{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:51:32Z","timestamp":1776750692367,"version":"3.51.2"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61573264"],"award-info":[{"award-number":["61573264"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The distributed assembly scheduling problem with a hybrid-flow shop for fabrication is seldom studied, and some real-life constraints such as factory eligibility are seldom handled. In this study, a distributed assembly hybrid-flow shop-scheduling problem (DAHFSP) with factory eligibility is investigated, which has some symmetries on machines. A shuffled frog-leaping algorithm with cooperations (CSFLA) is applied to minimize makespan. A problem-related feature is used. Memeplexes are evaluated, and group 1, with the two best memeplexes, and group 2, with the two worst memeplexes, are formed. A new cooperation between memeplexes and an adaptive search strategy are implemented in groups 1 and 2, respectively. An adaptive cooperation between groups 1 and 2 is also given. Population shuffling is executed every T generations. A number of computational experiments are conducted. Computational results demonstrate that new strategies are effective and CSFLA is a very competitive algorithm for DAHFSP with factory eligibility.<\/jats:p>","DOI":"10.3390\/sym15040786","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T04:31:05Z","timestamp":1679632265000},"page":"786","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Shuffled Frog-Leaping Algorithm with Cooperations for Distributed Assembly Hybrid-Flow Shop Scheduling with Factory Eligibility"],"prefix":"10.3390","volume":"15","author":[{"given":"Deming","family":"Lei","sequence":"first","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,23]]},"reference":[{"key":"ref_1","first-page":"68879","article-title":"Solving distributed hybrid flowshop scheduling problems by a hybrid brain storm optimization algorithm","volume":"7","author":"Hao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105536","DOI":"10.1016\/j.knosys.2020.105536","article-title":"A cooperative coevolution algorithm for multi-objective fuzzy distributed hybrid flow shop","volume":"194","author":"Zheng","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105527","DOI":"10.1016\/j.knosys.2020.105527","article-title":"Modeling and multi-neighborhood iterated greedy algorithm for distributed hybrid flow shop scheduling problem","volume":"194","author":"Shao","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"105482","DOI":"10.1016\/j.cor.2021.105482","article-title":"Effective constructive heuristics for distributed no-wait flexible flow shop scheduling problem","volume":"136","author":"Shao","year":"2021","journal-title":"Comput. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115453","DOI":"10.1016\/j.eswa.2021.115453","article-title":"Multi-objective evolutionary algorithm based on multiple neighborhoods local search for multi-objective distributed hybrid flow shop scheduling problem","volume":"183","author":"Shao","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3880","DOI":"10.1080\/00207543.2020.1753897","article-title":"A discrete artificial bee colony algorithm for distributed hybrid flowshop scheduling problem with sequence-dependent setup times","volume":"59","author":"Li","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1109\/TEVC.2021.3106168","article-title":"A cooperative memetic algorithm with learning-based agent for energy-aware distributed hybrid flow-shop scheduling","volume":"26","author":"Wang","year":"2022","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3951","DOI":"10.3233\/JIFS-202963","article-title":"A memetic algorithm for energy-efficient distributed re-entrant hybrid flow shop scheduling problem","volume":"41","author":"Geng","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s12293-021-00329-6","article-title":"Integrated production and distribution scheduling in distributed hybrid flow shops","volume":"13","author":"Qin","year":"2021","journal-title":"Memet. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Shao, Z.S., Shao, W.S., and Pi, D.C. (2022). A learning-Based Selection Hyper-Heuristic for Distributed Heterogeneous Hybrid Blocking Flow-shop Scheduling. IEEE Trans. Emerg. Top. Comput. Intell., Available online: https:\/\/ieeexplore.ieee.org\/abstract\/document\/9782097.","DOI":"10.1109\/TETCI.2022.3174915"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117256","DOI":"10.1016\/j.eswa.2022.117256","article-title":"A collaborative iterative greedy algorithm for the scheduling of distributed heterogeneous hybrid flow shop with blocking constraints","volume":"201","author":"Qin","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cai, J.C., Lei, D.M., Wang, J., and Wang, L. (2022). A novel shuffled frog-leaping algorithm with reinforcement learning for distributed assembly hybrid flow shop scheduling. Int. J. Prod. Res., Available online: https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00207543.2022.2031331.","DOI":"10.1080\/00207543.2022.2031331"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.eswa.2017.09.032","article-title":"Minimizing makespan for the distributed hybrid flowshop scheduling problem with multiprocessor tasks","volume":"92","author":"Ying","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103540","DOI":"10.1016\/j.engappai.2020.103540","article-title":"Dynamic shuffled frog-leaping algorithm for distributed hybrid flow shop scheduling with multiprocessor tasks","volume":"90","author":"Cai","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"646","DOI":"10.26599\/TST.2021.9010007","article-title":"Decomposition-based multi-objective optimization for energy-aware distributed hybrid flow shop scheduling with multiprocessor tasks","volume":"26","author":"Jiang","year":"2021","journal-title":"Tsinghua Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106638","DOI":"10.1016\/j.cie.2020.106638","article-title":"An improved artificial bee colony algorithm for distributed heterogeneous hybrid flow-shop scheduling problem with sequence-dependent setup times","volume":"147","author":"Li","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5404","DOI":"10.1080\/00207543.2020.1780333","article-title":"A shuffled frog-leaping algorithm with memeplex quality for bi-objective distributed scheduling in hybrid flow shop","volume":"59","author":"Cai","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1080\/0305215X.2019.1674295","article-title":"Solving distributed two-stage hybrid flow-shop scheduling using a shuffled frog-leaping algorithm with memeplex grouping","volume":"52","author":"Lei","year":"2020","journal-title":"Eng. Optimiz."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4159","DOI":"10.3233\/JIFS-210764","article-title":"Diversified teaching-learning-based optimization for fuzzy two-stage hybrid flow shop scheduling with setup time","volume":"41","author":"Lei","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5292","DOI":"10.1080\/00207543.2013.807955","article-title":"The distributed assembly permutation flowshop scheduling problem","volume":"51","author":"Hatami","year":"2013","journal-title":"Int. J. Prod. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.cor.2014.02.005","article-title":"Minimizing the total completion time in a distributed two stage assembly system with setup times","volume":"47","author":"Xiong","year":"2014","journal-title":"Comput. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.cie.2018.09.007","article-title":"Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment","volume":"125","author":"Zhang","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"100785","DOI":"10.1016\/j.swevo.2020.100785","article-title":"A matrix-cube-based estimation of distribution algorithm for the distributed assembly permutation flow-shop scheduling problem","volume":"60","author":"Zhang","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"ref_24","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 three-stage assembly scheduling with maintenance","volume":"117","author":"Wang","year":"2022","journal-title":"Appl. Soft. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1080\/0305215X.2021.1886289","article-title":"Distributed assembly permutation flow-shop scheduling problem with sequence-dependent set-up times using a novel biogeography-based optimization algorithm","volume":"54","author":"Huang","year":"2022","journal-title":"Eng. Optimiz."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/03052150500384759","article-title":"Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization","volume":"38","author":"Eusuff","year":"2006","journal-title":"Eng. Optimiz."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.1007\/s40747-021-00400-2","article-title":"A cooperated shuffled frog-leaping algorithm for distributed energy-efficient hybrid flow shop scheduling with fuzzy processing time","volume":"7","author":"Cai","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s00500-007-0210-y","article-title":"Solving a bi-criteria permutation flow-shop problem using shuffled frog-leaping algorithm","volume":"12","author":"Mirzaei","year":"2008","journal-title":"Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s00170-010-2775-3","article-title":"An effective shuffled frog-leaping algorithm for lot-streaming flow shop scheduling problem","volume":"52","author":"Pan","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1409","DOI":"10.1080\/0305215X.2012.737784","article-title":"An effective shuffled frog-leaping algorithm for solving the hybrid flow-shop scheduling problem with identical parallel machines","volume":"45","author":"Xu","year":"2013","journal-title":"Eng. Optimiz."},{"key":"ref_31","first-page":"191191","article-title":"Fuzzy distributed hybrid flow shop scheduling problem with heterogeneous factory and unrelated parallel machine: A shuffled frog leaping algorithm with collaboration of multiple search strategies","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.ins.2010.07.016","article-title":"An improved shuffled frog-leaping algorithm with extremal optimisation for continuous optimisation","volume":"192","author":"Li","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1840112","DOI":"10.1142\/S0217984918401127","article-title":"An improved SFLA for flexible job shop scheduling problem considering energy consumption","volume":"32","author":"Zhang","year":"2018","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"644","DOI":"10.2507\/IJSIMM16(4)7.400","article-title":"An effective use of hybrid metaheuristics algorithm for job shop scheduling problem","volume":"16","author":"Zhang","year":"2018","journal-title":"Int. J. Simul. Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/s10898-018-0705-3","article-title":"Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines","volume":"78","author":"Kong","year":"2020","journal-title":"J. Glob. Optim."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1007\/s00170-013-4940-y","article-title":"An effective shuffled frog-leaping algorithm for hybrid flow-shop scheduling with multiprocessor tasks","volume":"68","author":"Xu","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3226","DOI":"10.1080\/00207543.2017.1401241","article-title":"Scheduling distributed flowshops with flexible assembly and set-up time to minimise makespan","volume":"56","author":"Zhang","year":"2018","journal-title":"Int. J. Prod. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.cie.2017.01.006","article-title":"Improved discrete cuckoo optimization algorithm for the three-stage assembly flowshop scheduling problem","volume":"105","author":"Komaki","year":"2017","journal-title":"Comput. Ind. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1504\/IJAAC.2021.118529","article-title":"An improved whale optimisation algorithm for distributed assembly flow shop with crane transportation","volume":"15","author":"Li","year":"2021","journal-title":"Int. J. Autom. Control."},{"key":"ref_40","unstructured":"Montgomery, D.C. (2008). Design and Analysis of Experiments, Wiley."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/4\/786\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:01:53Z","timestamp":1760122913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/4\/786"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,23]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["sym15040786"],"URL":"https:\/\/doi.org\/10.3390\/sym15040786","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,23]]}}}