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Keywords = improved multi-population genetic algorithm

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19 pages, 1843 KB  
Article
Time-of-Use Electricity Pricing Strategy for Charging Based on Multi-Objective Optimization
by Yonghua Xu, Wei Liu and Xiangyi Tang
World Electr. Veh. J. 2026, 17(1), 53; https://doi.org/10.3390/wevj17010053 - 22 Jan 2026
Viewed by 34
Abstract
Efficient operation of electric vehicle (EV) charging stations is vital in the development of green transportation infrastructure. To address the challenge of balancing profitability, resource utilization, user behavior, and grid stability, this paper proposes a multi-objective dynamic pricing optimization framework based on a [...] Read more.
Efficient operation of electric vehicle (EV) charging stations is vital in the development of green transportation infrastructure. To address the challenge of balancing profitability, resource utilization, user behavior, and grid stability, this paper proposes a multi-objective dynamic pricing optimization framework based on a chaotic genetic algorithm (CGA). The model jointly maximizes operator profit and charging pile utilization while incorporating price-responsive user demand and grid load constraints. By integrating chaotic mapping into population initialization, the algorithm enhances diversity and global search capability, effectively avoiding premature convergence. Empirical results show that the proposed strategy significantly outperforms conventional methods: profits are 41% higher than with fixed pricing and 40% higher than with traditional time-of-use optimization, while charging pile utilization is 32.27% higher. These results demonstrate that the proposed CGA-based framework can efficiently balance multiple objectives, improve operational profitability, and enhance grid stability, offering a practical solution for next-generation charging station management. Full article
(This article belongs to the Section Charging Infrastructure and Grid Integration)
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17 pages, 1704 KB  
Article
Multi-Objective Optimization of Meat Sheep Feed Formulation Based on an Improved Non-Dominated Sorting Genetic Algorithm
by Haifeng Zhang, Yuwei Gao, Xiang Li and Tao Bai
Appl. Sci. 2026, 16(2), 912; https://doi.org/10.3390/app16020912 - 15 Jan 2026
Viewed by 162
Abstract
Feed formulation is a typical multi-objective optimization problem that aims to minimize cost while satisfying multiple nutritional constraints. However, existing methods often suffer from limitations in handling nonlinear constraints, high-dimensional decision spaces, and solution feasibility. To address these challenges, this study proposes a [...] Read more.
Feed formulation is a typical multi-objective optimization problem that aims to minimize cost while satisfying multiple nutritional constraints. However, existing methods often suffer from limitations in handling nonlinear constraints, high-dimensional decision spaces, and solution feasibility. To address these challenges, this study proposes a multi-objective feed formulation method based on an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II). A hybrid Dirichlet–Latin Hypercube Sampling (Dirichlet-LHS) strategy is introduced to generate an initial population with high feasibility and diversity, together with an iterative normalization-based dynamic repair operator to efficiently handle ingredient proportion and nutritional constraints. In addition, an adaptive termination mechanism based on the hypervolume improvement rate (Hypervolume Termination, HVT) is designed to avoid redundant computation while ensuring effective convergence of the Pareto front. Experimental results demonstrate that the Dirichlet–LHS strategy outperforms random sampling, Dirichlet sampling, and Latin hypercube sampling in terms of hypervolume and solution diversity. Under identical nutritional constraints, the improved NSGA-II reduces formulation cost by 1.52% compared with multi-objective Bayesian optimization and by 2.17% relative to conventional feed formulation methods. In a practical application to meat sheep diet formulation, the optimized feed cost is reduced to 1162.23 CNY per ton, achieving a 4.83% cost reduction with only a 1.09 s increase in computation time. These results indicate that the proposed method effectively addresses strongly constrained multi-objective feed formulation problems and provides reliable technical support for precision feeding in intelligent livestock production. Full article
(This article belongs to the Section Agricultural Science and Technology)
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27 pages, 2227 KB  
Article
Application of a Reinforcement Learning-Based Improved Genetic Algorithm in Flexible Job-Shop Scheduling Problems
by Guoli Zhao, Jiansha Lu, Gangqiang Liu, Weini Weng and Ning Wang
Mathematics 2026, 14(2), 307; https://doi.org/10.3390/math14020307 - 15 Jan 2026
Viewed by 197
Abstract
This paper addresses the limitations of genetic algorithms in solving the Flexible Job-Shop Scheduling Problem (FJSP) including slow convergence, susceptibility to local optima, and sensitivity to parameter settings. The paper proposes an Improved Genetic Algorithm based on Reinforcement Learning (IGARL). First, a hybrid [...] Read more.
This paper addresses the limitations of genetic algorithms in solving the Flexible Job-Shop Scheduling Problem (FJSP) including slow convergence, susceptibility to local optima, and sensitivity to parameter settings. The paper proposes an Improved Genetic Algorithm based on Reinforcement Learning (IGARL). First, a hybrid population selection mechanism that combines the Queen Bee Mating Flight (QBMF) strategy with the Tournament Selection (TS) method is introduced. This mechanism significantly accelerates convergence by optimizing the population structure. Second, a dynamic population update strategy based on tunnel vision, termed the Solution Space Diversity Awakening (SSDA) strategy, is developed. When the population becomes trapped in local optima, this strategy intelligently triggers random perturbations and introduces high-potential individuals to enhance the algorithm’s ability to escape local optima and promote population diversity. Third, a novel multi-Q-table reinforcement learning framework is embedded within the iterative process to dynamically adjust key genetic algorithm parameters (such as selection, mutation, and crossover rates) and enable multi-dimensional performance evaluation, thereby effectively guiding the search toward better solutions. Experimental results demonstrate that the IGARL algorithm achieves a 10% to 60% improvement in convergence speed on Brandimarte benchmark instances, with solution quality significantly surpassing that of the basic genetic algorithm. Moreover, the fluctuation of the average optimal solution remains within 20%, indicating strong stability and robustness. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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29 pages, 1782 KB  
Article
Reinforcement Learning-Guided NSGA-II Enhanced with Gray Relational Coefficient for Multi-Objective Optimization: Application to NASDAQ Portfolio Optimization
by Zhiyuan Wang, Qinxu Ding, Ding Ding, Siying Zhu, Jing Ren, Yue Wang and Chong Hui Tan
Mathematics 2026, 14(2), 296; https://doi.org/10.3390/math14020296 - 14 Jan 2026
Viewed by 178
Abstract
In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To this end, and to [...] Read more.
In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To this end, and to address existing gaps, we propose a novel reinforcement learning (RL)-guided non-dominated sorting genetic algorithm II (NSGA-II) enhanced with gray relational coefficients (GRC), termed RL-NSGA-II-GRC, which combines an RL agent controller and GRC-based selection to improve the convergence and diversity of the Pareto-optimal fronts. The agent adapts key evolutionary parameters online using population-level metrics of hypervolume, feasibility, and diversity, while the GRC-enhanced tournament operator ranks parents via a unified score simultaneously considering dominance rank, crowding distance, and geometric proximity to ideal reference. We evaluate the framework on the Kursawe and CONSTR benchmark problems and on a NASDAQ portfolio optimization application. On the benchmarks, RL-NSGA-II-GRC achieves convergence metric improvements of about 5.8% and 4.4% over the original NSGA-II, while preserving a well-distributed set of non-dominated solutions. In the portfolio application, the method produces a smooth and densely populated efficient frontier that supports the identification of the maximum Sharpe ratio portfolio (with annualized Sharpe ratio = 1.92), as well as utility-optimal portfolios for different risk-aversion levels. The main contributions of this work are three-fold: (1) we propose an RL-NSGA-II-GRC method that integrates an RL agent into the evolutionary framework to adaptively control key parameters using generational feedback; (2) we design a GRC-enhanced binary tournament selection operator that provides a comprehensive performance indicator to efficiently guide the search toward the Pareto-optimal front; (3) we demonstrate, on benchmark MOO problems and a NASDAQ portfolio case study, that the proposed method delivers improved convergence and well-populated efficient frontiers that support actionable investment insights. Full article
(This article belongs to the Special Issue Multi-Objective Evolutionary Algorithms and Their Applications)
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39 pages, 2204 KB  
Review
Breeding Smarter: Artificial Intelligence and Machine Learning Tools in Modern Breeding—A Review
by Ana Luísa Garcia-Oliveira, Sangam L. Dwivedi, Subhash Chander, Charles Nelimor, Diaa Abd El Moneim and Rodomiro Octavio Ortiz
Agronomy 2026, 16(1), 137; https://doi.org/10.3390/agronomy16010137 - 5 Jan 2026
Viewed by 1521
Abstract
Climate challenges, along with a projected global population increase of 2 billion by 2080, are intensifying pressures on agricultural systems, leading to biodiversity loss, land use constrains, soil fertility declining, and changes in water cycles, while crop yields struggle to meet the rising [...] Read more.
Climate challenges, along with a projected global population increase of 2 billion by 2080, are intensifying pressures on agricultural systems, leading to biodiversity loss, land use constrains, soil fertility declining, and changes in water cycles, while crop yields struggle to meet the rising food demand. These challenges, coupled with evolving legislation and rapid technology advancements, require innovative sustainable agricultural solutions. By reshaping farmers’ daily operations, real-time data acquisition and predictive models can support informed decision-making. In this context, smart farming (SM) applied to plant breeding can improve efficiency by reducing inputs and increasing outputs through the adoption of digital and data-driven technologies. Examples include the investment on common ontologies and metadata standards for phenotypes and environments, standardization of HTP protocols, integration of prediction outputs into breeding databases, and selection workflows, as well in building multi-partner field networks that collect diverse envirotypes. This review outlines how AI and machine learning (ML) can be integrated in modern plant breeding methodologies, including genomic selection (GS) and genetic algorithms (GAs), to accelerate the development of climate-resilient and sustainably performing crop varieties. While many reviews address smart farming or smart breeding independently, herein, these domains are bridged to provide an understandable strategic landscape by enhancing breeding efficiency. Full article
(This article belongs to the Collection AI, Sensors and Robotics for Smart Agriculture)
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24 pages, 5823 KB  
Article
Path Planning of an Underwater Vehicle by CFD Numerical Simulation Combined with a Migration-Based Genetic Algorithm
by Bing Yang, Ligang Yao, Leilei Chen and Weilin Luo
J. Mar. Sci. Eng. 2026, 14(1), 74; https://doi.org/10.3390/jmse14010074 - 30 Dec 2025
Viewed by 242
Abstract
This paper proposes a physics-informed global path planning framework for underwater vehicles integrating CFD simulation and the genetic algorithm. The CFD simulation models the flow field along the planned path of the underwater vehicle. The current velocity data are incorporated into the following [...] Read more.
This paper proposes a physics-informed global path planning framework for underwater vehicles integrating CFD simulation and the genetic algorithm. The CFD simulation models the flow field along the planned path of the underwater vehicle. The current velocity data are incorporated into the following path planning that is based on an improved genetic algorithm (GA), which uses migration operators to share the information about feasible solutions or paths, improving the fitness of the whole population. In the three steps of the GA procedure, an elite selection strategy is adopted to avoid losing excellent solutions. A segmented crossover strategy is adopted to avoid low-quality crossover. An adaptive mutation strategy is used to enhance the ability to escape a local optimal solution. Using the improved GA, single-target and multi-target underwater path planning are investigated. In multi-target path planning, a combined algorithm is proposed to solve the optimal traversal order of target points and plan a feasible path between target points. The simulation results show that the proposed algorithm has good planning ability for both simple and complex underwater scenarios. Compared with the conventional GA and an improved GA, the number of average iterations decreases by 45.3% and 29.9%, respectively, for 2D multi-target path planning. The number of average inflection points decreases by 50.3% and 44.2%, respectively, for 2D multi-target path planning. Full article
(This article belongs to the Section Ocean Engineering)
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31 pages, 3522 KB  
Article
An Improved Knowledge-Based Genetic Algorithm for High-Priority Task Scheduling in Relay Satellite Networks
by Yiwei Zhao, Liqian Wang and Jingke Zou
Appl. Sci. 2026, 16(1), 358; https://doi.org/10.3390/app16010358 - 29 Dec 2025
Viewed by 197
Abstract
This paper presents an improved knowledge-based genetic algorithm for relay satellite task scheduling. It aims to address the issue of ensuring high-priority tasks under complex constraints and resource competition. The algorithm enhances the high-priority task completion ratio by incorporating multiple knowledge sorting strategies [...] Read more.
This paper presents an improved knowledge-based genetic algorithm for relay satellite task scheduling. It aims to address the issue of ensuring high-priority tasks under complex constraints and resource competition. The algorithm enhances the high-priority task completion ratio by incorporating multiple knowledge sorting strategies and a dynamic crossover mechanism during population initialization. Simulation results show that the proposed algorithm improves the high-priority task completion ratio by an average of 11.78 percentage points compared to the second-best algorithm. In environments with high load, resource constraints, and capacity shrinkage, the proposed algorithm outperforms in scheduling efficiency, robustness, and adaptability. It demonstrates effectiveness in multi-task and multi-resource competitive environments. IKBGA provides a highly targeted and scalable optimization solution for relay satellite task scheduling, with strong application potential. Full article
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35 pages, 22109 KB  
Article
MEBCMO: A Symmetry-Aware Multi-Strategy Enhanced Balancing Composite Motion Optimization Algorithm for Global Optimization and Feature Selection
by Gelin Zhang, Minghao Gao and Xianmeng Zhao
Symmetry 2026, 18(1), 40; https://doi.org/10.3390/sym18010040 - 24 Dec 2025
Viewed by 222
Abstract
To address the limitations of the traditional Balancing Composite Motion Optimization (BCMO) algorithm—namely weak directional global exploration, insufficient local exploitation accuracy, and a tendency to fall into local optima with reduced population diversity in feature selection tasks—this paper proposes a Multi-Strategy Enhanced Balancing [...] Read more.
To address the limitations of the traditional Balancing Composite Motion Optimization (BCMO) algorithm—namely weak directional global exploration, insufficient local exploitation accuracy, and a tendency to fall into local optima with reduced population diversity in feature selection tasks—this paper proposes a Multi-Strategy Enhanced Balancing Composite Motion Optimization algorithm (MEBCMO). From a symmetry perspective, MEBCMO exploits the symmetric and asymmetric relationships among candidate solutions in the search space to achieve a better balance between exploration and exploitation. The performance of MEBCMO is enhanced through three complementary strategies. First, an adaptive heat-conduction search mechanism is introduced to simulate thermal transmission behavior, where a Sigmoid function adjusts the heat-conduction coefficient α_T from 0.9 to 0.2 during iterations. By utilizing the symmetric fitness–distance relationship between the current solution and the global best, this mechanism improves the directionality and efficiency of global exploration. Second, a quadratic interpolation search strategy is designed. By constructing a quadratic model based on the current individual, a randomly selected individual, and the global best, the algorithm exploits local symmetric characteristics of the fitness landscape to strengthen local exploitation and alleviate performance degradation in high-dimensional spaces. Third, an elite population genetic strategy is incorporated, in which the top three individuals generate new candidates through symmetric linear combinations with non-elite individuals and Gaussian perturbations, preserving population diversity and preventing premature convergence. To evaluate MEBCMO, extensive global optimization experiments are conducted on the CEC2017 benchmark suite with dimensions of 30, 50, and 100, and comparisons are made with eight mainstream algorithms, including PSO, DE, and GWO. Experimental results demonstrate that MEBCMO achieves superior performance across unimodal, multimodal, hybrid, and composite functions. Furthermore, MEBCMO is combined with LightGBM to form the MEBCMO-LightGBM model for feature selection on 14 public datasets, yielding lower fitness values, higher classification accuracy, and fewer selected features. Statistical tests and convergence analyses confirm the effectiveness, stability, and rapid convergence of MEBCMO in symmetric and complex optimization landscapes. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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20 pages, 2200 KB  
Article
CMOS LIF Spiking Neuron Designed with a Memristor Emulator Based on Optimized Operational Transconductance Amplifiers
by Carlos Alejandro Velázquez-Morales, Luis Hernández-Martínez, Esteban Tlelo-Cuautle and Luis Gerardo de la Fraga
Dynamics 2025, 5(4), 54; https://doi.org/10.3390/dynamics5040054 - 18 Dec 2025
Viewed by 360
Abstract
The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. [...] Read more.
The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. These size values are used to run the non-dominated sorting genetic algorithm (NSGA-II) to perform a multi-objective optimization of three OTA topologies. The gm/ID method begins with transistor characterization using MATLAB R2024a generated look-up tables (LUTs), which map normalized transconductance of the transistor channel dimensions, and key performance metrics of a complementary metal–oxide–semiconductor (CMOS) technology. The LUTs guide the initial population generation within NSGA-II during the optimization of OTAs to achieve not only a desired transconductance but also accuracy alongside linearity, high DC gain, low power consumption, and stability. The feasible W/L size solutions provided by NSGA-II are used to enhance the CMOS design of a memristor emulator, where the OTA with the desired transconductance is adapted to tune the behavior of the memristor, demonstrating improved pinched hysteresis loop characteristics. In addition, process, voltage and temperature (PVT) variations are performed by using TSMC 180 nm CMOS technology. The memristor-based on optimized OTAs is used to design a Leaky Integrate-and-Fire (LIF) neuron, which produces identical spike counts (seven spikes) under the same input conditions, though the time period varied with a CMOS inverter scaling. It is shown that increasing transistor widths by 100 in the inverter stage, the spike quantity is altered while changing the spiking period. This highlights the role of device sizing in modulating LIF neuron dynamics, and in addition, these findings provide valuable insights for energy-efficient neuromorphic hardware design. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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30 pages, 6108 KB  
Article
Sensor Placement Optimization for Power Grid Condition Monitoring Based on a Backup Coverage Model: A Case Study of Guangzhou
by Yuhang E, Dachuan Xu, Shijie Li, Yanjie Zhao, Zhaoping Liu, Cheng Su, Haojian Liang, Xiaohan Jiang, Linshuang Cui and Shaohua Wang
Appl. Sci. 2025, 15(23), 12570; https://doi.org/10.3390/app152312570 - 27 Nov 2025
Viewed by 476
Abstract
The increasing complexity and vulnerability of urban power grids necessitate advanced monitoring systems to ensure operational reliability and resilience. The optimal placement of sensors is a critical yet challenging task that directly impacts the effectiveness and cost of such systems. This study addresses [...] Read more.
The increasing complexity and vulnerability of urban power grids necessitate advanced monitoring systems to ensure operational reliability and resilience. The optimal placement of sensors is a critical yet challenging task that directly impacts the effectiveness and cost of such systems. This study addresses the need for a sensor deployment strategy that not only maximizes coverage but also guarantees monitoring redundancy for critical assets. We propose a novel optimization framework based on the Backup Coverage Sensor Location Problem (BCSLP). First, a multi-dimensional risk assessment, integrating infrastructure proximity and population density, was conducted using the Entropy Weight Method (EWM) to objectively determine the monitoring priority for each power tower in Guangzhou, China. Subsequently, the BCSLP model was formulated to optimize the trade-off between primary coverage (breadth) and backup coverage (resilience). The model was solved using both the Gurobi exact solver for a representative district and a bespoke improved Genetic Algorithm (GA) to ensure scalability. The case study in Guangzhou’s Haizhu District revealed that extreme strategies focusing solely on either breadth or resilience were suboptimal. We adopt a balanced, resilience-biased strategy (ω=0.4) that supports robust monitoring of critical towers while maintaining broad network coverage. The proposed risk-informed BCSLP framework provides a scientifically robust and scalable tool for designing resilient sensor networks for power grids, offering valuable decision support for enhancing urban infrastructure security in smart cities. Full article
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19 pages, 5699 KB  
Article
Behavior-Based Optimization of Emergency Shelter Siting: A TPB–NSGA-III Approach Applied to Hangzhou
by Ningzhe Yu, Shan Huang, Yanxi Wu, Jiale Liu and Mingjun Cheng
Symmetry 2025, 17(11), 1964; https://doi.org/10.3390/sym17111964 - 14 Nov 2025
Viewed by 430
Abstract
Urban disasters pose severe, concentrated risks to dense populations, generating asymmetric and time-critical demands on emergency services and infrastructure. To address these challenges, we develop a behaviorally informed shelter siting framework that integrates a Theory of Planned Behavior (TPB)-based choice model with a [...] Read more.
Urban disasters pose severe, concentrated risks to dense populations, generating asymmetric and time-critical demands on emergency services and infrastructure. To address these challenges, we develop a behaviorally informed shelter siting framework that integrates a Theory of Planned Behavior (TPB)-based choice model with a Non-dominated Sorting Genetic Algorithm III (NSGA-III) multi-objective spatial optimization to simulate aggregation willingness and determine optimal shelter locations. The model explicitly represents symmetric and asymmetric spatial patterns and jointly optimizes population coverage and travel time under three demand scenarios (general, emergency, vulnerable). Comparative experiments show consistent, measurable gains: coverage increases of 0.19~6.9% and travel-time reductions of 14~18% are obtained, with improvements concentrated in high-need pockets. These results indicate that behaviorally informed, symmetry-aware optimization improves access, equity, and robustness while offering a modular tool for planners. Full article
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20 pages, 4958 KB  
Article
Multi-UAV Task Allocation Based on Grid-Based Particle Swarm and Genetic Hybrid Algorithm
by Yuting Xiong and Liang Zhang
Mathematics 2025, 13(22), 3591; https://doi.org/10.3390/math13223591 - 9 Nov 2025
Viewed by 722
Abstract
To address the uneven distribution of the Pareto front and insufficient convergence in multi-UAV task allocation, this paper proposes GrEAPSO, an improved algorithm that hybridizes Particle Swarm Optimization (PSO) with Genetic Algorithm (GA). GrEAPSO balances exploitation and exploration through grid partitioning, adopts a [...] Read more.
To address the uneven distribution of the Pareto front and insufficient convergence in multi-UAV task allocation, this paper proposes GrEAPSO, an improved algorithm that hybridizes Particle Swarm Optimization (PSO) with Genetic Algorithm (GA). GrEAPSO balances exploitation and exploration through grid partitioning, adopts a dual-encoding scheme coupled with crossover and mutation to enhance population diversity, and employs a grid-based environmental selection mechanism to improve the uniformity of the Pareto set. After initialization, the algorithm iteratively performs a PSO-based local search, genetic crossover and mutation, and grid-based environmental selection. The offspring and parent populations are then merged, and the archive set is updated accordingly. Across three military UAV task-allocation scenarios (small, medium, and large), GrEAPSO is benchmarked against MOPSO, NSGA-II/III, MOEA/D-DE, RVEA, IBEA, MOMVO, and MaOGOA. All experiments use a population size of 100. Its reference point is undominated and dominates some competitors, with median gains of 55.78% in hypervolume and 8.11% in spacing. Finally, the sensitive analysis further indicates that dividing the objective space into 15–20 grids offers the best trade-off between search breadth and solution distribution. Full article
(This article belongs to the Section E: Applied Mathematics)
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28 pages, 1286 KB  
Article
Multi-Objective Emergency Path Planning Based on Improved Nondominant Sorting Genetic Algorithm
by Yiren Yuan, Hang Xu and Cuiyong Tang
Symmetry 2025, 17(11), 1818; https://doi.org/10.3390/sym17111818 - 29 Oct 2025
Viewed by 864
Abstract
Three-dimensional path planning in emergency logistics is a complex optimization problem, particularly challenging because it requires considering conflicting objectives such as flight time, energy consumption, and obstacle avoidance. Unlike most urban logistics research, this study examines emergency delivery path planning in mountainous environments [...] Read more.
Three-dimensional path planning in emergency logistics is a complex optimization problem, particularly challenging because it requires considering conflicting objectives such as flight time, energy consumption, and obstacle avoidance. Unlike most urban logistics research, this study examines emergency delivery path planning in mountainous environments during natural disasters. One of the most effective approaches to this problem is to employ multi-objective evolutionary algorithms. However, while multi-objective genetic algorithms can handle multiple conflicting objectives, they struggle when dealing with complex constraints. This paper proposes a multi-objective genetic optimization method, Adaptive Crossover-Mutation Multi-Objective Genetic Optimization (ACM-NSGA-II), based on the classic NSGA-II framework. Inspired by the principle of symmetry, this method dynamically adjusts the mutation and crossover rates based on population diversity to maintain a balanced exploration–exploitation trade-off. When population diversity is low, the mutation rate is increased to promote exploration of the solution space; when population diversity is high, the crossover rate is increased to promote better information exchange. The algorithm maintains symmetry by gradually adjusting the step size, balancing adaptability and stability. To address the obstacle avoidance problem, we introduced a dynamic path repair strategy that respects the symmetry of no-fly zone boundaries and terrain features, ensuring the safety and efficiency of Unmanned Aerial Vehicles. This algorithm jointly optimizes three objectives: safety cost, flight time, and energy consumption. The algorithm was tested in a mountainous environment model simulating a remote area. In experiments, ACM-NSGA-II was compared with several mainstream evolutionary algorithms. The Pareto set and hypervolume metrics of each method were recorded and statistically analyzed at a 5% significance level. The results show that ACM-NSGA-II outperforms the baseline algorithms in terms of diversity, convergence, and feasibility. Specifically, compared with the traditional NSGA-II, ACM-NSGA-II improved the average hypervolume metric by 53.39% and reduced the average flight time by 24.26%. ACM-NSGA-II also demonstrated significant advantages over other popular standard algorithms. Experimental results show that it can effectively solve the path planning challenge of emergency logistics Unmanned Aerial Vehicles in mountainous environments. Full article
(This article belongs to the Section Mathematics)
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28 pages, 1459 KB  
Article
Research on Computing Power Resources-Based Clustering Methods for Edge Computing Terminals
by Jian Wang, Jiali Li, Xianzhi Cao, Chang Lv and Liusong Yang
Appl. Sci. 2025, 15(20), 11285; https://doi.org/10.3390/app152011285 - 21 Oct 2025
Viewed by 650
Abstract
In the “cloud–edge–end” three-tier architecture of edge computing, the cloud, edge layer, and end-device layer collaborate to enable efficient data processing and task allocation. Certain computation-intensive tasks are decomposed into subtasks at the edge layer and assigned to terminal devices for execution. However, [...] Read more.
In the “cloud–edge–end” three-tier architecture of edge computing, the cloud, edge layer, and end-device layer collaborate to enable efficient data processing and task allocation. Certain computation-intensive tasks are decomposed into subtasks at the edge layer and assigned to terminal devices for execution. However, existing research has primarily focused on resource scheduling, paying insufficient attention to the specific requirements of tasks for computing and storage resources, as well as to constructing terminal clusters tailored to the needs of different subtasks.This study proposes a multi-objective optimization-based cluster construction method to address this gap, aiming to form matched clusters for each subtask. First, this study integrates the computing and storage resources of nodes into a unified concept termed the computing power resources of terminal nodes. A computing power metric model is then designed to quantitatively evaluate the heterogeneous resources of terminals, deriving a comprehensive computing power value for each node to assess its capability. Building upon this model, this study introduces an improved NSGA-III (Non-dominated Sorting Genetic Algorithm III) clustering algorithm. This algorithm incorporates simulated annealing and adaptive genetic operations to generate the initial population and employs a differential mutation strategy in place of traditional methods, thereby enhancing optimization efficiency and solution diversity. The experimental results demonstrate that the proposed algorithm consistently outperformed the optimal baseline algorithm across most scenarios, achieving average improvements of 18.07%, 7.82%, 15.25%, and 10% across the four optimization objectives, respectively. A comprehensive comparative analysis against multiple benchmark algorithms further confirms the marked competitiveness of the method in multi-objective optimization. This approach enables more efficient construction of terminal clusters adapted to subtask requirements, thereby validating its efficacy and superior performance. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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15 pages, 1079 KB  
Article
A Multi-Granularity Random Mutation Genetic Algorithm for Steel Cold Rolling Scheduling Optimization
by Hairong Yang, Xiao Ji, Haiyan Sun, Yonggang Li and Weidong Qian
Processes 2025, 13(10), 3311; https://doi.org/10.3390/pr13103311 - 16 Oct 2025
Viewed by 660
Abstract
Cold rolling is the precision finishing stage in the steel production process, and its scheduling optimization is essential for enhancing production efficiency. To address the complex process constraints and objectives, this paper proposes a multi-granularity random mutation genetic algorithm (MGRM-GA) for cold rolling [...] Read more.
Cold rolling is the precision finishing stage in the steel production process, and its scheduling optimization is essential for enhancing production efficiency. To address the complex process constraints and objectives, this paper proposes a multi-granularity random mutation genetic algorithm (MGRM-GA) for cold rolling scheduling optimization. First, a multi-objective collaborative optimization model is established to integrate the production cost and process constraints. Then, high-quality initial solutions are generated based on greedy heuristic rules to fulfill the cold rolling constraints. Finally, four random mutation strategies are designed at different task granularities and unit levels to search diverse candidates. The standard flexible job shop scheduling problem (FJSP) datasets and practical cold rolling production data are studied to validate the feasibility and competitiveness of the MGRM-GA. Experimental results show that the MGRM-GA achieves a 94.2% improvement in objective function optimization, a 14.8-fold increase in throughput, and a 94.8% reduction in execution time on cold rolling data. Compared with the heuristic mutation algorithm, MGRM-GA increases population heterogeneity and avoids premature convergence, which enhances global search ability and scheduling performance. Full article
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