{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T23:01:04Z","timestamp":1776207664905,"version":"3.50.1"},"reference-count":109,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T00:00:00Z","timestamp":1645660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010096","name":"Secretariat of Public Education","doi-asserted-by":"publisher","award":["UTCHI-014"],"award-info":[{"award-number":["UTCHI-014"]}],"id":[{"id":"10.13039\/100010096","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Subsecretariat of Higher Education","award":["UTCHI-014"],"award-info":[{"award-number":["UTCHI-014"]}]},{"name":"Technological University of Chihuahua","award":["UTCHI-014"],"award-info":[{"award-number":["UTCHI-014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Companies are constantly changing in their organization and the way they treat information. In this sense, relevant data analysis processes arise for decision makers. Similarly, to perform decision-making analyses, multi-criteria and metaheuristic methods represent a key tool for such analyses. These analysis methods solve symmetric and asymmetric problems with multiple criteria. In such a way, the symmetry transforms the decision space and reduces the search time. Therefore, the objective of this research is to provide a classification of the applications of multi-criteria and metaheuristic methods. Furthermore, due to the large number of existing methods, the article focuses on the particle swarm algorithm (PSO) and its different extensions. This work is novel since the review of the literature incorporates scientific articles, patents, and copyright registrations with applications of the PSO method. To mention some examples of the most relevant applications of the PSO method; route planning for autonomous vehicles, the optimal application of insulin for a type 1 diabetic patient, robotic harvesting of agricultural products, hybridization with multi-criteria methods, among others. Finally, the contribution of this article is to propose that the PSO method involves the following steps: (a) initialization, (b) update of the local optimal position, and (c) obtaining the best global optimal position. Therefore, this work contributes to researchers not only becoming familiar with the steps, but also being able to implement it quickly. These improvements open new horizons for future lines of research.<\/jats:p>","DOI":"10.3390\/sym14030455","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T21:11:52Z","timestamp":1645737112000},"page":"455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":78,"title":["PSO, a Swarm Intelligence-Based Evolutionary Algorithm as a Decision-Making Strategy: A Review"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1326-908X","authenticated-orcid":false,"given":"Dynhora-Danheyda","family":"Ram\u00edrez-Ochoa","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Ju\u00e1rez (UACJ), Juarez City 32310, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2541-4595","authenticated-orcid":false,"given":"Luis Asunci\u00f3n","family":"P\u00e9rez-Dom\u00ednguez","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Ju\u00e1rez (UACJ), Juarez City 32310, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7753-2545","authenticated-orcid":false,"given":"Erwin-Ad\u00e1n","family":"Mart\u00ednez-G\u00f3mez","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Ju\u00e1rez (UACJ), Juarez City 32310, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4778-8873","authenticated-orcid":false,"given":"David","family":"Luviano-Cruz","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Ju\u00e1rez (UACJ), Juarez City 32310, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107241","DOI":"10.1016\/j.cie.2021.107241","article-title":"Industry 4.0 reference architectures: State of the art and future trends","volume":"156","author":"Nakagawa","year":"2021","journal-title":"Comput. 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