{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T21:56:10Z","timestamp":1777067770508,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T00:00:00Z","timestamp":1680134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Initiation Foundation of Anhui Polytechnic University","award":["2022YQQ002"],"award-info":[{"award-number":["2022YQQ002"]}]},{"name":"Research Initiation Foundation of Anhui Polytechnic University","award":["Xjky2022002"],"award-info":[{"award-number":["Xjky2022002"]}]},{"name":"Research Initiation Foundation of Anhui Polytechnic University","award":["JCKJ2022B01"],"award-info":[{"award-number":["JCKJ2022B01"]}]},{"name":"Anhui Polytechnic University Research Project","award":["2022YQQ002"],"award-info":[{"award-number":["2022YQQ002"]}]},{"name":"Anhui Polytechnic University Research Project","award":["Xjky2022002"],"award-info":[{"award-number":["Xjky2022002"]}]},{"name":"Anhui Polytechnic University Research Project","award":["JCKJ2022B01"],"award-info":[{"award-number":["JCKJ2022B01"]}]},{"name":"Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices","award":["2022YQQ002"],"award-info":[{"award-number":["2022YQQ002"]}]},{"name":"Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices","award":["Xjky2022002"],"award-info":[{"award-number":["Xjky2022002"]}]},{"name":"Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices","award":["JCKJ2022B01"],"award-info":[{"award-number":["JCKJ2022B01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In real-world production processes, the same enterprise often has multiple factories or one factory has multiple production lines, and multiple objectives need to be considered in the production process. A dual-population genetic algorithm with Q-learning is proposed to minimize the maximum completion time and the number of tardy jobs for distributed hybrid flow shop scheduling problems, which have some symmetries in machines. Multiple crossover and mutation operators are proposed, and only one search strategy combination, including one crossover operator and one mutation operator, is selected in each iteration. A population assessment method is provided to evaluate the evolutionary state of the population at the initial state and after each iteration. Two populations adopt different search strategies, in which the best search strategy is selected for the first population and the search strategy of the second population is selected under the guidance of Q-learning. Experimental results show that the dual-population genetic algorithm with Q-learning is competitive for solving multi-objective distributed hybrid flow shop scheduling problems.<\/jats:p>","DOI":"10.3390\/sym15040836","type":"journal-article","created":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T05:22:14Z","timestamp":1680153734000},"page":"836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A Dual-Population Genetic Algorithm with Q-Learning for Multi-Objective Distributed Hybrid Flow Shop Scheduling Problem"],"prefix":"10.3390","volume":"15","author":[{"given":"Jidong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Anhui Institute of Information Technology, Wuhu 241000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1440-9849","authenticated-orcid":false,"given":"Jingcao","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"AnHui Key Laboratory of Detection Technology and Energy Saving Devices, AnHui Polytechnic University, Wuhu 241000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100992","DOI":"10.1016\/j.swevo.2021.100992","article-title":"An improved iterated greedy algorithm for the energy-efficient blocking hybrid flow shop scheduling problem","volume":"69","author":"Qin","year":"2022","journal-title":"Swarm Evol. 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