{"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":1781196293711,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,27]],"date-time":"2021-03-27T00:00:00Z","timestamp":1616803200000},"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 swarm intelligence algorithm has become an important method to solve optimization problems because of its excellent self-organization, self-adaptation, and self-learning characteristics. However, when a traditional swarm intelligence algorithm faces high and complex multi-peak problems, population diversity is quickly lost, which leads to the premature convergence of the algorithm. In order to solve this problem, dimension entropy is proposed as a measure of population diversity, and a diversity control mechanism is proposed to guide the updating of the swarm intelligence algorithm. It maintains the diversity of the algorithm in the early stage and ensures the convergence of the algorithm in the later stage. Experimental results show that the performance of the improved algorithm is better than that of the original algorithm.<\/jats:p>","DOI":"10.3390\/e23040397","type":"journal-article","created":{"date-parts":[[2021,3,28]],"date-time":"2021-03-28T22:09:01Z","timestamp":1616969341000},"page":"397","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Diversity Model Based on Dimension Entropy and Its Application to Swarm Intelligence Algorithm"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5466-7092","authenticated-orcid":false,"given":"Hongwei","family":"Kang","sequence":"first","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengfan","family":"Bei","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingping","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingyi","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,27]]},"reference":[{"key":"ref_1","first-page":"49","article-title":"Summaries on Some Novel Bionic Optimization Algorithms","volume":"18","author":"Jin","year":"2019","journal-title":"Softw. 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