{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T16:44:53Z","timestamp":1781196293493,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,11]],"date-time":"2021-09-11T00:00:00Z","timestamp":1631318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Particle swarm optimization (PSO) has the disadvantages of easily getting trapped in local optima and a low search accuracy. Scores of approaches have been used to improve the diversity, search accuracy, and results of PSO, but the balance between exploration and exploitation remains sub-optimal. Many scholars have divided the population into multiple sub-populations with the aim of managing it in space. In this paper, a multi-stage search strategy that is dominated by mutual repulsion among particles and supplemented by attraction was proposed to control the traits of the population. From the angle of iteration time, the algorithm was able to adequately enhance the entropy of the population under the premise of satisfying the convergence, creating a more balanced search process. The study acquired satisfactory results from the CEC2017 test function by improving the standard PSO and improved PSO.<\/jats:p>","DOI":"10.3390\/e23091200","type":"journal-article","created":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T21:45:57Z","timestamp":1631483157000},"page":"1200","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A Particle Swarm Algorithm Based on a Multi-Stage Search Strategy"],"prefix":"10.3390","volume":"23","author":[{"given":"Yong","family":"Shen","sequence":"first","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wangzhen","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5466-7092","authenticated-orcid":false,"given":"Hongwei","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingping","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingyi","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haigang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650504, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5099","DOI":"10.1007\/s00500-018-3177-y","article-title":"Extended Genetic Algorithm for solving open-shop scheduling problem","volume":"23","author":"Hosseinabadi","year":"2018","journal-title":"Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1007\/s00500-017-2547-1","article-title":"A self-adaptive artificial bee colony algorithm based on global best for global optimi-zation","volume":"22","author":"Xue","year":"2018","journal-title":"Soft Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/s00500-017-2833-y","article-title":"Self-feedback differential evolution adapting to fitness landscape characteristics","volume":"23","author":"Li","year":"2017","journal-title":"Soft Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.ejor.2017.08.035","article-title":"A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints","volume":"265","author":"Wei","year":"2018","journal-title":"Eur. 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