{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T19:21:42Z","timestamp":1780773702100,"version":"3.54.1"},"reference-count":54,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,22]],"date-time":"2022-10-22T00:00:00Z","timestamp":1666396800000},"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 real-life assembly production often has transportation between fabrication and assembly, and the capacity of transportation machine is often considered; however, the previous works are mainly about two-stage distributed assembly scheduling problems. In this study, a distributed energy-efficient assembly scheduling problem (DEASP) with transportation capacity is investigated, in which dedicated parallel machines with symmetry under the given conditions, transportation machines and an assembly machine are used. An adaptive imperialist competitive algorithm (AICA) is proposed to minimize makespan and total energy consumption. A heuristic and an energy-saving rule are used to produce initial solutions. An adaptive assimilation with adaptive global search and an adaptive revolution are implemented, in which neighborhood structures are chosen dynamically, and revolution probability and search times are decided by using the solution quality. The features of the problem are also used effectively. Computational experiments are conducted on a number of instances. The computational results demonstrate that the new strategies of AICA are effective and efficient and AICA can provide promising results for the considered DEASP.<\/jats:p>","DOI":"10.3390\/sym14112225","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T11:53:55Z","timestamp":1666612435000},"page":"2225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity"],"prefix":"10.3390","volume":"14","author":[{"given":"Deming","family":"Lei","sequence":"first","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinlin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.future.2021.10.003","article-title":"An effective hybrid collaborative algorithm for energy-efficient distributed permutation flow-shop inverse scheduling","volume":"128","author":"Mou","year":"2022","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108413","DOI":"10.1016\/j.knosys.2022.108413","article-title":"A hash map-based memetic algorithm for the distributed permutation flowshop scheduling problem with preventive maintenance to minimize total flowtime","volume":"242","author":"Mao","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109502","DOI":"10.1016\/j.asoc.2022.109502","article-title":"An effective iterative greedy algorithm for distributed blocking flowshop scheduling problem with balanced energy costs criterion","volume":"129","author":"Han","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108036","DOI":"10.1016\/j.knosys.2021.108036","article-title":"A referenced iterated greedy algorithm for the distributed assembly mixed no-idle permutation flowshop scheduling problem with the total tardiness criterion","volume":"239","author":"Li","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"107337","DOI":"10.1016\/j.cie.2021.107337","article-title":"Heuristics and iterated greedy algorithms for the distributed mixed no-idle flowshop with sequence-dependent setup times","volume":"157","author":"Rossi","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1287\/mnsc.39.5.616","article-title":"Minimizing the makespan in the 3-machine assembly-type flow shop scheduling problem","volume":"39","author":"Lee","year":"1993","journal-title":"Manag. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1287\/opre.43.2.346","article-title":"The two-stage assembly scheduling problem: Complexity and approximation","volume":"43","author":"Potts","year":"1995","journal-title":"Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.ejor.2018.04.033","article-title":"Deterministic assembly scheduling problems: A review and classification of current-type scheduling models and solution procedures","volume":"273","author":"Framinan","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2926","DOI":"10.1080\/00207543.2018.1550269","article-title":"Flow shop scheduling problems with assembly operations: A review and new trends","volume":"57","author":"Komaki","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.cor.2017.07.012","article-title":"The 2-stage assembly flowhop scheduling problem with total completion time: Efficient constructive heuristic and metaheuristic","volume":"88","author":"Framinan","year":"2017","journal-title":"Comput. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.swevo.2018.01.012","article-title":"A two-stage three-machine assembly flow shop scheduling with learning consideration to minimize the flowtime by six hybrids of particle swarm optimization","volume":"41","author":"Wu","year":"2018","journal-title":"Swarm Evol. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1080\/0305215X.2019.1632303","article-title":"A brand-and-bound algorithm and four meta-heuristics for minimizing total completion time for a two-stage assembly flow-shop scheduling problem with learning consideration","volume":"52","author":"Wu","year":"2020","journal-title":"Eng. Optimiz."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1398","DOI":"10.1080\/00207543.2018.1489156","article-title":"Hybrid branch and bound algorithms for the two-stage assembly scheduling problem with seperated setup times","volume":"57","author":"Luo","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"106223","DOI":"10.1016\/j.cie.2019.106223","article-title":"New efficient constructive heuristics for the two-stage multi-machine assembly scheduling problem","volume":"140","author":"Talens","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4713","DOI":"10.1080\/00207540600621029","article-title":"Evolutionary heuristics and an algorithm for the two-stage assembly scheduling problem to minimize makespan with setup times","volume":"44","author":"Allahverdi","year":"2006","journal-title":"Int. J. Prod. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3087","DOI":"10.1080\/00207540903536155","article-title":"A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem","volume":"49","author":"Shokrollahpour","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/j.jmsy.2014.06.002","article-title":"A model and imperialist competitive algorithm for hybrid flow shops with sublots and setup times","volume":"33","author":"Naderi","year":"2014","journal-title":"J. Manuf. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.engappai.2017.05.004","article-title":"The two stage assembly flow-shop scheduling problem with batching and delivery","volume":"63","author":"Kazemi","year":"2017","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9617","DOI":"10.1007\/s00500-018-3525-y","article-title":"Dominance rule and opposition-based particle swarm optimization for two-stage assembly scheduling with time cumulated learning effect","volume":"23","author":"Wang","year":"2019","journal-title":"Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1007\/s00170-010-2579-5","article-title":"Two meta-heuristics for three-stage asseembly flowshop scheduling with sequence-depdent setup times","volume":"50","author":"Hatami","year":"2010","journal-title":"Int. J. Adv. Manuf. Tech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1080\/00207543.2014.948575","article-title":"Multi-objective meta-heuristics to solve three-stage assembly flow shop scheduling problem with machine availability constraints","volume":"53","author":"Shoaardebili","year":"2015","journal-title":"Int. J. Prod. Res."},{"key":"ref_22","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_23","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_24","doi-asserted-by":"crossref","first-page":"3561","DOI":"10.1080\/00207543.2015.1084063","article-title":"A competitive memetic algorithm for the distributed two-stage assembly flow-shop scheduling problem","volume":"54","author":"Deng","year":"2016","journal-title":"Int. J. Prod. Res."},{"key":"ref_25","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_26","first-page":"1","article-title":"Cooperated teaching-learning-based optimisation for distributed two-stage flow shop scheduling","volume":"59","author":"Lei","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.ijpe.2015.07.027","article-title":"Heuristic and metaheuristics for the distributed assembly permutaiton flowshop scheduling problem with sequence dependent setup times","volume":"169","author":"Hatami","year":"2015","journal-title":"Int. J. Prod. Econ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.cie.2016.05.005","article-title":"An effective hybrid biogeography-based optimization algorithm for the distributed assembly permutation flow-shop scheduling problem","volume":"97","author":"Lin","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1945","DOI":"10.1109\/JSYST.2018.2825337","article-title":"Local search methods for a distributed assembly no-idle flow shop scheduling problem","volume":"13","author":"Shao","year":"2019","journal-title":"IEEE Syst. J."},{"key":"ref_30","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_31","first-page":"1368","article-title":"A biased-randomized iterated local search for the distributed assembly permutation flow-shop problem","volume":"27","author":"Ferone","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107750","DOI":"10.1016\/j.asoc.2021.107750","article-title":"An optimal block knowledge driven backtracking search algorithm for distributed assembly no-wait flow shop scheduling problem","volume":"111","author":"Zhao","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"107021","DOI":"10.1016\/j.cie.2020.107021","article-title":"An improved iterated greedy algorithm for the distributed assembly permutation flow shop scheduling problem","volume":"152","author":"Huang","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1016\/j.asoc.2014.08.024","article-title":"A survey on the imperialist competitive algorithm metaheuristic: Implementation in engineering domain and directions for future research","volume":"24","author":"Hosseini","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"9603","DOI":"10.1016\/j.apm.2013.05.002","article-title":"A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop","volume":"37","author":"Goldansaz","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1080\/00207543.2013.848490","article-title":"An efficient imperialist competitive algorithm for scheduling in the two-stage assembly flow shop problem","volume":"52","author":"Seidgar","year":"2014","journal-title":"Int. J. Prod. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.cor.2013.10.008","article-title":"Heuristics for an assembly flow-shop with non-identical assembly machines and sequence dependent setup times to minimize sum of holding and delay costs","volume":"44","author":"Navaei","year":"2014","journal-title":"Comput. Oper. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.asoc.2017.04.060","article-title":"Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm","volume":"58","author":"Zandieh","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.swevo.2019.05.006","article-title":"Two-level imperialist competitive algorithm for energy-efficient hybrid flow shop scheduling problem with relative importance of objectives","volume":"49","author":"Li","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1109\/TCYB.2018.2796119","article-title":"A two-Phase meta-heuristic for multiobjective flexible job shop scheduling problem with total energy consumption threshold","volume":"49","author":"Lei","year":"2019","journal-title":"IEEE Trans Cybern."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/00207543.2019.1598596","article-title":"An imperialist competitive algorithm with memory for distributed parallel machines scheduling","volume":"58","author":"Lei","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"12125","DOI":"10.3233\/JIFS-210198","article-title":"Two-phase imperialist competitive algorithm for energy-efficient flexible job shop scheduling","volume":"40","author":"Guo","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1080\/00207543.2018.1481301","article-title":"Integrated multi-factory production and distributed scheduling applying vehicle routing approach","volume":"57","author":"Marandi","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4545","DOI":"10.3233\/JIFS-201391","article-title":"A novel imperialist competitive algorithm for fuzzy distributed assembly flow shop scheduling","volume":"40","author":"Li","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1016\/j.ejor.2015.05.019","article-title":"Carbon-efficient scheduling of flow shops by multi-objective optimization","volume":"248","author":"Ding","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_46","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 Transac. Evolut. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.apm.2016.09.022","article-title":"Scheduling flexible job-shops with transportation times: Mathematical models and a hybrid imperialist competitive algorithm","volume":"41","author":"Karimi","year":"2017","journal-title":"Appl. Math. Model."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"100716","DOI":"10.1016\/j.swevo.2020.100716","article-title":"Energy-efficient distributed permutation flow shop scheduling problem using a multi-objective whale swarm algorithm","volume":"57","author":"Wang","year":"2020","journal-title":"Swarm Evol. Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"107526","DOI":"10.1016\/j.asoc.2021.107526","article-title":"A green scheduling algorithm for the distributed flowshop problem","volume":"109","author":"Li","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_50","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_51","doi-asserted-by":"crossref","unstructured":"Deng, J., Wang, L., Wu, C.G., Wang, J.J., and Zheng, X.L. (2016). A competitive memetic algorithm for carbon-efficient scheduling of distributed flow-shop. International Conference on Intelligent Computing, Springer.","DOI":"10.1007\/978-3-319-42291-6_48"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/4235.797969","article-title":"Multi-objective evolutionary algorithms: A comparative case study and the strength pareto approach","volume":"3","author":"Zitzler","year":"1999","journal-title":"IEEE Transac. Evolut. Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s00170-007-0945-8","article-title":"Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems","volume":"37","author":"Lei","year":"2008","journal-title":"Int. J. Adv. Manuf. Tech."},{"key":"ref_54","unstructured":"Taguchi, G. (1986). Introduction to Quality Engineering, Asian Productivity Organization."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2225\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:00:51Z","timestamp":1760144451000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,22]]},"references-count":54,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["sym14112225"],"URL":"https:\/\/doi.org\/10.3390\/sym14112225","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,22]]}}}