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Keywords = elite learning strategies

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27 pages, 1599 KiB  
Article
Optimization of Combined Urban Rail Transit Operation Modes Based on Intelligent Algorithms Under Spatiotemporal Passenger Imbalance
by Weisong Han, Zhihan Shi, Xiaodong Lv and Guangming Zhang
Sustainability 2025, 17(13), 6178; https://doi.org/10.3390/su17136178 - 5 Jul 2025
Viewed by 400
Abstract
With increasing attention to sustainability and energy efficiency in transportation systems, advanced intelligent algorithms provide promising solutions for optimizing urban rail transit operations. This study addresses the challenge of optimizing train operation plans for urban rail transit systems characterized by spatiotemporal passenger flow [...] Read more.
With increasing attention to sustainability and energy efficiency in transportation systems, advanced intelligent algorithms provide promising solutions for optimizing urban rail transit operations. This study addresses the challenge of optimizing train operation plans for urban rail transit systems characterized by spatiotemporal passenger flow imbalance. By exploring a combined short-turning and unpaired train operation mode, a three-objective optimization model was established, aiming to minimize operational costs, reduce passenger waiting times, and enhance load balancing. To effectively solve this complex problem, an Improved GOOSE (IGOOSE) algorithm incorporating elite opposition-based learning, probabilistic exploration based on elite solutions, and golden-sine mutation strategies were developed, significantly enhancing global search capability and solution robustness. A case study based on real operational data adjusted for confidentiality was conducted, and comparative analyses with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO) demonstrated the superiority of IGOOSE. Furthermore, an ablation study validated the effectiveness of each enhancement strategy within the IGOOSE algorithm. The optimized operation planning model reduced passenger waiting times by approximately 12.72%, improved load balancing by approximately 39.30%, and decreased the overall optimization objective by approximately 10.25%, highlighting its effectiveness. These findings provide valuable insights for urban rail transit operation management and indicate directions for future research, underscoring the significant potential for energy savings and emission reductions toward sustainable urban development. Full article
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15 pages, 1673 KiB  
Article
Smart Grid Self-Healing Enhancement E-SOP-Based Recovery Strategy for Flexible Interconnected Distribution Networks
by Wanjun Li, Zhenzhen Xu, Meifeng Chen and Qingfeng Wu
Energies 2025, 18(13), 3358; https://doi.org/10.3390/en18133358 - 26 Jun 2025
Viewed by 292
Abstract
With the development of modern power systems, AC distribution networks face increasing demands for supply flexibility and reliability. Energy storage-based soft open points (E-SOPs), which integrate energy storage systems into the DC side of traditional SOP connecting AC distribution networks, not only maintain [...] Read more.
With the development of modern power systems, AC distribution networks face increasing demands for supply flexibility and reliability. Energy storage-based soft open points (E-SOPs), which integrate energy storage systems into the DC side of traditional SOP connecting AC distribution networks, not only maintain power flow control capabilities but also enhance system supply performance, providing a novel approach to AC distribution network fault recovery. To fully leverage the advantages of E-SOPs in handling faults in flexible interconnected AC distribution networks (FIDNs), this paper proposes an E-SOP-based FIDN islanding recovery method. First, the basic structure and control modes of SOPs for AC distribution networks are elaborated, and the E-SOP-based AC distribution network structure is analyzed. Second, with maximizing total load recovery as the objective function, the constraints of E-SOPs are comprehensively considered, and recovery priorities are established based on load importance classification. Then, a multi-dimensional improvement of the dung beetle optimizer (DBO) algorithm is implemented through Logistic chaotic mapping, adaptive parameter adjustment, elite learning mechanisms, and local search strategies, resulting in an efficient solution for AC distribution network power supply restoration. Finally, the proposed FIDN islanding partitioning and fault recovery methods are validated on a double-ended AC distribution network structure. Simulation results demonstrate that the improved DBO (IDBO) algorithm exhibits a superior optimization performance and the proposed method effectively enhances the load recovery capability of AC distribution networks, significantly improving the self-healing ability and operational reliability of AC distribution systems. Full article
(This article belongs to the Special Issue Digital Modeling, Operation and Control of Sustainable Energy Systems)
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26 pages, 1854 KiB  
Article
Quantitative State Evaluation Method for Relay Protection Equipment Based on Improved Conformer Optimized by Two-Stage APO
by Yanhong Li, Min Zhang, Shaofan Zhang and Yifan Zhou
Symmetry 2025, 17(6), 951; https://doi.org/10.3390/sym17060951 - 15 Jun 2025
Viewed by 354
Abstract
State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules [...] Read more.
State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules and membership functions and exhibits limitations in high-dimensional data integration and analysis. The latter predominantly formulates state evaluation as a classification task, which demonstrates its ineffectiveness in identifying equipment at boundary states and faces challenges in model parameter selection. To address these limitations, this paper proposes a quantitative state evaluation method for relay protection equipment based on a two-stage artificial protozoa optimizer (two-stage APO) optimized improved Conformer (two-stage APO-IConf) model. First, we modify the Conformer architecture by replacing pre-layer normalization (Pre-LN) in residual networks with post-batch normalization (post-BN) and introducing dynamic weighting coefficients to adaptively regulate the connection strengths between the first and second feed-forward network layers, thereby enhancing the capability of the model to fit relay protection state evaluation data. Subsequently, an improved APO algorithm with two-stage optimization is developed, integrating good point set initialization and elitism preservation strategies to achieve dynamic equilibrium between global exploration and local exploitation in the Conformer hyperparameter space. Experimental validation using operational data from a substation demonstrates that the proposed model achieves a RMSE of 0.5064 and a MAE of 0.2893, representing error reductions of 33.6% and 35.0% compared to the baseline Conformer, and 9.1% and 15.2% error reductions over the improved Conformer, respectively. This methodology can provide a quantitative state evaluation and guidance for developing maintenance strategies for substations. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems)
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16 pages, 8564 KiB  
Article
Robotic Tack Welding Path and Trajectory Optimization Using an LF-IWOA
by Bingqi Jia, Haihong Pan, Lei Zhang, Yifan Yang, Huaxin Chen and Lin Chen
Actuators 2025, 14(6), 287; https://doi.org/10.3390/act14060287 - 10 Jun 2025
Viewed by 698
Abstract
Robotic tack welding poses challenges in path optimization due to local optimum entrapment, limited adaptability, and high-dimensional complexity. To overcome these challenges, a Lévy flight-enhanced improved whale optimization algorithm (LF-IWOA) was developed. The algorithm combines elite opposition-based learning (EOBL), differential evolution (DE), and [...] Read more.
Robotic tack welding poses challenges in path optimization due to local optimum entrapment, limited adaptability, and high-dimensional complexity. To overcome these challenges, a Lévy flight-enhanced improved whale optimization algorithm (LF-IWOA) was developed. The algorithm combines elite opposition-based learning (EOBL), differential evolution (DE), and Lévy flight (LF) to improve global exploration capability, increase population diversity, and improve convergence. Additionally, a dynamic trajectory optimization model is designed to consider joint-level constraints, including velocity, acceleration, and jerk. The performance of LF-IWOA was evaluated using two industrial workpieces with varying welding point distributions. Comparative experiments with metaheuristic algorithms, such as the genetic algorithm (GA), WOA and other recent nature-inspired methods, show that LF-IWOA consistently achieves shorter paths and faster convergence. For Workpiece 1, the algorithm reduces the welding path by up to 25.53% compared to the genetic algorithm, with an average reduction of 14.82% across benchmarks. For Workpiece 2, the optimized path is 18.41% shorter than the baseline. Moreover, the dynamic trajectory optimization strategy decreases execution time by 26.83% and reduces mechanical energy consumption by 15.40% while maintaining smooth and stable joint motion. Experimental results demonstrated the effectiveness and practical applicability of the LF-IWOA in robotic welding tasks. Full article
(This article belongs to the Section Actuators for Robotics)
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21 pages, 2359 KiB  
Article
Learning-Enhanced Differential Evolution for Multi-Mode Resource-Constrained Multi-Project Scheduling Problem in Industrial Prefabrication
by Zijie Xing, Chen Chen and Robert Lee Kong Tiong
Buildings 2025, 15(12), 1996; https://doi.org/10.3390/buildings15121996 - 10 Jun 2025
Viewed by 361
Abstract
Efficient scheduling in industrial prefabrication environments—such as Prefabricated Bathroom Unit (PBU) production—faces increasing challenges due to resource limitations, overlapping projects, and complex task dependencies. To address these challenges, this paper presents a Learning-Enhanced Differential Evolution (LEDE) framework for solving the Multi-Mode Resource-Constrained Multi-Project [...] Read more.
Efficient scheduling in industrial prefabrication environments—such as Prefabricated Bathroom Unit (PBU) production—faces increasing challenges due to resource limitations, overlapping projects, and complex task dependencies. To address these challenges, this paper presents a Learning-Enhanced Differential Evolution (LEDE) framework for solving the Multi-Mode Resource-Constrained Multi-Project Scheduling Problem (MRCMPSP). The MRCMPSP models the operational difficulty of coordinating interdependent activities across multiple PBU projects under limited resource availability. To address the computational intractability of this NP-hard problem, we first formulate a mixed-integer linear programming (MILP) model, and then develop an adaptive DE-based metaheuristic. The proposed LEDE method co-evolves activity sequencing and mode assignment using floating-point encodings, incorporating strategy switching, parameter adaptation, elitism, stagnation handling, and rank-based crossover control. Evaluated on real-world production data from the PBU industry, the algorithm produces high-quality solutions with strong scalability. These results demonstrate its practical potential as a decision-support tool for dynamic, resource-constrained industrial scheduling. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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26 pages, 11136 KiB  
Article
Composition Optimization of Coating Machine Oven Manufacturing Services Based on Improved Sparrow Search Algorithm
by Zhenjie Gao, Shanhui Liu, Langze Zhu, Chaoyang Li, Yangzhen Cao and Gan Shi
Coatings 2025, 15(6), 636; https://doi.org/10.3390/coatings15060636 - 25 May 2025
Viewed by 363
Abstract
Aiming at the problem of the low collaborative efficiency of outsourced processing of coating machine oven parts under the network collaborative manufacturing mode, this paper proposes a composition optimization method for coating machine oven-manufacturing services based on an improved sparrow search algorithm. We [...] Read more.
Aiming at the problem of the low collaborative efficiency of outsourced processing of coating machine oven parts under the network collaborative manufacturing mode, this paper proposes a composition optimization method for coating machine oven-manufacturing services based on an improved sparrow search algorithm. We establish a framework for the service composition optimization problem on the oven manufacturing service platform; complete an evaluation of the manufacturing service quality of service indicators (QoS) and energy consumption indicators; construct a dual-objective service composition optimization mathematical model considering the QoS and energy consumption indicators; and embed the Tent chaotic mapping, elite reverse learning, and Lévy flight improvement differential evolution strategies into the sparrow search algorithm. We named this algorithm the LCSSA_DE algorithm, using it to solve the mathematical model of the manufacturing service combination problem of coating machine ovens, and obtain the optimal manufacturing service combination recommendation scheme. The experimental results demonstrate that this algorithm can effectively improve the convergence speed compared with the suboptimal multi-objective artificial vulture optimization algorithm (MOAVOA), with the average convergence time improved by 7.26%, avoiding falling into the local optimum during the search, while 69%–77% of the test points are more in line with the preference criteria of the Pareto frontier, and can be adapted to the optimization of the coating machine oven manufacturing service composition optimization problem at different scales. Full article
(This article belongs to the Section Surface Characterization, Deposition and Modification)
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31 pages, 5457 KiB  
Article
Multi-Strategy-Improvement-Based Slime Mould Algorithm
by Donghai Huang, Tianbing Tang and Yi Yan
Appl. Sci. 2025, 15(10), 5456; https://doi.org/10.3390/app15105456 - 13 May 2025
Viewed by 485
Abstract
In addressing the challenges posed by the sluggish convergence rate, suboptimal stability, and susceptibility to local optimization in function optimization problems, a multi-strategy-based enhanced slime mold optimization algorithm (MSSMA) has been proposed. This algorithm integrates chaotic mapping and inverse learning to enhance the [...] Read more.
In addressing the challenges posed by the sluggish convergence rate, suboptimal stability, and susceptibility to local optimization in function optimization problems, a multi-strategy-based enhanced slime mold optimization algorithm (MSSMA) has been proposed. This algorithm integrates chaotic mapping and inverse learning to enhance the convergence speed of the initial population. Additionally, a novel balancing factor, B, has been introduced to ensure a more equitable distribution of the algorithm’s exploration and exploitation. The enhanced Lévy flight strategy and the elite tangent search strategy have been integrated to further enhance the algorithm’s global search capability and optimization finding ability. The simulation experiments have demonstrated that the enhanced algorithm exhibits faster convergence speed, enhanced stability, and a superior ability to escape local optima when compared to the other five algorithms in 50 benchmark test functions and multi-UAV cooperative path planning scenarios. Full article
(This article belongs to the Special Issue Heuristic and Evolutionary Algorithms for Engineering Optimization)
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36 pages, 7184 KiB  
Article
Elite Evolutionary Discrete Particle Swarm Optimization for Recommendation Systems
by Shanxian Lin, Yifei Yang, Yuichi Nagata and Haichuan Yang
Mathematics 2025, 13(9), 1398; https://doi.org/10.3390/math13091398 - 24 Apr 2025
Viewed by 566
Abstract
Recommendation systems (RSs) play a vital role in e-commerce and content platforms, yet balancing efficiency and recommendation quality remains challenging. Traditional deep models are computationally expensive, while heuristic methods like particle swarm optimization struggle with discrete optimization. To address these limitations, this paper [...] Read more.
Recommendation systems (RSs) play a vital role in e-commerce and content platforms, yet balancing efficiency and recommendation quality remains challenging. Traditional deep models are computationally expensive, while heuristic methods like particle swarm optimization struggle with discrete optimization. To address these limitations, this paper proposes elite-evolution-based discrete particle swarm optimization (EEDPSO), a novel framework specifically designed to optimize high-dimensional combinatorial recommendation tasks. EEDPSO restructures the velocity and position update mechanisms to operate effectively in discrete spaces, integrating neighborhood search, elite evolution strategies, and roulette-wheel selection to balance exploration and exploitation. Experiments on the MovieLens and Amazon datasets show that EEDPSO outperforms five metaheuristic algorithms (GA, DE, SA, SCA, and PSO) in both recommendation quality and computational efficiency. For datasets below the million-level scale, EEDPSO also demonstrates superior performance compared to deep learning models like FairGo. The results establish EEDPSO as a robust optimization strategy for recommendation systems that effectively handles the cold-start problem. Full article
(This article belongs to the Special Issue Machine Learning and Evolutionary Algorithms: Theory and Applications)
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31 pages, 7050 KiB  
Article
mESC: An Enhanced Escape Algorithm Fusing Multiple Strategies for Engineering Optimization
by Jia Liu, Jianwei Yang and Lele Cui
Biomimetics 2025, 10(4), 232; https://doi.org/10.3390/biomimetics10040232 - 8 Apr 2025
Viewed by 537
Abstract
A multi-strategy enhanced version of the escape algorithm (mESC, for short) is proposed to address the challenges of balancing exploration and development stages and low convergence accuracy in the escape algorithm (ESC). Firstly, an adaptive perturbation factor strategy was employed to maintain population [...] Read more.
A multi-strategy enhanced version of the escape algorithm (mESC, for short) is proposed to address the challenges of balancing exploration and development stages and low convergence accuracy in the escape algorithm (ESC). Firstly, an adaptive perturbation factor strategy was employed to maintain population diversity. Secondly, introducing a restart mechanism to enhance the exploration capability of mESC. Finally, a dynamic centroid reverse learning strategy was designed to balance local development. In addition, in order to accelerate the global convergence speed, a boundary adjustment strategy based on the elite pool is proposed, which selects elite individuals to replace bad individuals. Comparing mESC with the latest metaheuristic algorithm and high-performance winner algorithm in the CEC2022 testing suite, numerical results confirmed that mESC outperforms other competitors. Finally, the superiority of mESC in handling problems was verified through several classic real-world optimization problems. Full article
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14 pages, 2054 KiB  
Article
The Interaction of Fitness and Fatigue on Physical and Tactical Performance in Football
by Mauro Mandorino, Tim J. Gabbett, Antonio Tessitore, Cedric Leduc, Valerio Persichetti and Mathieu Lacome
Appl. Sci. 2025, 15(7), 3574; https://doi.org/10.3390/app15073574 - 25 Mar 2025
Cited by 1 | Viewed by 1719
Abstract
Elite football players face increasing physical and tactical demands due to rising match schedules emphasizing the need for effective load monitoring strategies to optimize performance and reduce injury risk. This study integrates fitness and fatigue indices derived from a machine learning approach to [...] Read more.
Elite football players face increasing physical and tactical demands due to rising match schedules emphasizing the need for effective load monitoring strategies to optimize performance and reduce injury risk. This study integrates fitness and fatigue indices derived from a machine learning approach to develop a performance score based on Banister’s fitness–fatigue model. Data were collected over two seasons (2022/23 and 2023/24) from 23 elite players of an Italian professional team. Fitness was assessed via heart rate collected during small-sided games, while fatigue was evaluated through PlayerLoad recorded during training sessions; both were normalized using z-scores. Match outcomes, including physical (e.g., total distance, high-sprint distance) and tactical metrics (e.g., field tilt, territorial domination), were analyzed in relation to performance conditions (optimal, intermediate, poor). Results revealed that players in the optimal performance condition exhibited significantly higher second-half physical outputs, including total distance (z-TD2ndHalf: p < 0.05, ES = 0.29) and distance covered at >14.4 km/h (z-D14.42ndHalf: p < 0.01, ES = 0.52), alongside improved match tactical parameters as territorial domination (%TDO2ndHalf: p < 0.01, r = 0.431). This study underscores the utility of invisible monitoring in football, providing actionable insights for weekly training periodization. This research establishes a foundation for integrating data-driven strategies to enhance physical and tactical performance in professional football. Full article
(This article belongs to the Special Issue Load Monitoring in Team Sports)
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20 pages, 963 KiB  
Article
A Deep Reinforcement Learning-Based Evolutionary Algorithm for Distributed Heterogeneous Green Hybrid Flowshop Scheduling
by Hua Xu, Lingxiang Huang, Juntai Tao, Chenjie Zhang and Jianlu Zheng
Processes 2025, 13(3), 728; https://doi.org/10.3390/pr13030728 - 3 Mar 2025
Viewed by 921
Abstract
Due to increasing energy consumption, green scheduling in the manufacturing industry has attracted great attention. In distributed manufacturing involving heterogeneous plants, accounting for complex work sequences and energy consumption poses a major challenge. To address distributed heterogeneous green hybrid flowshop scheduling (DHGHFSP) while [...] Read more.
Due to increasing energy consumption, green scheduling in the manufacturing industry has attracted great attention. In distributed manufacturing involving heterogeneous plants, accounting for complex work sequences and energy consumption poses a major challenge. To address distributed heterogeneous green hybrid flowshop scheduling (DHGHFSP) while optimising total weighted delay (TWD) and total energy consumption (TEC), a deep reinforcement learning-based evolutionary algorithm (DRLBEA) is proposed in this article. In the DRLBEA, a problem-based hybrid heuristic initialization with random-sized population is designed to generate a desirable initial solution. A bi-population evolutionary algorithm with global search and local search is used to obtain the elite archive. Moreover, a distributional Deep Q-Network (DQN) is trained to select the best local search strategy. Experimental results on 20 instances show a 9.8% increase in HV mean value and a 35.6% increase in IGD mean value over the state-of-the-art method. The results show the effectiveness and efficiency of the DRLBEA in solving DHGHFSP. Full article
(This article belongs to the Section Process Control and Monitoring)
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23 pages, 672 KiB  
Article
Metaheuristic Optimization for Robust RSSD-Based UAV Localization with Position Uncertainty
by Yuanyuan Zhang, Jiping Li, T. Aaron Gulliver, Huafeng Wu, Guangqian Xie, Xiaojun Mei, Jiangfeng Xian, Weijun Wang and Linian Liang
Drones 2025, 9(2), 147; https://doi.org/10.3390/drones9020147 - 18 Feb 2025
Cited by 1 | Viewed by 832
Abstract
Unmanned aerial vehicles (UAVs) have garnered significant research interest across various fields due to their excellent maneuverability, scalability, and flexibility. However, potential collisions and other issues can disrupt communication and hinder functionality in real-world applications. Therefore, accurate localization of UAVs is crucial. Nonetheless, [...] Read more.
Unmanned aerial vehicles (UAVs) have garnered significant research interest across various fields due to their excellent maneuverability, scalability, and flexibility. However, potential collisions and other issues can disrupt communication and hinder functionality in real-world applications. Therefore, accurate localization of UAVs is crucial. Nonetheless, environmental factors and inherent stability issues can lead to node positional errors in UAV networks, compounded by inaccuracies in transmit power estimation, complicating the effectiveness of signal strength-based localization methods in achieving high accuracy. To mitigate the adverse effects of these issues, a novel received signal strength difference (RSSD)-based localization scheme based on a robust enhanced salp swarm algorithm (RESSA) is presented. In this algorithm, an elitism strategy based on tent opposition-based learning (TOL) is proposed to promote the leader to move around the food source. Differential evolution (DE) is then used to enhance the exploration ability of each agent and improve global search. In addition, a dynamic movement mechanism for followers is designed, enabling the swarm to swiftly converge towards the food source, thereby accelerating the overall convergence process. The RSSD-based Cramér–Rao lower bound (CRLB) with position uncertainty is derived to evaluate the performance. Experimental results are presented, which show that the proposed RESSA provides better localization performance than related methods in the literature. Full article
(This article belongs to the Special Issue Space–Air–Ground Integrated Networks for 6G)
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26 pages, 4719 KiB  
Article
An Efficient Multi-Objective White Shark Algorithm
by Wenyan Guo, Yufan Qiang, Fang Dai, Junfeng Wang and Shenglong Li
Biomimetics 2025, 10(2), 112; https://doi.org/10.3390/biomimetics10020112 - 13 Feb 2025
Cited by 1 | Viewed by 828
Abstract
To balance the diversity and stringency of Pareto solutions in multi-objective optimization, this paper introduces a multi-objective White Shark Optimization algorithm (MONSWSO) tailored for multi-objective optimization. MONSWSO integrates non-dominated sorting and crowding distance into the White Shark Optimization framework to select the optimal [...] Read more.
To balance the diversity and stringency of Pareto solutions in multi-objective optimization, this paper introduces a multi-objective White Shark Optimization algorithm (MONSWSO) tailored for multi-objective optimization. MONSWSO integrates non-dominated sorting and crowding distance into the White Shark Optimization framework to select the optimal solution within the population. The uniformity of the initial population is enhanced through a chaotic reverse initialization learning strategy. The adaptive updating of individual positions is facilitated by an elite-guided forgetting mechanism, which incorporates escape energy and eddy aggregation behavior inspired by marine organisms to improve exploration in key areas. To evaluate the effectiveness of MONSWSO, it is benchmarked against five state-of-the-art multi-objective algorithms using four metrics: inverse generation distance, spatial homogeneity, spatial distribution, and hypervolume on 27 typical problems, including 23 multi-objective functions and 4 multi-objective project examples. Furthermore, the practical application of MONSWSO is demonstrated through an example of optimizing the design of subway tunnel foundation pits. The comprehensive results reveal that MONSWSO outperforms the comparison algorithms, achieving impressive and satisfactory outcomes. Full article
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30 pages, 3329 KiB  
Article
Multi-Objective Remanufacturing Processing Scheme Design and Optimization Considering Carbon Emissions
by Yangkun Liu, Guangdong Tian, Xuesong Zhang and Zhigang Jiang
Symmetry 2025, 17(2), 266; https://doi.org/10.3390/sym17020266 - 10 Feb 2025
Cited by 1 | Viewed by 811
Abstract
In the face of escalating environmental degradation and dwindling resources, the imperatives of prioritizing environmental protection, and conserving resources have come sharply into focus. Therefore, remanufacturing processing, as the core of remanufacturing, becomes a key step in solving the above problems. However, with [...] Read more.
In the face of escalating environmental degradation and dwindling resources, the imperatives of prioritizing environmental protection, and conserving resources have come sharply into focus. Therefore, remanufacturing processing, as the core of remanufacturing, becomes a key step in solving the above problems. However, with the increasing number of failing products and the advent of Industry 5.0, there is a heightened request for remanufacturing in the context of environmental protection. In response to these shortcomings, this study introduces a novel remanufacturing process planning model to address these gaps. Firstly, the failure characteristics of the used parts are extracted by the fault tree method, and the failure characteristics matrix is established by the numerical coding method. This matrix includes both symmetry and asymmetry, thereby reflecting each attribute of each failure feature, and the remanufacturing process is expeditiously generated. Secondly, a multi-objective optimization model is devised, encompassing the factors of time, cost, energy consumption, and carbon emission. This model integrates considerations of failure patterns inherent in used parts and components, alongside the energy consumption and carbon emissions entailed in the remanufacturing process. To address this complex optimization model, an improved teaching–learning-based optimization (TLBO) algorithm is introduced. This algorithm amalgamates Pareto and elite retention strategies, complemented by local search techniques, bolstering its efficacy in addressing the complexities of the proposed model. Finally, the validity of the model is demonstrated by means of a single worm gear. The proposed algorithm is compared with NSGA-III, MPSO, and MOGWO to demonstrate the superiority of the algorithm in solving the proposed model. Full article
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37 pages, 9637 KiB  
Article
An Optimized Method for Solving the Green Permutation Flow Shop Scheduling Problem Using a Combination of Deep Reinforcement Learning and Improved Genetic Algorithm
by Yongxin Lu, Yiping Yuan, Jiarula Yasenjiang, Adilanmu Sitahong, Yongsheng Chao and Yunxuan Wang
Mathematics 2025, 13(4), 545; https://doi.org/10.3390/math13040545 - 7 Feb 2025
Viewed by 1309
Abstract
This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the [...] Read more.
This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the PFSP is modeled using an end-to-end deep reinforcement learning (DRL) approach, named PFSP_NET, which is designed based on the characteristics of the PFSP, with the actor–critic algorithm employed to train the model. Once trained, this model can quickly and directly produce relatively high-quality solutions. Secondly, to further enhance the quality of the solutions, the outputs from PFSP_NET are used as the initial population for the improved genetic algorithm (IGA). Building upon the traditional genetic algorithm, the IGA utilizes three crossover operators, four mutation operators, and incorporates hamming distance, effectively preventing the algorithm from prematurely converging to local optimal solutions. Then, to optimize energy consumption, an energy-saving strategy is proposed that reasonably adjusts the job scheduling order by shifting jobs backward without increasing the maximum completion time. Finally, extensive experimental validation is conducted on the 120 test instances of the Taillard standard dataset. By comparing the proposed method with algorithms such as the standard genetic algorithm (SGA), elite genetic algorithm (EGA), hybrid genetic algorithm (HGA), discrete self-organizing migrating algorithm (DSOMA), discrete water wave optimization algorithm (DWWO), and hybrid monkey search algorithm (HMSA), the results demonstrate the effectiveness of the proposed method. Optimal solutions are achieved in 28 test instances, and the latest solutions are updated in instances Ta005 and Ta068 with values of 1235 and 5101, respectively. Additionally, experiments on 30 instances, including Taillard 20-10, Taillard 50-10, and Taillard 100-10, indicate that the proposed energy strategy can effectively reduce energy consumption. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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