{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:14:12Z","timestamp":1777457652706,"version":"3.51.4"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,9,14]],"date-time":"2017-09-14T00:00:00Z","timestamp":1505347200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No.61074099"],"award-info":[{"award-number":["No.61074099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"crossref","award":["No.F2016203249"],"award-info":[{"award-number":["No.F2016203249"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Cultivation Program Project for Leading Talent of innovation team in Colleges and universities of Hebei Province","award":["No. LJRC013"],"award-info":[{"award-number":["No. LJRC013"]}]},{"name":"Innovation Project for Postgraduate of Hebei Province","award":["NO.CXZZBS2017049"],"award-info":[{"award-number":["NO.CXZZBS2017049"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s00500-017-2840-z","type":"journal-article","created":{"date-parts":[[2017,9,14]],"date-time":"2017-09-14T05:02:31Z","timestamp":1505365351000},"page":"1219-1237","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["MOEA3D: a MOEA based on dominance and decomposition with probability distribution model"],"prefix":"10.1007","volume":"23","author":[{"given":"Ziyu","family":"Hu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingming","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"Cui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lixin","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,14]]},"reference":[{"key":"2840_CR1","doi-asserted-by":"publisher","unstructured":"Bader J, Zitzler E (2011) Hype: an algorithm for fast hypervolume-based many-objective optimization. Evolut Comput 19(1):45\u201376. doi:\n                    10.1162\/EVCO_a_00009\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/6793178\/","DOI":"10.1162\/EVCO_a_00009"},{"issue":"2","key":"2840_CR2","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s10710-005-6164-x","volume":"6","author":"CAC Coello","year":"2005","unstructured":"Coello CAC, Cort\u00e9s NC (2005) Solving multiobjective optimization problems using an artificial immune system. Genet Program Evol Mach 6(2):163\u2013190. doi:\n                    10.1007\/s10710-005-6164-x","journal-title":"Genet Program Evol Mach"},{"key":"2840_CR3","doi-asserted-by":"publisher","unstructured":"\u010crepin\u0161ek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):35:1\u201335:33. doi:\n                    10.1145\/2480741.2480752","DOI":"10.1145\/2480741.2480752"},{"key":"2840_CR4","doi-asserted-by":"publisher","unstructured":"Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evolut Comput 18(4):577\u2013601. doi:\n                    10.1109\/TEVC.2013.2281535\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/6600851\/","DOI":"10.1109\/TEVC.2013.2281535"},{"key":"2840_CR5","doi-asserted-by":"publisher","unstructured":"Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput 6(2):182\u2013197. doi:\n                    10.1109\/4235.996017\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=996017","DOI":"10.1109\/4235.996017"},{"key":"2840_CR6","doi-asserted-by":"publisher","unstructured":"Giagkiozis I, Fleming P (2015) Methods for multi-objective optimization: an analysis. Inf Sci 293:338\u2013350. doi:\n                    10.1016\/j.ins.2014.08.071\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020025514009074","DOI":"10.1016\/j.ins.2014.08.071"},{"key":"2840_CR7","doi-asserted-by":"publisher","unstructured":"Giagkiozis I, Purshouse RC, Fleming PJ (2013a) Generalized decomposition. Springer, Berlin, chap Evolutionary multi-criterion optimization, pp 428\u2013442. doi:\n                    10.1007\/978-3-642-37140-0_33","DOI":"10.1007\/978-3-642-37140-0_33"},{"issue":"9","key":"2840_CR8","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1080\/00207721.2013.823526","volume":"46","author":"I Giagkiozis","year":"2013","unstructured":"Giagkiozis I, Purshouse RC, Fleming PJ (2013) An overview of population-based algorithms for multi-objective optimisation. Int J Syst Sci 46(9):1572\u20131599. doi:\n                    10.1080\/00207721.2013.823526","journal-title":"Int J Syst Sci"},{"key":"2840_CR9","doi-asserted-by":"publisher","unstructured":"Gong W, Cai Z (2009) An improved multiobjective differential evolution based on Pareto-adaptive \n                    \n                      \n                    \n                    $$\\varepsilon $$\n                    \n                      \n                        \u03b5\n                      \n                    \n                  -dominance and orthogonal design. EUR J Oper Res 198(2):576\u2013601. doi:\n                    10.1016\/j.ejor.2008.09.022\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0377221708007704","DOI":"10.1016\/j.ejor.2008.09.022"},{"issue":"5","key":"2840_CR10","doi-asserted-by":"publisher","first-page":"3677","DOI":"10.1007\/978-3-642-37140-0_33","volume":"8","author":"F Gu","year":"2012","unstructured":"Gu F, Liu HL, Tan KC (2012) A multiobjective evolutionary algorithm using dynamic weight design method. Int J Innov Comput Inf Control IJICIC 8(5):3677\u20133688. doi:\n                    10.1007\/978-3-642-37140-0_33","journal-title":"Int J Innov Comput Inf Control IJICIC"},{"issue":"11","key":"2840_CR11","doi-asserted-by":"publisher","first-page":"3249","DOI":"10.1007\/s00500-014-1480-9","volume":"19","author":"F Gu","year":"2015","unstructured":"Gu F, Liu HL, Tan KC (2015) A hybrid evolutionary multiobjective optimization algorithm with adaptive multi-fitness assignment. Soft Comput 19(11):3249\u20133259. doi:\n                    10.1007\/s00500-014-1480-9","journal-title":"Soft Comput"},{"issue":"4","key":"2840_CR12","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1162\/evco.2007.15.4.493","volume":"15","author":"AG Hernandez-Diaz","year":"2007","unstructured":"Hernandez-Diaz AG, Santana-Quintero LV, Coello Coello CA, Molina J (2007) Pareto-adaptive \n                    \n                      \n                    \n                    $$\\varepsilon $$\n                    \n                      \n                        \u03b5\n                      \n                    \n                  -dominance. Evol Comput 15(4):493\u2013517. doi:\n                    10.1162\/evco.2007.15.4.493","journal-title":"Evol Comput"},{"key":"2840_CR13","doi-asserted-by":"publisher","unstructured":"Hu Z, Yang J, Zhao Z, Sun H, Che H (2016) Multi-objective optimization of rolling schedules on aluminum hot tandem rolling. Int J Adv Manuf Technol 85(1):85\u201397. doi:\n                    10.1007\/s00170-015-7909-1","DOI":"10.1007\/s00170-015-7909-1"},{"key":"2840_CR14","doi-asserted-by":"publisher","unstructured":"Hu Z, Yang J, Sun H, Wei L, Zhao Z (2017) An improved multi-objective evolutionary algorithm based on environmental and history information. Neurocomputing 222:170\u2013182. doi:\n                    10.1016\/j.neucom.2016.10.014\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0925231216311766","DOI":"10.1016\/j.neucom.2016.10.014"},{"key":"2840_CR15","doi-asserted-by":"publisher","unstructured":"Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evolut Comput 10(5):477\u2013506. doi:\n                    10.1109\/TEVC.2005.861417\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=1705400","DOI":"10.1109\/TEVC.2005.861417"},{"key":"2840_CR16","doi-asserted-by":"publisher","unstructured":"Ishibuchi H, Murata T (1998) A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans Syst Man Cybern Part C (Appl Rev) 28(3):392\u2013403. doi:\n                    10.1109\/5326.704576\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/704576\/","DOI":"10.1109\/5326.704576"},{"issue":"3","key":"2840_CR17","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1162\/106365602760234108","volume":"10","author":"M Laumanns","year":"2002","unstructured":"Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multiobjective optimization. Evol Comput 10(3):263\u2013282. doi:\n                    10.1162\/106365602760234108","journal-title":"Evol Comput"},{"key":"2840_CR18","doi-asserted-by":"publisher","unstructured":"Li K, Kwong S, Deb K (2015) A dual-population paradigm for evolutionary multiobjective optimization. Inf Sci 309:50\u201372. doi:\n                    10.1016\/j.ins.2015.03.002\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020025515001498","DOI":"10.1016\/j.ins.2015.03.002"},{"key":"2840_CR19","doi-asserted-by":"publisher","unstructured":"Li M, Yang S, Liu X (2016) Pareto or non-Pareto: bi-criterion evolution in multiobjective optimization. IEEE Trans Evolut Comput 20(5):645\u2013665. doi:\n                    10.1109\/TEVC.2015.2504730\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=7347391","DOI":"10.1109\/TEVC.2015.2504730"},{"key":"2840_CR20","doi-asserted-by":"publisher","unstructured":"Lin Q, Liu Z, Yan Q, Du Z, Coello CAC, Liang Z, Wang W, Chen J (2016) Adaptive composite operator selection and parameter control for multiobjective evolutionary algorithm. Inf Sci 339:332\u2013352. doi:\n                    10.1016\/j.ins.2015.12.022\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020025515009111","DOI":"10.1016\/j.ins.2015.12.022"},{"key":"2840_CR21","doi-asserted-by":"publisher","unstructured":"Lu Z, Zhao H, Xiao H, Wang H, Wang H (2015) An improved multi-objective bacteria colony chemotaxis algorithm and convergence analysis. Appl Soft Comput 31:274\u2013292. doi:\n                    10.1016\/j.asoc.2015.02.046\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S1568494615001684","DOI":"10.1016\/j.asoc.2015.02.046"},{"key":"2840_CR22","doi-asserted-by":"publisher","unstructured":"Moubayed NA, Petrovski A, McCall J (2014) D2MOPSO: MOPSO based on decomposition and dominance with archiving using crowding distance in objective and solution spaces. Evolut Comput 22(1):47\u201377. doi:\n                    10.1162\/EVCO_a_00104\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/6818671\/?denied","DOI":"10.1162\/EVCO_a_00104"},{"issue":"5","key":"2840_CR23","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1007\/s00500-014-1346-1","volume":"19","author":"C Mu","year":"2015","unstructured":"Mu C, Jiao L, Liu Y, Li Y (2015) Multiobjective nondominated neighbor coevolutionary algorithm with elite population. Soft Comput 19(5):1329\u20131349. doi:\n                    10.1007\/s00500-014-1346-1","journal-title":"Soft Comput"},{"issue":"11","key":"2840_CR24","doi-asserted-by":"publisher","first-page":"2119","DOI":"10.1007\/s00500-013-1187-3","volume":"18","author":"L Nguyen","year":"2014","unstructured":"Nguyen L, Bui LT, Abbass HA (2014) Dmea-ii: the direction-based multi-objective evolutionary algorithm-ii. Soft Comput 18(11):2119\u20132134. doi:\n                    10.1007\/s00500-013-1187-3","journal-title":"Soft Comput"},{"key":"2840_CR25","doi-asserted-by":"publisher","unstructured":"Poli R, Galv\u00e1n-L\u00f3pez E (2012) The effects of constant and bit-wise neutrality on problem hardness, fitness distance correlation and phenotypic mutation rates. IEEE Trans Evolut Comput 16(2):279\u2013300. doi:\n                    10.1109\/TEVC.2011.2132726\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/xpls\/icp.jsp?arnumber=6129403","DOI":"10.1109\/TEVC.2011.2132726"},{"key":"2840_CR26","doi-asserted-by":"publisher","unstructured":"Qiu X, Xu JX, Tan KC, Abbass HA (2016) Adaptive cross-generation differential evolution operators for multiobjective optimization. IEEE Trans Evolut Comput 20(2):232\u2013244. doi:\n                    10.1109\/TEVC.2015.2433672\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/7138611\/","DOI":"10.1109\/TEVC.2015.2433672"},{"issue":"4","key":"2840_CR27","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1109\/TEVC.2010.2064321","volume":"15","author":"O Schutze","year":"2011","unstructured":"Schutze O, Lara A, Coello CAC (2011) On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Trans Evolut Comput 15(4):444\u2013455","journal-title":"IEEE Trans Evolut Comput"},{"key":"2840_CR28","doi-asserted-by":"publisher","unstructured":"Wang R, Purshouse RC, Fleming PJ (2015a) Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res 243(2):423\u2013441. doi:\n                    10.1016\/j.ejor.2014.05.019\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0377221714004263","DOI":"10.1016\/j.ejor.2014.05.019"},{"key":"2840_CR29","doi-asserted-by":"publisher","unstructured":"Wang R, Purshouse RC, Fleming PJ (2015b) Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res 243(2):423\u2013441. doi:\n                    10.1016\/j.ejor.2014.05.019\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0377221714004263","DOI":"10.1016\/j.ejor.2014.05.019"},{"issue":"99","key":"2840_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TEVC.2016.2521175","volume":"PP","author":"R Wang","year":"2016","unstructured":"Wang R, Zhang Q, Zhang T (2016) Decomposition based algorithms using Pareto adaptive scalarizing methods. IEEE Trans Evolut Comput PP(99):1\u20131. doi:\n                    10.1109\/TEVC.2016.2521175","journal-title":"IEEE Trans Evolut Comput"},{"key":"2840_CR31","doi-asserted-by":"publisher","unstructured":"Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67\u201382. doi:\n                    10.1109\/4235.585893\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=585893","DOI":"10.1109\/4235.585893"},{"key":"2840_CR32","doi-asserted-by":"publisher","unstructured":"Yen GG, He Z (2014) Performance metric ensemble for multiobjective evolutionary algorithms. IEEE Trans Evolut Comput 18(1):131\u2013144. doi:\n                    10.1109\/TEVC.2013.2240687\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/xpls\/icp.jsp?arnumber=6413195","DOI":"10.1109\/TEVC.2013.2240687"},{"key":"2840_CR33","doi-asserted-by":"publisher","unstructured":"Zhang Q, Li H (2007) MOEA\/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evolut Comput 11(6):712\u2013731. doi:\n                    10.1109\/TEVC.2007.892759\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=4358754","DOI":"10.1109\/TEVC.2007.892759"},{"key":"2840_CR34","doi-asserted-by":"publisher","unstructured":"Zhang Q, Zhou A, Jin Y (2008a) RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans Evolut Comput 12(1):41\u201363. doi:\n                    10.1109\/TEVC.2007.894202\n                    \n                  . \n                    http:\/\/ieeexplore.ieee.org\/document\/4358761\/","DOI":"10.1109\/TEVC.2007.894202"},{"key":"2840_CR35","unstructured":"Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008b) Multiobjective optimization test instances for the CEC 2009 special session and competition. University of Essex. \n                    http:\/\/dces.essex.ac.uk\/staff\/zhang\/MOEAcompetition\/cec09testproblem0904.pdf"},{"key":"2840_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2196-9","author":"SX Zhang","year":"2016","unstructured":"Zhang SX, Zheng LM, Liu L, Zheng SY, Pan YM (2016) Decomposition-based multi-objective evolutionary algorithm with mating neighborhood sizes and reproduction operators adaptation. Soft Comput. doi:\n                    10.1007\/s00500-016-2196-9","journal-title":"Soft Comput"},{"key":"2840_CR37","doi-asserted-by":"publisher","unstructured":"Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evolut Comput 1(1):32\u201349. doi:\n                    10.1016\/j.swevo.2011.03.001\n                    \n                  . \n                    http:\/\/www.sciencedirect.com\/science\/article\/pii\/S2210650211000058","DOI":"10.1016\/j.swevo.2011.03.001"},{"key":"2840_CR38","doi-asserted-by":"publisher","unstructured":"Zitzler E, K\u00fcnzli S (2004) Indicator-based selection in multiobjective search, Springer, Berlin, book section Parallel problem solving from nature\u2014PPSN VIII, pp 832\u2013842. doi:\n                    10.1007\/978-3-540-30217-9_84","DOI":"10.1007\/978-3-540-30217-9_84"},{"key":"2840_CR39","doi-asserted-by":"publisher","unstructured":"Zitzler E, Laumanns M (2001) SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of Eurogen evolutionary methods for design optimization control with applications to industrial problems. doi:\n                    10.3929\/ethz-a-004284029","DOI":"10.3929\/ethz-a-004284029"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-017-2840-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2840-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2840-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,6]],"date-time":"2019-02-06T01:02:58Z","timestamp":1549414978000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-017-2840-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,14]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["2840"],"URL":"https:\/\/doi.org\/10.1007\/s00500-017-2840-z","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,14]]},"assertion":[{"value":"14 September 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declared that we have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}