{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:03:07Z","timestamp":1785409387386,"version":"3.56.0"},"reference-count":53,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T00:00:00Z","timestamp":1781049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Xinjiang Uygur Autonomous Region of China","award":["2025D01A16"],"award-info":[{"award-number":["2025D01A16"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61035003"],"award-info":[{"award-number":["61035003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["61035003"],"award-info":[{"award-number":["61035003"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Particle swarm optimization (PSO) is a simple and efficient metaheuristic algorithm that has been widely applied to solving various practical problems. However, PSO has some inherent limitations, such as a tendency to get trapped in local optima and an imbalance between global exploration and local exploitation. To overcome these challenges, this paper proposes a novel algorithm called the multi-swarm particle swarm optimization algorithm with multi-learning strategy (MPLPSO). First, the entire swarm is randomly partitioned into multiple sub-swarms, each comprising three distinct types of particles, which enables the algorithm to explore multiple potential solutions simultaneously. Next, a pool elite learning strategy combined with a convergence learning mechanism is employed to effectively reduce the risk of premature convergence. Furthermore, an elimination-replacement mechanism is integrated with a hierarchical competition strategy to further enhance the solution accuracy. Extensive experiments conducted on the CEC 2017 and CEC 2022 benchmark test suites demonstrate that the proposed MPLPSO significantly outperforms the classical PSO and several state-of-the-art PSO variants. Additionally, MPLPSO is also applied to the traveling salesman problem, and the experimental results further validate the superior performance and robustness of the proposal.<\/jats:p>","DOI":"10.3390\/a19060474","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T02:59:31Z","timestamp":1781146771000},"page":"474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Swarm Particle Swarm Optimization with Multi-Learning Strategy"],"prefix":"10.3390","volume":"19","author":[{"given":"Jie","family":"Sun","sequence":"first","affiliation":[{"name":"School of Information Engineering, Changji University, Changji 831100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengchao","family":"Pu","sequence":"additional","affiliation":[{"name":"Institute of Computer Software, Baoji University of Arts and Sciences, Baoji 721007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6806-8103","authenticated-orcid":false,"given":"Dongping","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Changji University, Changji 831100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuyu","family":"Fan","sequence":"additional","affiliation":[{"name":"Institute of Computer Software, Baoji University of Arts and Sciences, Baoji 721007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinghao","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Computer Software, Baoji University of Arts and Sciences, Baoji 721007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Changji University, Changji 831100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siyu","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Changji University, Changji 831100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/2.294849","article-title":"Genetic algorithms: A survey","volume":"27","author":"Srinivas","year":"1994","journal-title":"Computer"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102226","DOI":"10.1016\/j.swevo.2025.102226","article-title":"Particle swarm optimization based on k-means clustering and adaptive dual-groups strategy","volume":"100","author":"Fan","year":"2026","journal-title":"Swarm Evol. 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