{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:24:21Z","timestamp":1762341861758,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T00:00:00Z","timestamp":1657670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science and Engineering Research Counsel of Canada"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming.<\/jats:p>","DOI":"10.3390\/a15070246","type":"journal-article","created":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T22:06:00Z","timestamp":1657749960000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot Streaming"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3107-9263","authenticated-orcid":false,"given":"Danial","family":"Rooyani","sequence":"first","affiliation":[{"name":"School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7717-7686","authenticated-orcid":false,"given":"Fantahun","family":"Defersha","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106605","DOI":"10.1016\/j.cie.2020.106605","article-title":"An efficient two-stage genetic algorithm for a flexible job-shop scheduling problem with sequence dependent attached\/detached setup, machine release date and lag-time","volume":"147","author":"Defersha","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1080\/00207543.2011.574952","article-title":"Jobshop lot streaming with routing flexibility, sequence-dependent setups, machine release dates and lag time","volume":"50","author":"Defersha","year":"2012","journal-title":"Int. J. Prod. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1080\/00207540412331325396","article-title":"A comprehensive review of lot streaming","volume":"43","author":"Chang","year":"2005","journal-title":"Int. J. Prod. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1086\/294867","article-title":"A system for managing job shop production","volume":"34","author":"Reiter","year":"1966","journal-title":"J. Buss."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7023","DOI":"10.1080\/00207543.2013.774506","article-title":"A review of lot streaming","volume":"51","author":"Cheng","year":"2013","journal-title":"Int. J. Prod. Res."},{"key":"ref_6","first-page":"2003","article-title":"An integrated tabu search algorithm for the lot streaming problem in flexible job shops","volume":"46","author":"Lu","year":"2012","journal-title":"J. Shanghai Jiaotong Univ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1080\/00207540802660544","article-title":"A hybrid genetic algorithm for flowshop lot streaming with setups and variable sublots","volume":"48","author":"Defersha","year":"2010","journal-title":"Int. J. Prod. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1007\/s10845-012-0650-9","article-title":"A new genetic algorithm for lot-streaming flow shop scheduling with limited capacity buffers","volume":"24","author":"Ventura","year":"2013","journal-title":"J. Intell. Manuf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2211","DOI":"10.1080\/00207543.2013.848492","article-title":"An improved NSGA-II algorithm for multi-objective lot-streaming flow shop scheduling problem","volume":"52","author":"Han","year":"2014","journal-title":"Int. J. Prod. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.swevo.2017.06.003","article-title":"An improved migrating birds optimization for an integrated lot-streaming flow shop scheduling problem","volume":"38","author":"Meng","year":"2018","journal-title":"Swarm Evol. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.knosys.2018.02.029","article-title":"A novel hybrid multi-objective artificial bee colony algorithm for blocking lot-streaming flow shop scheduling problems","volume":"148","author":"Gong","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s10288-020-00449-8","article-title":"Dynamic programming algorithms and Lagrangian lower bounds for a discrete lot streaming problem in a two-machine flow shop","volume":"19","author":"Alfieri","year":"2021","journal-title":"4OR"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1080\/01605682.2020.1796533","article-title":"Speed scaling in two-machine lot-streaming flow shops with consistent sublots","volume":"72","author":"Fang","year":"2021","journal-title":"J. Oper. Res. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107874","DOI":"10.1016\/j.knosys.2021.107874","article-title":"A two-stage discrete water wave optimization algorithm for the flowshop lot-streaming scheduling problem with intermingling and variable lot sizes","volume":"238","author":"Wang","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.1080\/00207549608905076","article-title":"The impact of lot sizing and sequencing on manufacturing performance in a two-stage hybrid flow shop","volume":"34","author":"Tsubone","year":"1996","journal-title":"Int. J. Prod. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/S0305-0483(97)00015-7","article-title":"Transfer batch scheduling for a two-stage flowshop with identical parallel machines at each stage","volume":"25","author":"Kim","year":"1997","journal-title":"Omega"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.ijpe.2004.04.005","article-title":"Multi-job lot streaming to minimize the mean completion time in m-1 hybrid flowshops","volume":"96","author":"Zhang","year":"2005","journal-title":"Int. J. Prod. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.ejor.2006.06.066","article-title":"Single-job lot streaming in m - 1 two-stage hybrid flowshops","volume":"187","author":"Liu","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10898-015-0298-z","article-title":"Two-stage, single-lot, lot streaming problem for a 1 + 2 hybrid flow shop","volume":"66","author":"Cheng","year":"2016","journal-title":"J. Glob. Optim."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6893","DOI":"10.1080\/00207543.2019.1571251","article-title":"Two-stage hybrid flow shop batching and lot streaming with variable sublots and sequence-dependent setups","volume":"57","author":"Wang","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00170-011-3798-0","article-title":"Mathematical model and parallel genetic algorithm for hybrid flexible flowshop lot streaming problem","volume":"62","author":"Defersha","year":"2012","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s00170-013-5265-6","article-title":"Multi-job lot streaming to minimize the weighted completion time in a hybrid flow shop scheduling problem with work shift constraint","volume":"70","author":"Nejati","year":"2014","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.asoc.2016.12.021","article-title":"An effective modified migrating birds optimization for hybrid flowshop scheduling problem with lot streaming","volume":"52","author":"Zhang","year":"2017","journal-title":"Appl. Soft Comput. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"89782","DOI":"10.1109\/ACCESS.2020.2993881","article-title":"Improved Migrating Birds Optimization Algorithm to Solve Hybrid Flowshop Scheduling Problem with Lot-Streaming","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1007\/s10479-018-2969-x","article-title":"Multi-objective genetic algorithm for energy-efficient hybrid flow shop scheduling with lot streaming","volume":"290","author":"Chen","year":"2020","journal-title":"Ann. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100600","DOI":"10.1016\/j.swevo.2019.100600","article-title":"Efficient multi-objective algorithm for the lot-streaming hybrid flowshop with variable sub-lots","volume":"52","author":"Li","year":"2020","journal-title":"Swarm Evol. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107819","DOI":"10.1016\/j.knosys.2021.107819","article-title":"An automatic multi-objective evolutionary algorithm for the hybrid flowshop scheduling problem with consistent sublots","volume":"238","author":"Zhang","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.rcim.2007.01.001","article-title":"Lot streaming for product assembly in job shop environment","volume":"24","author":"Chan","year":"2008","journal-title":"Robot. -Comput.-Integr. Manuf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1016\/j.cie.2009.04.002","article-title":"A resource-constrained assembly job shop scheduling problem with Lot Streaming technique","volume":"57","author":"Wong","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_30","unstructured":"Chan, F.T., Wong, T.C., and Chan, P.L. (2004, January 2\u20134). Equal size lot streaming to job-shop scheduling problem using genetic algorithms. Proceedings of the IEEE International Symposium on Intelligent Control, Taipei, Taiwan."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3387","DOI":"10.1080\/00207540701577369","article-title":"The application of genetic algorithms to lot streaming in a job-shop scheduling problem","volume":"47","author":"Chan","year":"2009","journal-title":"Int. J. Prod. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1080\/09511920902866104","article-title":"Lot streaming for customer order scheduling problem in job shop environments","volume":"22","author":"Liu","year":"2009","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1080\/00207543.2012.657255","article-title":"Lot streaming multiple jobs with values exponentially deteriorating over time in a job-shop environment","volume":"51","author":"Liu","year":"2013","journal-title":"Int. J. Prod. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4930","DOI":"10.1080\/00207543.2013.784404","article-title":"Scheduling job shop with lot streaming and transportation through a modified artificial bee colony","volume":"51","author":"Lei","year":"2013","journal-title":"Int. J. Prod. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1080\/00207543.2014.889328","article-title":"An effective genetic algorithm for flexible job-shop scheduling with overlapping in operations","volume":"52","author":"Demir","year":"2014","journal-title":"Int. J. Prod. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5278","DOI":"10.1080\/00207543.2018.1467575","article-title":"A hybrid artificial bee colony algorithm for a flexible job shop scheduling problem with overlapping in operations","volume":"56","author":"Meng","year":"2018","journal-title":"Int. J. Prod. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"6391","DOI":"10.1080\/00207543.2017.1346322","article-title":"Flexible job shop scheduling with lot streaming and sublot size optimisation","volume":"56","author":"Werner","year":"2018","journal-title":"Int. J. Prod. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.cie.2018.02.010","article-title":"Linear programming assisted (not embedded) genetic algorithm for flexible jobshop scheduling with lot streaming","volume":"117","author":"Defersha","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.cie.2019.07.011","article-title":"Production scheduling and lot streaming at flexible job-shops environments using constraint programming","volume":"136","author":"Novas","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1080\/0305215X.2021.1887168","article-title":"Scheduling in a flexible job shop followed by some parallel assembly stations considering lot streaming","volume":"54","author":"Daneshamooz","year":"2022","journal-title":"Eng. Optim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107928","DOI":"10.1016\/j.cie.2021.107928","article-title":"Research on discrete intelligent workshop lot-streaming scheduling with variable sublots under engineer to order","volume":"165","author":"Li","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Sang, H.Y., and Duan, J.H. (2012, January 29\u201331). An efficient discrete artificial bee colony algorithm for total flowtime lot-streaming flowshop. Proceedings of the 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, (FSKD 2012), Chongqing, China.","DOI":"10.1109\/FSKD.2012.6234319"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.ijpe.2012.03.034","article-title":"A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling","volume":"141","author":"Chiang","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.eswa.2016.05.009","article-title":"A population initialization method for evolutionary algorithms based on clustering and Cauchy deviates","volume":"60","author":"Bajer","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1016\/j.camwa.2006.07.013","article-title":"A novel population initialization method for accelerating evolutionary algorithms","volume":"53","author":"Rahnamayan","year":"2007","journal-title":"Comput. Math. Appl."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Luo, J., and El Baz, D. (2018, January 21\u201325). A survey on parallel genetic algorithms for shop scheduling problems. Proceedings of the 2018 IEEE 32nd International Parallel and Distributed Processing Symposium Workshops, (IPDPSW 2018), Vancouver, BC, Canada.","DOI":"10.1109\/IPDPSW.2018.00103"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"6389","DOI":"10.1080\/00207540701441962","article-title":"A parallel genetic algorithm for dynamic cell formation in cellular manufacturing systems","volume":"46","author":"Defersha","year":"2008","journal-title":"Int. J. Prod. Res."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/7\/246\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:49:55Z","timestamp":1760140195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/7\/246"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,13]]},"references-count":47,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["a15070246"],"URL":"https:\/\/doi.org\/10.3390\/a15070246","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,7,13]]}}}