{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:44:10Z","timestamp":1760240650494,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T00:00:00Z","timestamp":1566518400000},"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) is a search algorithm inspired by the collective behavior of flocking birds and fishes. This algorithm is widely adopted for solving optimization problems involving one objective. The evaluation of the PSO progress is usually measured by the fitness of the best particle and the average fitness of the particles. When several objectives are considered, the PSO may incorporate distinct strategies to preserve nondominated solutions along the iterations. The performance of the multiobjective PSO (MOPSO) is usually evaluated by considering the resulting swarm at the end of the algorithm. In this paper, two indices based on the Shannon entropy are presented, to study the swarm dynamic evolution during the MOPSO execution. The results show that both indices are useful for analyzing the diversity and convergence of multiobjective algorithms.<\/jats:p>","DOI":"10.3390\/e21090827","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T04:38:23Z","timestamp":1566794303000},"page":"827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Shannon Performance in a Multiobjective Particle Swarm Optimization"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3224-4926","authenticated-orcid":false,"given":"E. J. Solteiro","family":"Pires","sequence":"first","affiliation":[{"name":"INESC TEC\u2014INESC Technology and Science (UTAD pole), ECT\u2013UTAD Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-811 Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"J. A. Tenreiro","family":"Machado","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, ISEP\u2014Institute of Engineering, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernadino de Almeida, 4249-015 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4283-1243","authenticated-orcid":false,"given":"P. B. de Moura","family":"Oliveira","sequence":"additional","affiliation":[{"name":"INESC TEC\u2014INESC Technology and Science (UTAD pole), ECT\u2013UTAD Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-811 Vila Real, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2017.06.002","article-title":"A survey on multi-objective evolutionary algorithms for the solution of the environmental\/economic dispatch problems","volume":"38","author":"Qu","year":"2018","journal-title":"Swarm Evol. 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