{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:42Z","timestamp":1760145642134,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"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>The method of quantum dynamics is employed to investigate the mean strategy in the swarm intelligence algorithm. The physical significance of the population mean point is explained as the location where the optimal solution with the highest likelihood can be found once a quantum system has reached a ground state. Through the use of the double well function and the CEC2013 test suite, controlled experiments are conducted to perform a comprehensive performance analysis of the mean strategy. The empirical results indicate that implementing the mean strategy not only enhances solution diversity but also yields accurate, efficient, stable, and effective outcomes for finding the optimal solution.<\/jats:p>","DOI":"10.3390\/e26090719","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T03:59:09Z","timestamp":1724644749000},"page":"719","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Dynamical Interpretation of the Mean Strategy"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1099-1659","authenticated-orcid":false,"given":"Fang","family":"Wang","sequence":"first","affiliation":[{"name":"Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610213, China"},{"name":"School of Computer Science and Engineering, Southwest Minzu University, Chengdu 610041, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5876-4650","authenticated-orcid":false,"given":"Peng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Southwest Minzu University, Chengdu 610041, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6213-5902","authenticated-orcid":false,"given":"Yuwei","family":"Jiao","sequence":"additional","affiliation":[{"name":"Sichuan Digital Transportation Technology Co., Ltd., Chengdu 610095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"Volume 4","author":"Eberhart","year":"1995","journal-title":"Proceedings of the IEEE International Conference on Neural Networks"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/CEC.2004.1330875","article-title":"Particle swarm optimization with particles having quantum behavior","volume":"Volume 1","author":"Sun","year":"2004","journal-title":"Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. 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