over the other two metaheuristic algorithms; ENN-GA and SVR-BO as well as the classical technique inform of LR. The quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively. The MAPE values ranges between 0.00–41.00% in the training and 0.00–32.20% in the validation phases respectively. ANN-PSO illustrates the lowest MAPE values in both the training and validation stages, while SVR-BO showed highest MAPE values in the training phase and ENN-GA depicts the highest MAPE values in the validation stage. Correspondingly, the MAE results range between 0.000 to 0.450 and 0.000 to 0.376 in the calibration and validation phases respectively. Similarly, the MSE values range between 0.000 to 32.453 and 0.000 to 7.361 in the calibration and validation phases respectively.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" 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=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\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\\u003eResults of the hybrid metaheuristic algorithms\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e\\u003ccolgroup cols=\\\"6\\\"\\u003e\\u003c/colgroup\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eCalibration\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eR2\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003ePCC\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eMSE\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eMAE\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eMAPE\\u003c/p\\u003e \\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eANN-PSO\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eENN-GA\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.196\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.442\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e32.453\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.027\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.027\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSVR-BO\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.435\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.659\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e22.811\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.450\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.450\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eLR\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.439\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.662\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e22.647\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.080\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.080\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eValidation\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eANN-PSO\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eENN-GA\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.268\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.518\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e7.361\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.376\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.376\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSVR-BO\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.337\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.581\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e6.665\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.042\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.042\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eLR\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.345\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.587\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e6.589\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.080\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.080\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/table\\u003e\\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eTherefore, the performance of the models can also be demonstrated graphically using various visualizations. In order to understand and analyze the data used in the training and evaluation of AI models, visualizations are essential. They make it easier to see trends, outliers, and linkages in the data. Additionally, when an AI model is not performing as expected, visualizations can be used to pinpoint where and why errors are occurring. Also, Visualizations can offer immediate feedback on the effectiveness of an AI model while it is being trained. This may contain learning curves that demonstrate how a model’s performance increases over time and feature maps that display the model’s learning at various layer depths. Consequently, visualizations can help in explaining AI model predictions to stakeholders who may not have a deep understanding of machine learning, which can serve as a step crucial for building trust and transparency in AI systems. For instance, the bump plot presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, which was also known as a rank chart or a slope graph, is a type of data visualization that is often used to display the ranking of items or categories over time or across different conditions. It’s particularly useful for visualizing changes in rank order and comparing the relative positions of items or categories. More also, Figure b demonstrates the comparative performance of the hybrid metaheuristic algorithms (ANN-PSO, ENN-GA and SVR-BO) as well as the classical LR technique using five different performance metrics; MSE, MAPE, MAE, PCC and R\\u003csup\\u003e2\\u003c/sup\\u003e. The bump plot demonstrates that ANN-PSO showed the lowest ranking for the error metrics; MSE, MAE and MAPE and highest ranking for PCC and R2. This indicates that ANN-PSO has outperformed other approaches (ENN-GA and SVR-BO) used in the current study in both the calibration and validation stages respectively. Also, the performance presented by the bump plot is in line with the quantitative performance results depicted in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eFurthermore, the modelling performance can equally be visualized using the Fan plot (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e). The distribution of data over many categories, features or metrics is shown using a fan plot, sometimes it is referred to as a wind rose chart or polar bar chart. Moreover, data with both directional and frequency components are frequently represented using it. Therefore, the Fan plot was utilized in the current study to depict the comaparative performance of an individual metric used in the current study such as the MSE, MAE, PCC and R\\u003csup\\u003e2\\u003c/sup\\u003e. For example, the plot indicates that ANN-PSO depicts lower error performance based on MSE and MAE values and higher performance fitness for PCC and R\\u003csup\\u003e2\\u003c/sup\\u003e. Furthermore, the plot indicates that for MAE values the models; ANN-PSO, ENN-GA, SVR-BO and LR depicts the following results 0.000, 0.027, 0.450, 0.080 in training and 0.000, 0.376, 0.042, 0.080 in validation phases respectively. Hence, the performance of the techniques can be depicted in the following order Hence, the performance of the techniques can be depicted in the following order ANN-PSO \\u0026gt; ENN-GA \\u0026gt; LR \\u0026gt; SVR-BO in the training and ANN-PSO \\u0026gt; SVR-BO \\u0026gt; LR \\u0026gt; ENN-GA in the validation stage respectively.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eFurthermore, the classical visulizations techniques inform of scatter plot and response plot were equally used to compare the performance of the metaheuristics techniques used in the current study for modelling the air quality based on PM 2.5 as the target variable (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e). A scatter plot is a type of graph that uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables. For the current study the scatter plot illustrates the simulated PM 2.5 using various techniques in the y-axis and the observe PM 2.5 in the x-axis and hence presents the relationship between the two using dots. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e demosntrates close relation between ANN-PSO PM 2.5 simulated values and the observe PM 2.5 values over ENN-GA, SVR-BO and LR simulated PM 2.5 values.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eFurthermore, the response plot is a data visualization that displays data points in sequential order, typically at equally spaced time intervals. Response plots are used to visualize how data changes over time, making them valuable for identifying trends, patterns, and anomalies in temporal data. Therefore, the current study utilizes the response plot to show the trend between the actual and simulated values and the best method will show similar or closely related trend with the actual PM 2.5 values. Figure e illustrates that ANN-PSO showed closely related trend with the observe PM 2.5 than ENN-GA, SVR-BO and LR (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec18\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.2 Modelling results of the Ensemble techniques\\u003c/h2\\u003e \\u003cp\\u003eThe utilization of single approach has gain remarkable attention over the years, even though, in various instances, it was found to provide lower accuracies owing to different reasons. Therefore, ensemble techniques were proposed to boost the performance of the models at certain instances as well to compare their performance with the metaheuristic algorithms for PM 2.5 modelling. Table c presents the performance of the ensemble paradigms for modelling PM 2.5 using both linear ensemble paradigm informs of SA and non-linear ensemble technique using NNE. Even though, the SA technique doesn’t provide robust performance as expected in the calibration and validation phases but was able to provide higher performance than SVR-BO and ENN-GA, though, considered as a linear approach. Moreover, SA as a linear ensemble paradigm was able to boost the prediction performance of the LR classical technique up to 19.2% in the calibration and 23.8% in the validation phases respectively based on their PCC performance metrics values. Therefore, this illustrates the importance of the ensemble paradigms over the classical techniques. Furthermore, the non-linear NNE technique demonstrates outstanding performance, which has the ability of improving the performance of both the classical LR linear technique, SA and SVR-BO and ENN-GA metaheuristic approaches. Furthermore, NNE depicts relatively lower performance than ANN-PSO especially considering their MSE, MAE and MAPE performance metrics differences. Nevertheless, NNE depicts an outstanding performance for PM 2.5 modelling than SA linear technique (see Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" 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=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\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\\u003eResults of the Ensemble techniques\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e\\u003ccolgroup cols=\\\"6\\\"\\u003e\\u003c/colgroup\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eCalibration\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eR\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003ePCC\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eMSE\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eMAE\\u003c/p\\u003e \\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eMAPE\\u003c/p\\u003e \\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eNNE\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.999\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1.000\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.032\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.005\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.004\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSA\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.730\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.854\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e2.714\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.084\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.055\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eValidation\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eNNE\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.999\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.999\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.010\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.004\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.003\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u003cb\\u003eSA\\u003c/b\\u003e\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.681\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.825\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e12.852\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.126\\u003c/p\\u003e \\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.108\\u003c/p\\u003e \\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/table\\u003e\\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003cp\\u003eMoreover, the performance of the two ensemble paradigms can be graphically compared using the bar chart based on their respective MSE and MAE error performance metrics (see \\u003cb\\u003eFig.\\u0026nbsp;7\\u003c/b\\u003e). Based on Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig7\\\" class=\\\"InternalRef\\\"\\u003e8\\u003c/span\\u003e SA presents higher MSE and MAE values than NNE in both the calibration and validation phases. Also, we are aware the lower the error performance the better the performance of the technique and vice-versa. Also, the performance of the techniques can be visualized using the time series plot. As mentioned earlier this plot shows data points gathered at progressively longer intervals of time. The time is represented by the x-axis in a time series diagram, while the variable being measured is represented by the y-axis. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e demonstrates both the actual and simulated values generated over a period of time. For the simulation values to be accepted, it should follow the same trend as the actual values. Hence, NNE showed more affinity to following same trend with the actual PM 2.5 than SA ensemble paradigm.\\u003c/p\\u003e \\u003cp\\u003eMoreover, the scatter plot just like the time series plot presents the fitness between the simulated and actual values (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e). Whereby, the model that illustrates higher agreement between the values is considered the best and vice-versa. For Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e, NNE simulated values showed higher affinity to the actual PM 2.5 values than SA. Therefore, NNE technique is considered as more robust technique than SA in modelling PM 2.5. Additionally, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms can be presented in the following order for modelling PM 2.5 using various air quality attributes; ANN-PSO \\u0026gt; NNE \\u0026gt; SA \\u0026gt; ENN-GA \\u0026gt; LR \\u0026gt; SVR-BO in the training and ANN-PSO \\u0026gt; NNE \\u0026gt; SA \\u0026gt; SVR-BO \\u0026gt; LR \\u0026gt; ENN-GA in the validation stage respectively. Furthermore, the performance obtained by the current study for modelling PM 2.5 as a potential approach for sustainable eco-friendly air quality management step can be compared with recent studies published in the technical literature. For example, Yu et al., (Yu et al., \\u003cspan citationid=\\\"CR85\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) reported the prediction of PM 2.5 concentration using deep ensemble machine learning framework (DEML) using three different stages. The performance results obtained from the three stages composed of R\\u003csup\\u003e2\\u003c/sup\\u003e = 0. 87 and RMSE = 5.38. Therefore, the to compare our results and theirs, in our results the best performing techniques consists of ANN-PSO and NNE with R\\u003csup\\u003e2\\u003c/sup\\u003e = 1. 00, MSE = 0.00 and R\\u003csup\\u003e2\\u003c/sup\\u003e = 0. 99, MSE = 0.01 in the testing phase respectively. Hence, this indicates the robust ability of our results over theirs. Also, Sihag et al., (Sihag, \\u003cspan citationid=\\\"CR66\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e) presented the use of various soft computing techniques for modelling PM 2.5. Whereby, random forest (RF) emerges as the best performing model with PCC-values = 0.8312, MAE = 30.7757 and R\\u003csup\\u003e2\\u003c/sup\\u003e = 0.6909. Therefore, the performance depicted by the best technique is lower than the performance presented in the current study by both NNE and ANN-PSO in the prediction of PM 2.5. Additionally, Gokul et al., (Gokul et al., \\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) recently employed various AI-based techniques for modelling PM 2.5 in Hyderabad city. XGBoost regression and LSTM deep learning emerged as the best performing models having R\\u003csup\\u003e2\\u003c/sup\\u003e = 0.82, MAE = 7.01 and R\\u003csup\\u003e2\\u003c/sup\\u003e = 0.89, MAE = 5.78 respectively. A fair comparison with the best models in our study indicates that NNE with R\\u003csup\\u003e2\\u003c/sup\\u003e = 1. 00, MAE = 0.00 and R\\u003csup\\u003e2\\u003c/sup\\u003e = 0. 99, MAE = 0.004 in the testing phase has outperformed their models. Therefore, it is worthy of note to mention that based on various studies reported in the recent published technical article for prediction and modelling PM 2.5 using various models including soft computing techniques, deep learning, metaheuristic algorithms, ensemble ML, hybrid models etc, the performance depicted by NNE and ANN-PSO is outstanding, reliable and robust over other techniques. Hence, can be used as a reliable potential approach for sustainable eco-friendly air quality management for modelling PM 2.5 concentration.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003c/div\\u003e \\u003cp\\u003e\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"Conclusion\",\"content\":\"\\u003cp\\u003eSustainable eco-friendly air quality management is a comprehensive approach to improving air quality that minimizes environmental and social impacts. It involves a combination of strategies, including; minimizing emissions from stationary and mobile sources, educating and empowering the public to act to improve air quality, Protecting and enhancing natural air quality filters (this includes planting trees, restoring wetlands, and protecting forests) etc. Sustainable eco-friendly air quality management is essential for protecting human health and the environment. It can also create economic opportunities and improve quality of life. Therefore, this work reported the use of both Metaheuristic algorithms and Ensemble techniques for modelling PM 2.5 as potential approach for improving air quality management. Furthermore, various pre-analysis techniques were conducted for data clean up and for understanding the behaviour of the variables prior to dwelling into modelling step such as through handling missing data by imputing values, Exploratory Data Analysis (EDA) using the distribution plot to understand data distributions, relationships, and patterns using histograms, descriptive statistics and correlation analysis. Hence, the obtained results of the study can be summarized as follows;\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003e \\u003c/p\\u003e\\u003cul\\u003e \\u003cli\\u003e \\u003cp\\u003eThe correlation matrix results indicate that RSPM (0.60) showed the highest correlation with the target PM 2.5 then followed by NO\\u003csub\\u003e2\\u003c/sub\\u003e (0.42) and SO\\u003csub\\u003e2\\u003c/sub\\u003e (0.25),\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eThe quantitative performance results obtained from the Metaheuristic algorithms indicates that ANN-PSO outperformed all the other techniques including; SVR-BO, ENN-GA and LR.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eThe quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively based on their R\\u003csup\\u003e2\\u003c/sup\\u003e-values.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eAlso, recent and novel visualizations such as Fan plot and Bump chart were used to rank the performance results obtained in PM 2.5 prediction.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eMoreover, NNE equally showed superior potentials over SA ensemble technique for modelling PM 2.5.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eMoreover, SA as a linear ensemble paradigm was able to boost the prediction performance of the LR classical technique up to 19.2% in the calibration and 23.8% in the validation phases respectively based on their PCC performance metrics values. Therefore, this illustrates the importance of the ensemble paradigms over the classical techniques.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eTo conclude, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms can be presented in the following order for modelling PM 2.5 using various air quality attributes; ANN-PSO \\u0026gt; NNE \\u0026gt; SA \\u0026gt; ENN-GA \\u0026gt; LR \\u0026gt; SVR-BO in the training and ANN-PSO \\u0026gt; NNE \\u0026gt; SA \\u0026gt; SVR-BO \\u0026gt; LR \\u0026gt; ENN-GA in the validation stage respectively.\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003eFinally, the study recommends that other Metaheuristic algorithms such as HHO, BBO can be used in boosting the performance of the models for PM 2.5 prediction.\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/ul\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e \\u003ch2\\u003eEthical Approval:\\u003c/h2\\u003e \\u003cp\\u003eNot applicable.\\u003c/p\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cstrong\\u003eConsent to Participate:\\u003c/strong\\u003e \\u003cp\\u003eNot applicable.\\u003c/p\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cstrong\\u003eConsent to Publish:\\u003c/strong\\u003e \\u003cp\\u003eNot applicable.\\u003c/p\\u003e \\u003c/p\\u003e\\u003cp\\u003e \\u003ch2\\u003eCompeting Interests:\\u003c/h2\\u003e \\u003cp\\u003eThe authors declare no competing interests.\\u003c/p\\u003e \\u003c/p\\u003e\\u003ch2\\u003eFunding:\\u003c/h2\\u003e \\u003cp\\u003eNot applicable.\\u003c/p\\u003e\\u003ch2\\u003eAuthor Contribution\\u003c/h2\\u003e\\u003cp\\u003eAuthor's Contributions: AGU, SIA, SM, JU and SRN write the initial manuscript draft and AI experimental analysis. MA, AA, and SD analyzed and interpreted the data, and contributed to editing the manuscript. MMJ, AGU, SMR, and AB analyzed and interpreted the data and were a major contributor to the software. All authors read and approved the final manuscript.\\u003c/p\\u003e\\u003ch2\\u003eData Availability\\u003c/h2\\u003e\\u003cp\\u003eData Availability Statement: The supported data associated with this researcher are available upon request from the corresponding author.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eAarnink, J. A., Zhao, Y., Calvet, S., \\u0026amp; Torres, A. G. 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(2022). \\u003cem\\u003eDeep Ensemble Machine Learning Framework for the Estimation of PM 2: 5\\u003c/em\\u003e. \\u003cem\\u003e130\\u003c/em\\u003e(March), 1\\u0026ndash;11.\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eZhang, L., Liu, P., Zhao, L., Wang, G., Zhang, W., \\u0026amp; Liu, J. (2021). Air quality predictions with a semi-supervised bidirectional LSTM neural network. Atmospheric Pollution Research, \\u003cem\\u003e12\\u003c/em\\u003e(1), 328\\u0026ndash;339. \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://doi.org/https://doi.org/10.1016/j.apr.2020.09.003\\u003c/span\\u003e\\u003cspan address=\\\"10.1016/j.apr.2020.09.003\\\" 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\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"Air quality, pollution, PM 2.5, Ensemble ML, Meta-heuristic optimization algorithms\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4663193/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4663193/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eParticulate Matter 2.5 (PM 2.5) is a major air pollutant that can deeply penetrate the respiratory system and enter the bloodstream when inhaled. Therefore, it is significant to monitor and model PM 2.5, which is also considered as a key indicator of overall air quality. The current study employs the use of both Nature inspired Meta-heuristic optimization algorithms and Ensemble Machine learning (ML) techniques for the prediction of PM 2.5 using Sulfur dioxide (SO\\u003csub\\u003e2\\u003c/sub\\u003e), Nitrogen Dioxide (NO\\u003csub\\u003e2\\u003c/sub\\u003e), Respiratory suspended particulate matter (RSPM). Prior to dwelling into the modelling step, various pre-analysis techniques were conducted for data clean up and to understand the behaviour of the data. The quantitative performance results obtained from the Metaheuristic algorithms indicates that ANN-PSO outperformed all the other techniques including; SVR-BO, ENN-GA and LR. Furthermore, the quantitative outcomes indicate that ANN-PSO has the ability of improving the performance of the other techniques up to 80.4% and 73.2% in the calibration and validation phases respectively. More also, recent visualizations such as Fan plot and Bump chart were used in ranking the performance results obtained in PM 2.5 prediction. Moreover, Neural network ensemble (NNE) technique equally showed superior potentials over Simple average (SA) ensemble technique. To conclude, the quantitative and visualized performances of both the Metaheuristic algorithms and the ensemble paradigms indicates their importance in modelling and mitigation of PM 2.5 pollution, which requires concerted efforts at the local, and international levels to mitigate its effects and improve air quality on a global scale.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Nature inspired Meta-heuristic optimization integrated with ensemble machine learning for PM2.5 modeling: a potential approach for sustainable eco-friendly health risk management\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-07-29 11:50:58\",\"doi\":\"10.21203/rs.3.rs-4663193/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"ee3dac31-865f-4ef6-9b2c-8eaeaac610a4\",\"owner\":[],\"postedDate\":\"July 29th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2024-08-05T07:59:18+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2024-07-29 11:50:58\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-4663193\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-4663193\",\"identity\":\"rs-4663193\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}