{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T12:06:34Z","timestamp":1780661194852,"version":"3.54.1"},"reference-count":43,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100006469","name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006469","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Soft Computing"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.asoc.2026.115226","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T06:25:47Z","timestamp":1776234347000},"page":"115226","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Surrogate-assisted backtracking search optimization for two-stage hybrid flow shop scheduling"],"prefix":"10.1016","volume":"199","author":[{"given":"LiangChao","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5162-0224","authenticated-orcid":false,"given":"Yan","family":"Qiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"KaiZhou","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2743-359X","authenticated-orcid":false,"given":"Mohammadhossein","family":"Ghahramani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5125-7082","authenticated-orcid":false,"given":"SiWei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6782-458X","authenticated-orcid":false,"given":"NaiQi","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.asoc.2026.115226_bib1","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1016\/j.cor.2012.10.015","article-title":"A genetic algorithm for two-stage no-wait hybrid flow shop scheduling problem","volume":"40","author":"Wang","year":"2013","journal-title":"Comput. Oper. Res."},{"issue":"12","key":"10.1016\/j.asoc.2026.115226_bib2","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.1080\/00207543.2016.1162341","article-title":"Robust scheduling of a two-stage hybrid flow shop with uncertain interval processing times","volume":"54","author":"Feng","year":"2016","journal-title":"Int. J. Prod. Res"},{"key":"10.1016\/j.asoc.2026.115226_bib3","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2022.118068","article-title":"Adaptive genetic algorithm for two-stage hybrid flow-shop scheduling with sequence-independent setup time and no-interruption requirement","volume":"208","author":"Qiao","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.asoc.2026.115226_bib4","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2024.108299","article-title":"Scheduling analysis of automotive glass manufacturing systems subject to sequence-independent setup time, no-idle machines, and permissive maximum total tardiness constraint","volume":"133","author":"He","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"5","key":"10.1016\/j.asoc.2026.115226_bib5","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1016\/j.cor.2009.08.001","article-title":"A two-stage flow shop scheduling problem on a batching machine and a discrete machine with blocking and shared setup times","volume":"37","author":"Gong","year":"2010","journal-title":"Comput. Oper. Res."},{"key":"10.1016\/j.asoc.2026.115226_bib6","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/s10878-017-0155-8","article-title":"Two-stage no-wait hybrid flowshop scheduling with inter-stage flexibility","volume":"35","author":"Zhong","year":"2018","journal-title":"J. Comb. Optim."},{"issue":"7","key":"10.1016\/j.asoc.2026.115226_bib7","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/j.cor.2011.10.006","article-title":"Two-stage hybrid flow shop scheduling with dynamic job arrivals","volume":"39","author":"Yao","year":"2012","journal-title":"Comput. Oper. Res."},{"issue":"4","key":"10.1016\/j.asoc.2026.115226_bib8","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1057\/jors.1988.63","article-title":"Two-stage hybrid flowshop scheduling problem","volume":"39","author":"Gupta","year":"1988","journal-title":"J. Oper. Res. Soc."},{"key":"10.1016\/j.asoc.2026.115226_bib9","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2025.113094","article-title":"Multi-search mechanism-improved differential evolution algorithm for the no-wait flow shop scheduling problem","volume":"175","author":"Li","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib10","first-page":"298","article-title":"Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm","volume":"318","author":"Cococcioni","year":"2018","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"10.1016\/j.asoc.2026.115226_bib11","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1080\/00207543.2014.949363","article-title":"A branch-and-bound algorithm for two-stage no-wait hybrid flow-shop scheduling","volume":"53","author":"Wang","year":"2015","journal-title":"Int. J. Prod. Res"},{"issue":"3","key":"10.1016\/j.asoc.2026.115226_bib12","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1016\/j.cor.2011.05.020","article-title":"Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage","volume":"39","author":"Carpov","year":"2012","journal-title":"Comput. Oper. Res."},{"issue":"2","key":"10.1016\/j.asoc.2026.115226_bib13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1080\/0952813X.2012.682752","article-title":"No-wait two stage hybrid flow shop scheduling with genetic and adaptive imperialist competitive algorithms","volume":"25","author":"Moradinasab","year":"2013","journal-title":"J. Exp. Theor. Artif. Intell."},{"key":"10.1016\/j.asoc.2026.115226_bib14","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2022.108040","article-title":"Two-stage no-wait hybrid flow shop with inter-stage flexibility for operating room scheduling","volume":"168","author":"Azaiez","year":"2022","journal-title":"Comput. Ind. Eng."},{"issue":"2","key":"10.1016\/j.asoc.2026.115226_bib15","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0925-5273(03)00011-2","article-title":"A case study in a two-stage hybrid flow shop with setup time and dedicated machines","volume":"86","author":"Lin","year":"2003","journal-title":"Int. J. Prod. Econ."},{"issue":"2","key":"10.1016\/j.asoc.2026.115226_bib16","doi-asserted-by":"crossref","first-page":"46","DOI":"10.13189\/ujeee.2019.060202","article-title":"Particle swarm optimization algorithms for two-stage hybrid flowshop scheduling problem with no-wait","volume":"6","author":"Ghaleb","year":"2019","journal-title":"Univ. J. Electr. Electron. Eng."},{"key":"10.1016\/j.asoc.2026.115226_bib17","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2024.111593","article-title":"A discrete artificial bee colony algorithm and its application in flexible flow shop scheduling with assembly and machine deterioration effect","volume":"159","author":"Li","year":"2024","journal-title":"Appl. Soft Comput."},{"issue":"5","key":"10.1016\/j.asoc.2026.115226_bib18","doi-asserted-by":"crossref","first-page":"6692","DOI":"10.1109\/TII.2022.3192881","article-title":"A population-based iterated greedy algorithm for distributed assembly no-wait flow-shop scheduling problem","volume":"19","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Ind. Inf."},{"key":"10.1016\/j.asoc.2026.115226_bib19","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2023.110908","article-title":"A review of metaheuristic algorithms for solving TSP-based scheduling optimization problems","volume":"148","author":"Toaza","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib20","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2022.101176","article-title":"Comparative study of regression vs pairwise models for surrogate-based heuristic optimisation","volume":"75","author":"Naharro","year":"2022","journal-title":"Swarm Evol. Comput."},{"issue":"1","key":"10.1016\/j.asoc.2026.115226_bib21","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/TEVC.2018.2802784","article-title":"A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization","volume":"23","author":"Pan","year":"2019","journal-title":"IEEE Trans. Evol. Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib22","doi-asserted-by":"crossref","first-page":"4043","DOI":"10.1016\/j.procs.2023.10.400","article-title":"Fitness approximation surrogate-assisted hyper-heuristic for the permutation flowshop problem","volume":"225","author":"Mekki","year":"2023","journal-title":"Procedia Comput. Sci."},{"issue":"6","key":"10.1016\/j.asoc.2026.115226_bib23","doi-asserted-by":"crossref","first-page":"6875","DOI":"10.1007\/s40747-023-01113-4","article-title":"A pairwise ranking estimation model for surrogate-assisted evolutionary algorithms","volume":"9","author":"Harada","year":"2023","journal-title":"Complex Intell. Syst."},{"key":"10.1016\/j.asoc.2026.115226_bib24","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2023.101323","article-title":"A pairwise comparison based surrogate-assisted evolutionary algorithm for expensive multi-objective optimization","volume":"80","author":"Tian","year":"2023","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib25","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2024.109931","article-title":"Surrogate-assisted metaheuristics for the facility location problem with distributed demands on network edges","volume":"188","author":"Sulaman","year":"2024","journal-title":"Comput. Ind. Eng."},{"key":"10.1016\/j.asoc.2026.115226_bib26","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TEVC.2016.2622301","article-title":"A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization","volume":"22","author":"Chugh","year":"2018","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"10.1016\/j.asoc.2026.115226_bib27","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1109\/TSMC.2020.3044418","article-title":"Evolutionary optimization of high-dimensional multiobjective and many-objective expensive problems assisted by a dropout neural network","volume":"52","author":"Guo","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"10.1016\/j.asoc.2026.115226_bib28","first-page":"1","article-title":"MOEA\/DS 3: MOEA\/D using SVM-based surrogates adjusted to subproblems for many-objective optimization","author":"Sonoda","year":"2020","journal-title":"Proc. IEEE Congr. Evol. Comput. (CEC)"},{"issue":"2","key":"10.1016\/j.asoc.2026.115226_bib29","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1109\/TEVC.2020.3017865","article-title":"A classifier-assisted level-based learning swarm optimizer for expensive optimization","volume":"25","author":"Wei","year":"2021","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"6","key":"10.1016\/j.asoc.2026.115226_bib30","first-page":"119","article-title":"A statistical approach to some basic mine valuation problems on the Witwatersrand","volume":"52","author":"Krige","year":"1951","journal-title":"J. South. Afr. Inst. Min. Met."},{"key":"10.1016\/j.asoc.2026.115226_bib31","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1039\/B918972F","article-title":"Support vector machines for classification and regression","volume":"135","author":"Brereton","year":"2010","journal-title":"Analyst"},{"key":"10.1016\/j.asoc.2026.115226_bib32","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn"},{"key":"10.1016\/j.asoc.2026.115226_bib33","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1145\/2939672.2939785","article-title":"XGBoost: A scalable tree boosting system","author":"Chen","year":"2016","journal-title":"Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discov. Data Min."},{"key":"10.1016\/j.asoc.2026.115226_bib34","article-title":"Surrogate-assisted differential evolution for expensive optimization with equality constraints","volume":"154","author":"Zhang","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib35","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2025.102060","article-title":"A surrogate-assisted memetic algorithm for permutation-based combinatorial optimization problems","volume":"98","author":"Ikeguchi","year":"2025","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2026.115226_bib36","doi-asserted-by":"crossref","DOI":"10.1109\/TSMC.2025.3647894","article-title":"A pairwise comparison relation-assisted multiobjective evolutionary neural architecture search method with multipopulation mechanism","author":"Xue","year":"2026","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"1","key":"10.1016\/j.asoc.2026.115226_bib37","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10479-023-05499-9","article-title":"Survey on Lagrangian relaxation for MILP: Importance, challenges, historical review, recent advancements, and opportunities","volume":"333","author":"Bragin","year":"2024","journal-title":"Ann. Oper. Res."},{"issue":"15","key":"10.1016\/j.asoc.2026.115226_bib38","first-page":"8121","article-title":"Backtracking search optimization algorithm for numerical optimization problems","volume":"219","author":"Civicioglu","year":"2013","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"10.1016\/j.asoc.2026.115226_bib39","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1504\/EJIE.2022.119365","article-title":"An improved backtracking search algorithm for the flexible job shop rescheduling problem with new job insertions","volume":"16","author":"Caldeira","year":"2022","journal-title":"Eur. J. Ind. Eng."},{"issue":"2","key":"10.1016\/j.asoc.2026.115226_bib40","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1109\/TEVC.2019.2919762","article-title":"Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems","volume":"24","author":"Cai","year":"2020","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"6","key":"10.1016\/j.asoc.2026.115226_bib41","doi-asserted-by":"crossref","first-page":"3488","DOI":"10.1109\/TCSS.2022.3205699","article-title":"Optimization of inventory space in smart factory for integrated periodic production and delivery scheduling","volume":"10","author":"Chen","year":"2023","journal-title":"IEEE Trans. Comput. Soc. Syst."},{"key":"10.1016\/j.asoc.2026.115226_bib42","first-page":"2825","article-title":"Scikit-learn","volume":"12","author":"Pedregosa","year":"2011","journal-title":"Mach. Learn. Python J. Mach. Learn. Res"},{"key":"10.1016\/j.asoc.2026.115226_bib43","first-page":"2623","article-title":"Optuna: a next-generation hyperparameter optimization framework","author":"Akiba","year":"2019","journal-title":"Proc. 25th ACM SIGKDD Int. Conf. Knowl. Discov. Data Min."}],"container-title":["Applied Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626006745?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626006745?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T11:29:29Z","timestamp":1780658969000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1568494626006745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":43,"alternative-id":["S1568494626006745"],"URL":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115226","relation":{},"ISSN":["1568-4946"],"issn-type":[{"value":"1568-4946","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Surrogate-assisted backtracking search optimization for two-stage hybrid flow shop scheduling","name":"articletitle","label":"Article Title"},{"value":"Applied Soft Computing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115226","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115226"}}