{"title":"PSO–KMeans niching for multimodal optimisation with metal-GPU realisation on Apple M-series","authors":"Ankit Ruhi, Ramesh Kolluru","doi":"10.1016/j.swevo.2026.102522","DOIUrl":"10.1016/j.swevo.2026.102522","url":null,"abstract":"<div><div>Multimodal optimisation seeks several high-quality solutions from different basins of attraction, rather than one final solution. We study a lightweight PSO–KMeans niching method implemented in Apple Metal for Apple M-series GPUs. The method extends standard PSO with one Lloyd clustering step on particle-best positions, cluster-best social attractors, and reseeding for weak clusters.</div><div>We evaluate the method on 2D multimodal benchmarks—Rastrigin, Ackley, Himmelblau, Six-Hump Camel, and Hölder Table—with exploratory 5D and 10D tests. Each method returns a bounded fitness-only solution set; BestCov is computed only after this set is formed, by matching members to known optima. Results depend on the benchmark and metric. Under a matched 40-trial GPU protocol, PSO–KMeans significantly improves BestCov over plain PSO on Himmelblau (0.98 vs. 0.55) and Hölder Table (0.49 vs. 0.25), and is competitive with ring/lbest on Himmelblau. For Six-Hump Camel (two global minima), plain PSO already reaches high coverage (0.93) and both niching methods saturate. Exploratory CPU crowding DE and niching CMA-ES are not included in the GPU ranking.</div><div>The implementation uses a multiphase Metal pipeline, deterministic reductions, and Philox random-number generation, with released scripts and artefacts. An enhanced adaptive-<span><math><mi>K</mi></math></span> variant with optional refinement is a trade-off, not the default. Evidence is strongest on synthetic 2D benchmarks; 5D/10D tests are exploratory, and a reparameterised engineering-style surrogate with a nonempty feasible region remains inconclusive. Real-world objectives and CUDA/SYCL ports are left for future work.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102522"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148953521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A framework for ensuring invariance of multi-objective evolutionary algorithms to order-preserving transformation of objective functions","authors":"Yutaro Yamada, Kento Uchida, Shinichi Shirakawa","doi":"10.1016/j.swevo.2026.102527","DOIUrl":"10.1016/j.swevo.2026.102527","url":null,"abstract":"<div><div>Invariance properties are important for evolutionary algorithms to ensure consistent behavior and performance on broader classes of objective functions. Owing to the ranking-based transformation, many evolutionary algorithms for single-objective optimization possess the invariance property to order-preserving transformations of objective functions, which reduces parameter tuning costs. In contrast, in multi-objective evolutionary algorithms (MOEAs), order-preserving transformations of objective functions often change the behavior of existing methods and degrade their performance because they can change the shape of the Pareto front to intractable forms, such as concave and discontinuous shapes. This study proposes the ranking-based transformation (RT) framework that gives the invariance property to order-preserving transformations to existing MOEAs. After MOEA generates candidate solutions following its original procedure, RT-framework computes the utility values of the parent and candidate solutions for each objective function. These utility values are given by a monotonically increasing transformation of their ranking on the external archive of non-dominated solutions. RT-framework then updates the population so that the MOEA acquires Pareto optimal solutions on the utility functions. Afterward, the external archive is updated with newly discovered non-dominated solutions while considering the uniformity of solutions in the archive. The experimental results show that RT-framework can resolve the performance deterioration of existing MOEAs under order-preserving transformations both on bi-objective and three-objective problems.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102527"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148953568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jorge Sánchez, Guadalupe García-Isla, Sandra Perez-Herrero, Beatriz Trenor, Javier Saiz
{"title":"Frenetic Cat-inspired particle optimization: A Markov state-switching hybrid swarm optimizer with application to cardiac digital twinning","authors":"Jorge Sánchez, Guadalupe García-Isla, Sandra Perez-Herrero, Beatriz Trenor, Javier Saiz","doi":"10.1016/j.swevo.2026.102524","DOIUrl":"10.1016/j.swevo.2026.102524","url":null,"abstract":"<div><div>Designing optimizers that remain effective under tight evaluation budgets is critical in expensive black-box settings such as cardiac digital twinning. We propose <em>Frenetic Cat-inspired Particle Optimization</em> (FCPO), a hybrid swarm method that couples particle swarm optimization-like dynamics with an explicit-state Markov switching controller to schedule exploration and refinement operators online. FCPO integrates (i) state-conditioned bounded motion, (ii) an elite-difference global jump operator to escape stagnation, (iii) eigen-space guided local refinement from elite covariance, and (iv) linear population size reduction to control late-stage computational cost. We benchmark FCPO on five representative functions from the Congress on Evolutionary Computation (CEC) 2022 suite (F1, F2, F3, F6 and F10) at dimensions <span><math><mrow><mi>D</mi><mo>∈</mo><mrow><mo>{</mo><mn>10,20</mn><mo>}</mo></mrow></mrow></math></span> over 30 independent runs, comparing against PSO, CSO, CLPSO, SHADE, L-SHADE, HO and CMA-ES. FCPO achieves the lowest mean runtime across the ten benchmark cases among the full methods (average 0.181<!--> <!-->s). HO, CMA-ES, and L-SHADE required approximately 2.33, 2.39, and 2.56 times the mean runtime of FCPO, respectively, in our Python implementation. Across the eight full methods, the aggregate rank analysis placed CMA-ES first, followed by FCPO, L-SHADE, and HO, with average ranks of 1.90, 3.40, 3.60, and 4.10, respectively. On structured landscapes (F1–F3) and on the hybrid function (F6), CMA-ES remains the most accurate method, while FCPO substantially improves over classical swarms and maintains a favorable accuracy–runtime trade-off. Finally, in a ventricular activation digital twin calibration task, FCPO reaches the target electrocardiogram (ECG) fidelity (RMSE <span><math><mrow><mo><</mo><mn>0.1</mn></mrow></math></span> <!--> <!-->mV) within <span><math><mrow><mo>∼</mo><mn>40</mn></mrow></math></span> iterations and produces physiologically plausible activation maps with robust convergence across repeated initializations, supporting its use as a practical optimizer for expensive inverse problems.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102524"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148953571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enhanced Proximal Policy Optimization for dynamic cross-regional agricultural machinery dispatching under demand uncertainty","authors":"Wenkang Zhang, Ming Wang, Longzhe Quan, Jian Chu","doi":"10.1016/j.swevo.2026.102528","DOIUrl":"10.1016/j.swevo.2026.102528","url":null,"abstract":"<div><div>This paper studies dynamic cross-regional agricultural machinery dispatching in which heterogeneous machines must be reassigned after new plot demands arrive during execution. The scientific challenge is to make fast residual rescheduling decisions from the true field state, while respecting typed service compatibility, time windows, cross-cooperative coordination costs, and mandatory return-to-home operations. This paper formulates a route-based mixed-integer linear model that unifies static dispatching and event-driven residual rescheduling through machine-state interpolation and closed-loop makespan minimization. Enhanced Proximal Policy Optimization is then developed (Enhanced PPO), which aligns training with residual deployment states, mitigates delayed reward propagation in terminal-makespan objectives, and combines learned dispatch preferences with feasibility-aware online repair. On a 20-case benchmark covering four disturbance archetypes, Enhanced PPO obtains the best static and dynamic makespan in all 40 case–scale–scenario comparisons. Across competing algorithms, the median static makespan gaps range from 6.10% to 9.51%, while the median dynamic gaps range from 1.19% to 3.49%; statistical tests further show significant and more stable performance across all disturbance scenarios.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102528"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148953565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large-scale expensive offline data-driven evolutionary optimization via hierarchical teaching and cooperative coevolution","authors":"Er-chao Li, WanJi Yuan, Li-sen Wei","doi":"10.1016/j.swevo.2026.102516","DOIUrl":"10.1016/j.swevo.2026.102516","url":null,"abstract":"<div><div>Data-driven evolutionary algorithms (DDEAs) have gained increasing attention over the past decade for their effectiveness in solving expensive optimization problems. However, most research has focused on small-scale problems, while large-scale expensive optimization problems (LSEOPs) remain underexplored due to the challenges posed by the high-dimensional search space—commonly referred to as the “curse of dimensionality.” Although cooperative co-evolution (CC) offers a promising way to mitigate this issue, many of its advanced grouping strategies require frequent real fitness evaluations, rendering them unsuitable for DDEAs. To overcome this limitation, we propose a hierarchical teaching-cooperative data-driven evolutionary algorithm, termed HTC-DDEA. Firstly, a distribution-aware grouping strategy is designed to partition the decision space into multiple subspaces with different levels of population diversity. Then, a dual-stage search mechanism is developed to dynamically adjust the diversity and convergence of each subpopulation according to the grouping scheme, thereby maintaining a proper balance between exploration and exploitation throughout the optimization process, and a novel surrogate modeling framework is introduced to enable a smooth transition from local search to global search. Experiments on up to 1000-dimensional problems and the comparisons with state-of-the-art DDEAs validate the effectiveness of HTC-DDEA.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102516"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148855790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A hybrid deep learning–ensemble forecasting and swarm-evolutionary optimization framework for multiobjective electric vehicle charging station planning under contextual demand uncertainty","authors":"Chun-Chih Chiu, Nguyen Thao Huong","doi":"10.1016/j.swevo.2026.102513","DOIUrl":"10.1016/j.swevo.2026.102513","url":null,"abstract":"<div><div>The rapid growth of electric vehicle (EV) adoption has intensified the need for robust, cost-effective charging station planning under highly variable and uncertain demand. Charging infrastructure deployment directly affects feeder-level energy efficiency through technical losses and voltage regulation, and may increase operational stress on distribution assets under demand volatility, requiring joint siting-and-sizing decisions that balance investment cost, service reliability, and network operating constraints. This study proposes a contextual simulation-based multiobjective planning framework integrating demand forecasting, uncertainty modeling, and optimization. A hybrid Long Short-Term Memory–eXtreme Gradient Boosting (LSTM–XGBoost) model generates baseline demand profiles, upon which context-dependent stochastic scenarios are constructed via contextual simulation and Monte Carlo modeling of EV user behavior, representing realistic demand variability including extreme operating conditions. The resulting siting-and-sizing problem is formulated as a multiobjective mixed-integer nonlinear program and solved using a hybrid Arithmetic Optimization Algorithm –Nondominated Sorting Simplified Swarm Optimization (AOA–NSSSO) algorithm balancing global exploration with local refinement. Experiments on IEEE benchmark systems show that the framework improves network performance, voltage security, and robustness under worst-case conditions, achieving 100% feasibility and zero voltage-violation probability. Incorporating investment cost as an explicit objective reveals clear techno-economic trade-offs between expenditure and operational performance, reducing deployment scale and cost without compromising voltage security.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102513"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148856315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yonglin He, Cheng He, Zhichao Lu, Ye Tian, Handing Wang, Yinglan Feng, Hongbin Li
{"title":"Reinforcement learning enhanced zeroth-order optimization for large-scale multiobjective optimization problems","authors":"Yonglin He, Cheng He, Zhichao Lu, Ye Tian, Handing Wang, Yinglan Feng, Hongbin Li","doi":"10.1016/j.swevo.2026.102514","DOIUrl":"10.1016/j.swevo.2026.102514","url":null,"abstract":"<div><div>“The curse of dimensionality” poses a major challenge to the scalability of multiobjective evolutionary algorithms (MOEAs) for large-scale multiobjective optimization problems (LSMOPs). Although existing MOEAs have achieved encouraging performance on problems with hundreds of decision variables, solving higher-dimensional LSMOPs remains computationally demanding. To mitigate these scalability challenges, we propose MOZO, an evolutionary zeroth-order (ZO) optimization method that combines zeroth-order directional estimation with a population-based MOEA backbone. Specifically, MOZO first estimates and aggregates objective-wise ZO gradients to provide search directions in high-dimensional decision spaces. It then refines these directions using acceleration and adaptation modules and embeds them within a population-based evolutionary search process to improve robustness against noisy estimates and objective conflicts. In addition, MOZO incorporates a reinforcement learning mechanism to adaptively configure suitable ZO and MOEA modules during the search process. Experimental results on benchmark LSMOPs with up to 100,000 decision variables demonstrate the effectiveness, efficiency, and scalability of MOZO compared with five state-of-the-art large-scale MOEAs. We further apply MOZO to the fine-tuning of <span>OPT-2.7B</span> and <span>OPT-6.7B</span> large language models on a single GPU, where the results show its practical potential under memory-constrained settings.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102514"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148856318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regional-isolation-aware multi-agent target allocation via adaptive curriculum reinforcement learning and metaheuristic optimization","authors":"Ziheng Wang, Xuewei Yu, Guangming Xie, Jianlei Zhang","doi":"10.1016/j.swevo.2026.102533","DOIUrl":"10.1016/j.swevo.2026.102533","url":null,"abstract":"<div><div>Multi-agent target allocation is a fundamental problem in intelligent systems. In practical applications, due to incomplete information and limited communication caused by regional isolation, agents often have to make cooperative decisions based solely on local observations, which significantly increases the difficulty of problem solving. To address this issue, this paper investigates the target allocation problem with regional isolation awareness and proposes a staged solution framework that integrates adaptive curriculum reinforcement learning with metaheuristic optimization. The framework decomposes the global allocation process into two stages: inter-group target cluster selection and intra-group target assignment. In the group selection stage, an adaptive curriculum reinforcement learning mechanism with a nested structure is designed to improve training stability and policy quality by progressively increasing task complexity. In the intra-group assignment stage, the problem is formulated as an acyclic multiple traveling salesman problem, and an improved Energy Valley Optimization algorithm is proposed to efficiently search for high-quality solutions. On this basis, extensive ablation studies, comparative experiments, and extended experiments are conducted to systematically evaluate the proposed method. The results demonstrate that the proposed method achieves superior performance and attains a favorable balance between solution quality and computational efficiency, validating the effectiveness and application potential of combining reinforcement learning with metaheuristic optimization in complex multi-agent cooperative decision-making problems.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102533"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149004180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A maximum mean discrepancy indicator-based evolutionary algorithm for solving dynamic multi-objective optimization problems with undetectable changes","authors":"Fei Li, Hao Pan, Kaifeng Yang, Hao Wang","doi":"10.1016/j.swevo.2026.102530","DOIUrl":"10.1016/j.swevo.2026.102530","url":null,"abstract":"<div><div>Most existing research on dynamic multi-objective optimization problems assumes that environmental changes can be detected. However, in real-world applications, many environmental changes are undetectable, posing significant challenges to traditional dynamic multi-objective evolutionary algorithms. The key issue is how to improve population diversity without sacrificing convergence. To address the challenge, a maximum mean discrepancy indicator-based evolutionary algorithm (MMDEA) is proposed. First, an MMD indicator-based front evolution assessment strategy is designed to monitor the state of the evolutionary process. Based on the ability of MMD to effectively measure the distance between distributions, we employ it to identify the evolutionary state of the population. By calculating the MMD indicator value between the current and previous approximated optimal fronts, the population state can be classified as either a convergence state or a diversity state. When the population is in the convergence state, a convergence enhancement strategy is employed that guides the evolution of non-dominated solutions based on the deviation between them and their nearest dominated solutions. When the population is in the diversity state, a diversity enhancement strategy is proposed that guides the evolution of dominated solutions based on the deviation between non-dominated solutions and their nearest dominated solutions. Experimental results have been presented for various dynamic multi-objective optimization problems, compared with several state-of-the-art algorithms. The comprehensive results demonstrate that the proposed algorithm is highly effective and superior in solving these problems, with undetectable changes.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102530"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148953566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Surrogate-assisted heuristic optimization for post-earthquake power system restoration: A maximum flow approach","authors":"Xinzhu Qiao, Gaoyang Shi, Qiang Xie","doi":"10.1016/j.swevo.2026.102538","DOIUrl":"10.1016/j.swevo.2026.102538","url":null,"abstract":"<div><div>Rapid post-earthquake restoration planning is essential for the stable operation of power systems, yet direct optimization using power flow models is computationally intensive when applied to numerous random damage scenarios. This computational burden limits the rapid implementation of restoration strategies. To address this issue, a surrogate-assisted heuristic optimization framework is proposed. Damage scenarios are generated using spatially correlated ground motions and component fragility models, and a representative test set is selected through K-medoids clustering based on component damage, load supply, and topological features. A dual-fidelity evaluation system integrating high-fidelity (HF) and low-fidelity (LF) models is established. The HF model combines island identification with AC optimal power flow (AC-OPF) to accurately evaluate system functionality. The LF surrogate is constructed using a maximum flow (MF) model. It requires no offline training and updates directly with system states. Its low computational cost enables rapid exploration of the solution space while retaining explicit physical meaning. Based on this framework, a surrogate-assisted genetic algorithm (SAGA) with an LF-dominated, HF-corrected mechanism and a surrogate-assisted adaptive iterative local search algorithm (SAAILS) with an HF-dominated, LF-pre-screened mechanism are developed. The results show that the dual-fidelity framework effectively balances optimization accuracy and computational cost. SAGA reduces the number of HF model evaluations and computational time while maintaining comparable optimization performance, thereby shortening the time required to achieve equivalent solution quality. SAAILS achieves higher solution quality under the same time budget, particularly in high-dimensional damage scenarios. This study provides a scalable framework for efficient post-earthquake power system restoration.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"108 ","pages":"Article 102538"},"PeriodicalIF":9.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149004181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}