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Keywords = novel multi-objective gray wolf optimizer

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67 pages, 3288 KB  
Article
An Optimization-Driven Fuzzy Transformer–Deep Belief Network for PM2.5 Air Pollution Prediction: A Spatio-Temporal Framework Based on Aerosol Optical Depth
by Mohammad Mehdi Sharifi Nevisi, Pardis Sadatian Moghaddam, Mehrdad Kaveh, Diego Martín, Nuria Serrano and José Vicente Álvarez-Bravo
Mathematics 2026, 14(13), 2402; https://doi.org/10.3390/math14132402 (registering DOI) - 5 Jul 2026
Abstract
Forecasting fine particulate matter with a diameter of 2.5 μm (PM2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM2.5 assessment, [...] Read more.
Forecasting fine particulate matter with a diameter of 2.5 μm (PM2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM2.5 assessment, especially in complex urban regions. Consequently, aerosol optical depth (AOD) derived from satellite imagery, combined with advanced deep learning (DL) techniques, has emerged as an effective alternative by offering wide spatial coverage and rich spatio-temporal information. This paper proposed an optimization-driven fuzzy transformer–deep belief network (ODFT-DBN) for accurate PM2.5 air pollution prediction. The proposed framework integrates a fuzzy inference module to model uncertainty and nonlinear environmental relationships, a transformer encoder to capture long-range spatio-temporal dependencies, and a DBN to extract hierarchical features and improve prediction robustness. In addition, a novel multi-objective gray wolf optimizer (NMOGWO) is employed to jointly optimize the model hyper-parameters and fuzzy membership functions. The proposed approach is implemented for the city of Tehran, Iran, using meteorological variables, topographical features, ground-based PM2.5 measurements, and satellite-derived AOD data. The ODFT-DBN model is compared with several benchmark methods, including bidirectional encoder representations from transformers (BERT), transformer, long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), DBN, and extreme gradient boosting (XGBoost). Experimental results demonstrate that the proposed framework achieves superior predictive performance, attaining an R2 value of 0.94 and root mean square error (RMSE) of 0.8 μg/m3. Scatter plot analyses indicate a strong agreement between predicted and observed PM2.5 values, while the proposed model exhibits low variance, stable convergence behavior, and acceptable computational time. Overall, the results confirm the effectiveness, robustness, and practical applicability of the proposed ODFT-DBN framework for spatio-temporal PM2.5 forecasting. Full article
(This article belongs to the Special Issue Applications of Optimization Algorithms and Evolutionary Computation)
37 pages, 5024 KB  
Article
Optimal Ship Pipe Route Design: A MOA*-Based Software Approach
by Zongran Dong, Kai Li, Heng Chen and Chenghao Sun
J. Mar. Sci. Eng. 2025, 13(11), 2149; https://doi.org/10.3390/jmse13112149 - 13 Nov 2025
Cited by 1 | Viewed by 1235
Abstract
For the ship pipe routing design (SPRD) problem, previous studies have mainly employed bio-inspired algorithms such as multi-objective ant colony optimization (MOACO), non-dominated sorting genetic algorithm II (NSGA-II), and multi-objective particle swarm optimization (MOPSO). This paper proposes a novel approach based on the [...] Read more.
For the ship pipe routing design (SPRD) problem, previous studies have mainly employed bio-inspired algorithms such as multi-objective ant colony optimization (MOACO), non-dominated sorting genetic algorithm II (NSGA-II), and multi-objective particle swarm optimization (MOPSO). This paper proposes a novel approach based on the multi-objective A* (MOA*) algorithm to solve the SPRD. First, the optimization objectives and constraints of the SPRD problem are defined, and then an MOA*-based routing framework is developed. The time and space complexities of the approach are analyzed, and key components such as the cost functions, the solution dominance relationship, dynamic probability-based pruning, and neighbor node exploration strategy are designed to enhance solution diversity and search efficiency. Additionally, a space cascade expansion method is proposed to improve the computational efficiency of the MOA* in large-scale grid spaces. Comparative studies with MOACO, NSGA-II, GA-A*, and gray wolf optimization (GWO) on simulated cases of varying complexities and practical piping scenarios demonstrate the effectiveness of the MOA*. Furthermore, the applicability of the MOA* is validated against practical piping requirements, including the rapid generation of sub-optimal solutions, non-orthogonal routing, and partitioned pipe layouts. Experimental results, supported by a C++/OpenGL-based prototype software, show that the MOA* requires no extensive parameter tuning, exhibits stable computational efficiency and optimization capability, and demonstrates competitive performance in Pareto-optimal diversity compared with other algorithms. Full article
(This article belongs to the Section Ocean Engineering)
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28 pages, 1897 KB  
Article
Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach
by Tamer F. Abdelmaguid 
Algorithms 2024, 17(8), 371; https://doi.org/10.3390/a17080371 - 21 Aug 2024
Cited by 2 | Viewed by 1770
Abstract
This paper presents a novel, multi-objective scatter search algorithm (MOSS) for a bi-objective, dynamic, multiprocessor open-shop scheduling problem (Bi-DMOSP). The considered objectives are the minimization of the maximum completion time (makespan) and the minimization of the mean weighted flow time. Both are particularly [...] Read more.
This paper presents a novel, multi-objective scatter search algorithm (MOSS) for a bi-objective, dynamic, multiprocessor open-shop scheduling problem (Bi-DMOSP). The considered objectives are the minimization of the maximum completion time (makespan) and the minimization of the mean weighted flow time. Both are particularly important for improving machines’ utilization and customer satisfaction level in maintenance and healthcare diagnostic systems, in which the studied Bi-DMOSP is mostly encountered. Since the studied problem is NP-hard for both objectives, fast algorithms are needed to fulfill the requirements of real-life circumstances. Previous attempts have included the development of an exact algorithm and two metaheuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective gray wolf optimizer (MOGWO). The exact algorithm is limited to small-sized instances; meanwhile, NSGA-II was found to produce better results compared to MOGWO in both small- and large-sized test instances. The proposed MOSS in this paper attempts to provide more efficient non-dominated solutions for the studied Bi-DMOSP. This is achievable via its hybridization with a novel, bi-objective tabu search approach that utilizes a set of efficient neighborhood search functions. Parameter tuning experiments are conducted first using a subset of small-sized benchmark instances for which the optimal Pareto front solutions are known. Then, detailed computational experiments on small- and large-sized instances are conducted. Comparisons with the previously developed NSGA-II metaheuristic demonstrate the superiority of the proposed MOSS approach for small-sized instances. For large-sized instances, it proves its capability of producing competitive results for instances with low and medium density. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Real-World Applications)
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22 pages, 5982 KB  
Article
Predicting PM10 Concentrations Using Evolutionary Deep Neural Network and Satellite-Derived Aerosol Optical Depth
by Yasser Ebrahimian Ghajari, Mehrdad Kaveh and Diego Martín
Mathematics 2023, 11(19), 4145; https://doi.org/10.3390/math11194145 - 30 Sep 2023
Cited by 7 | Viewed by 2696
Abstract
Predicting particulate matter with a diameter of 10 μm (PM10) is crucial due to its impact on human health and the environment. Today, aerosol optical depth (AOD) offers high resolution and wide coverage, making it a viable way to estimate PM concentrations. Recent [...] Read more.
Predicting particulate matter with a diameter of 10 μm (PM10) is crucial due to its impact on human health and the environment. Today, aerosol optical depth (AOD) offers high resolution and wide coverage, making it a viable way to estimate PM concentrations. Recent years have also witnessed in-creasing promise in refining air quality predictions via deep neural network (DNN) models, out-performing other techniques. However, learning the weights and biases of the DNN is a task classified as an NP-hard problem. Current approaches such as gradient-based methods exhibit significant limitations, such as the risk of becoming ensnared in local minimal within multi-objective loss functions, substantial computational requirements, and the requirement for continuous objective functions. To tackle these challenges, this paper introduces a novel approach that combines the binary gray wolf optimizer (BGWO) with DNN to improve the optimization of models for air pollution prediction. The BGWO algorithm, inspired by the behavior of gray wolves, is used to optimize both the weight and bias of the DNN. In the proposed BGWO, a novel sigmoid function is proposed as a transfer function to adjust the position of the wolves. This study gathers meteorological data, topographic information, PM10 pollution data, and satellite images. Data preparation includes tasks such as noise removal and handling missing data. The proposed approach is evaluated through cross-validation using metrics such as correlation rate, R square, root-mean-square error (RMSE), and accuracy. The effectiveness of the BGWO-DNN framework is compared to seven other machine learning (ML) models. The experimental evaluation of the BGWO-DNN method using air pollution data shows its superior performance compared with traditional ML techniques. The BGWO-DNN, CapSA-DNN, and BBO-DNN models achieved the lowest RMSE values of 16.28, 19.26, and 20.74, respectively. Conversely, the SVM-Linear and GBM algorithms displayed the highest levels of error, yielding RMSE values of 36.82 and 32.50, respectively. The BGWO-DNN algorithm secured the highest R2 (88.21%) and accuracy (93.17%) values, signifying its superior performance compared with other models. Additionally, the correlation between predicted and actual values shows that the proposed model surpasses the performance of other ML techniques. This paper also observes relatively stable pollution levels during spring and summer, contrasting with significant fluctuations during autumn and winter. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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16 pages, 429 KB  
Article
Multi-Objective Gray Wolf Optimizer with Cost-Sensitive Feature Selection for Predicting Students’ Academic Performance in College English
by Liya Yue, Pei Hu, Shu-Chuan Chu and Jeng-Shyang Pan
Mathematics 2023, 11(15), 3396; https://doi.org/10.3390/math11153396 - 3 Aug 2023
Cited by 18 | Viewed by 2328
Abstract
Feature selection is a widely utilized technique in educational data mining that aims to simplify and reduce the computational burden associated with data analysis. However, previous studies have overlooked the high costs involved in acquiring certain types of educational data. In this study, [...] Read more.
Feature selection is a widely utilized technique in educational data mining that aims to simplify and reduce the computational burden associated with data analysis. However, previous studies have overlooked the high costs involved in acquiring certain types of educational data. In this study, we investigate the application of a multi-objective gray wolf optimizer (GWO) with cost-sensitive feature selection to predict students’ academic performance in college English, while minimizing both prediction error and feature cost. To improve the performance of the multi-objective binary GWO, a novel position update method and a selection mechanism for a, b, and d are proposed. Additionally, the adaptive mutation of Pareto optimal solutions improves convergence and avoids falling into local traps. The repairing technique of duplicate solutions expands population diversity and reduces feature cost. Experiments using UCI datasets demonstrate that the proposed algorithm outperforms existing state-of-the-art algorithms in hypervolume (HV), inverted generational distance (IGD), and Pareto optimal solutions. Finally, when predicting the academic performance of students in college English, the superiority of the proposed algorithm is again confirmed, as well as its acquisition of key features that impact cost-sensitive feature selection. Full article
(This article belongs to the Special Issue Evolutionary Computation 2022)
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23 pages, 3674 KB  
Article
A Multiobjective Evolutionary Approach for Solving the Multi-Area Dynamic Economic Emission Dispatch Problem Considering Reliability Concerns
by Hossein Lotfi
Sustainability 2023, 15(1), 442; https://doi.org/10.3390/su15010442 - 27 Dec 2022
Cited by 14 | Viewed by 2950
Abstract
Economic dispatch (ED) problems, especially in multi-area power networks, have been challenging concerns for power system operators for several decades. In this paper, we introduce a novel approach for solving the multiobjective multi-area dynamic ED (MADED) problem in the presence of practical constraints [...] Read more.
Economic dispatch (ED) problems, especially in multi-area power networks, have been challenging concerns for power system operators for several decades. In this paper, we introduce a novel approach for solving the multiobjective multi-area dynamic ED (MADED) problem in the presence of practical constraints such as valve-point effect (VPE), prohibited operating zone (POZ), multi-fuel operation (MFO), and ramp rate (RR) limitations. Different objective functions including energy not supplied (ENS), generation costs, and emissions are investigated. The reliability objective, which has been less studied in economic dispatch area, distinguishes the proposed study from other studies. A compromise has been made from economic and reliability points of view. The MADED problem in the power system is inherently a complex and nonlinear problem, considering the operational constraint increments and the intricacy of the problem. Hence, the modified grasshopper optimization (MGO) algorithm based on a chaos mechanism is presented to prevent being trapped in local optima. The proposed method is tested on two systems including a 10 unit, 3-zone test system and a 40-unit 3-zone test system, and then, the outcomes are compared with those of other evolutionary techniques such as gray wolf optimization (GWO) and modified honey bee mating optimization (MHBMO). The simulation results demonstrate that the suggested strategy is successful in resolving both single-objective and multiobjective MADED problems. Full article
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