{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:53:03Z","timestamp":1760057583387,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T00:00:00Z","timestamp":1739232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a Distributed Mixed No-Idle Permutation Flowshop Scheduling Problem with Sequence-Dependent Setup Times (DMNIPFSP\/SDST) is studied. Firstly, a multi-objective optimization model with completion time (makespan), Total Energy Consumption (TEC), and Total Tardiness (TT) as objectives is established. Based on problem characteristics and multi-objective characteristics, a Q-Learning Evolutionary Algorithm (QLEA) is proposed. Secondly, in order to improve the quality and diversity of the initial solution, two improved initialization strategies are proposed. Based on the characteristics of the problem solved (In the distributed system, symmetry design is adopted to ensure that the load of each workstation is relatively balanced in different time periods, avoid resource waste or bottleneck, and achieve the goal of no idle.), a novel population updating mechanism is designed to balance the ability of global exploration and local development of the algorithm. At the same time, a variable neighborhood local search based on Q-Learning is used to refine the non-dominated solution, thus guiding the population evolution. Finally, the simulation results show that this method has good performance in solving the multi-objective DMNIPFSP\/SDST and can provide good economic benefits for enterprises.<\/jats:p>","DOI":"10.3390\/sym17020276","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T11:01:08Z","timestamp":1739271668000},"page":"276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Q-Learning Evolutionary Algorithm for Solving the Distributed Mixed No-Idle Permutation Flowshop Scheduling Problem"],"prefix":"10.3390","volume":"17","author":[{"given":"Fangchi","family":"Zeng","sequence":"first","affiliation":[{"name":"School of Mechanical and Transportation Engineering, Hunan University, Changsha, Hunan 410082, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8004-6030","authenticated-orcid":false,"given":"Junjia","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Mechanical and Transportation Engineering, Hunan University, Changsha, Hunan 410082, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116921","DOI":"10.1016\/j.eswa.2022.116921","article-title":"A discrete learning fruit fly algorithm based on knowledge for the distributed no-wait flow shop scheduling with due windows","volume":"198","author":"Zhu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, X., Yuan, J., and Chen, X. (2022). Development of an improved water cycle algorithm for solving an energy-efficient disassembly-line balancing problem. Processes, 10.","DOI":"10.3390\/pr10101908"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.cor.2009.06.019","article-title":"The distributed permutation flowshop scheduling problem","volume":"37","author":"Naderi","year":"2010","journal-title":"Comput. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"100742","DOI":"10.1016\/j.swevo.2020.100742","article-title":"An effective iterated greedy method for the distributed permutation flowshop scheduling problem with sequence-dependent setup times","volume":"59","author":"Huang","year":"2020","journal-title":"Swarm Evol. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1080\/01605682.2022.2039569","article-title":"Heuristics to optimize total completion time subject to makespan in no-wait flow shops with sequence-dependent setup times","volume":"74","author":"Almeida","year":"2023","journal-title":"J. Oper. Res. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108128","DOI":"10.1016\/j.cie.2022.108128","article-title":"A new hybridization of adaptive large neighborhood search with constraint programming for open shop scheduling with sequence-dependent setup times","volume":"168","author":"Abreu","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108328","DOI":"10.1016\/j.knosys.2022.108328","article-title":"An effective metaheuristic with a differential flight strategy for the distributed permutation flowshop scheduling problem with sequence-dependent setup times","volume":"242","author":"Guo","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108366","DOI":"10.1016\/j.cie.2022.108366","article-title":"An iterated greedy algorithm for distributed blocking flow shop with setup times and maintenance operations to minimize makespan","volume":"171","author":"Miyata","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105733","DOI":"10.1016\/j.cor.2022.105733","article-title":"An evolution strategy approach for the distributed permutation flowshop scheduling problem with sequence-dependent setup times","volume":"142","author":"Karabulut","year":"2022","journal-title":"Comput. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1109\/JSYST.2021.3076481","article-title":"A knowledge-based multiobjective memetic algorithm for green job shop scheduling with variable machining speeds","volume":"16","author":"Lu","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1016\/j.cor.2006.08.016","article-title":"Minimising total tardiness in the m-machine flowshop problem: A review and evaluation of heuristics and metaheuristics","volume":"35","author":"Vallada","year":"2008","journal-title":"Comput. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1080\/00207543.2018.1457812","article-title":"Minimising makespan in distributed mixed no-idle flowshops","volume":"57","author":"Cheng","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"257","DOI":"10.23919\/CSMS.2021.0027","article-title":"A review of reinforcement learning based intelligent optimization for manufacturing scheduling","volume":"1","author":"Wang","year":"2021","journal-title":"Complex Syst. Model. Simul."},{"key":"ref_14","unstructured":"Kool, W., van Hoof, H., and Welling, M. (2018). Attention, Learn to Solve Routing Problems. arXiv."},{"key":"ref_15","unstructured":"Bello, I., Pham, H., Le, Q.V., Norouzi, M., and Bengio, S. (2017). Neural combinatorial optimization with reinforcement learning. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106778","DOI":"10.1016\/j.cie.2020.106778","article-title":"A self-learning genetic algorithm based on reinforcement learning for flexible job-shop scheduling problem","volume":"149","author":"Chen","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s10845-018-1454-3","article-title":"Adaptive job shop scheduling strategy based on weighted Q-learning algorithm","volume":"31","author":"Wang","year":"2020","journal-title":"J. Intell. Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106208","DOI":"10.1016\/j.asoc.2020.106208","article-title":"Dynamic scheduling for flexible job shop with new job insertions by deep reinforcement learning","volume":"91","author":"Luo","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117380","DOI":"10.1016\/j.eswa.2022.117380","article-title":"A reinforcement learning based RMOEA\/D for bi-objective fuzzy flexible job shop scheduling","volume":"203","author":"Li","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"108371","DOI":"10.1016\/j.asoc.2021.108371","article-title":"An adaptive artificial bee colony with reinforcement learning for distributed threestage assembly scheduling with maintenance","volume":"117","author":"Wang","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5965","DOI":"10.1007\/s40747-024-01482-4","article-title":"An improved fruit fly optimization algorithm with Q-learning for solving distributed permutation flow shop scheduling problems","volume":"10","author":"Zhao","year":"2024","journal-title":"Complex Intell. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105492","DOI":"10.1016\/j.asoc.2019.105492","article-title":"Effective constructive heuristics and meta-heuristics for the distributed assembly permutation flowshop scheduling problem","volume":"81","author":"Pan","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/S0377-2217(00)00137-5","article-title":"Constructive and composite heuristic solutions to the P\/\/\u2211 Ci scheduling problem","volume":"132","author":"Liu","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/4235.797969","article-title":"Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach","volume":"3","author":"Zitzler","year":"1999","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ejor.2004.01.022","article-title":"Solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics","volume":"165","author":"Ruiz","year":"2005","journal-title":"Eur. J. Oper. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1016\/j.ejor.2006.07.029","article-title":"An iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives","volume":"187","author":"Ruiz","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"110252","DOI":"10.1016\/j.knosys.2023.110252","article-title":"A multi-class teaching\u2013learning-based optimization for multi-objective distributed hybrid flow shop scheduling","volume":"263","author":"Lei","year":"2023","journal-title":"Knowl. Based Syst."},{"key":"ref_29","unstructured":"Montgomery, D.C. (2017). Design and Analysis of Experiments, John Wiley & Sons."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1007\/s40747-022-00830-6","article-title":"Improved NSGA-II for energy-efficient distributed no-wait flow-shop with sequence-dependent setup time","volume":"9","author":"Zeng","year":"2023","journal-title":"Complex Intell. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"117555","DOI":"10.1016\/j.eswa.2022.117555","article-title":"A pareto-based hybrid iterated greedy algorithm for energy-efficient scheduling of distributed hybrid flowshop","volume":"204","author":"Lu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.swevo.2016.06.002","article-title":"A competitive memetic algorithm for multi-objective distributed permutation flow shop scheduling problem","volume":"32","author":"Deng","year":"2017","journal-title":"Swarm Evol. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wilcoxon, F. (1992). Individual Comparisons by Ranking Methods, Springer.","DOI":"10.1007\/978-1-4612-4380-9_16"},{"key":"ref_34","first-page":"910","article-title":"Research on the scheduling problem of public transportation vehicles considering abnormal train numbers","volume":"43","author":"Yu","year":"2023","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_35","first-page":"1446","article-title":"Multi warehouse order splitting with time windows and joint optimization method for heterogeneous vehicle paths","volume":"43","author":"Tanng","year":"2023","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_36","first-page":"1232","article-title":"Research on Optimization of Multi tank Depot and Multi trip Gas Station Distribution Considering Tank Capacity Limitation","volume":"43","author":"Liu","year":"2023","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_37","first-page":"1736","article-title":"Research on Multi warehouse Collaborative Product Selection Strategy in Manufacturing Production Logistics","volume":"43","author":"Li","year":"2023","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_38","first-page":"1978","article-title":"A Crowdsourcing Logistics Task Allocation Model for Dual Agent Collaborative Learning","volume":"43","author":"Xiangi","year":"2023","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_39","first-page":"100598","article-title":"A distributed permutation flow-shop considering sustainability criteria and real-time scheduling","volume":"39","author":"Lyne","year":"2024","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"106454","DOI":"10.1016\/j.engappai.2023.106454","article-title":"Problem-specific knowledge MOEA\/D for energy-efficient scheduling of distributed permutation flow shop in heterogeneous factories","volume":"123","author":"Luo","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"110022","DOI":"10.1016\/j.asoc.2023.110022","article-title":"An effective hyper heuristic-based memetic algorithm for the distributed assembly permutation flow-shop scheduling problem","volume":"135","author":"Song","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.jmsy.2024.03.009","article-title":"An improved genetic programming hyper-heuristic for the dynamic flexible job shop scheduling problem with reconfigurable manufacturing cells","volume":"74","author":"Guo","year":"2024","journal-title":"J. Manuf. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jmsy.2024.03.002","article-title":"Flexible job shop scheduling with stochastic machine breakdowns by an improved tuna swarm optimization algorithm","volume":"74","author":"Fan","year":"2024","journal-title":"J. Manuf. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.jmsy.2024.03.005","article-title":"An improved memetic algorithm for multi-objective resource-constrained flexible job shop inverse scheduling problem: An application for machining workshop","volume":"74","author":"Wei","year":"2024","journal-title":"J. Manuf. Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/276\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:31:14Z","timestamp":1760027474000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,11]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020276"],"URL":"https:\/\/doi.org\/10.3390\/sym17020276","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,11]]}}}