{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T20:57:48Z","timestamp":1772053068581,"version":"3.50.1"},"reference-count":41,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T00:00:00Z","timestamp":1637107200000},"content-version":"vor","delay-in-days":320,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Decomposition\u2010based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition\u2010based algorithm called reference vector\u2010guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle\u2010penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state\u2010of\u2010the\u2010art decomposition\u2010based algorithms on 3\u2010, 5\u2010, 8\u2010, and 10\u2010objective MaF1\u2013MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.<\/jats:p>","DOI":"10.1155\/2021\/8870356","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T00:50:11Z","timestamp":1637196611000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Adaptive Reference Vector Adjustment Strategy and Improved Angle\u2010Penalized Value Method for RVEA"],"prefix":"10.1155","volume":"2021","author":[{"given":"Wenbo","family":"Qiu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianghan","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4715-6267","authenticated-orcid":false,"given":"Huangchao","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingfeng","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lisu","family":"Huo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,11,17]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2013.2290082"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2016.2560130"},{"key":"e_1_2_9_3_2","doi-asserted-by":"crossref","unstructured":"SayyadA. 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On the value of user preferences in search-based software engineering: a case study in software product lines Proceedings of the 2013 35th International Conference on Software Engineering (ICSE) May 2013 San Francisco CA USA 492\u2013501 https:\/\/doi.org\/10.1109\/icse.2013.6606595 2-s2.0-84886494195.","DOI":"10.1109\/ICSE.2013.6606595"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.996017"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2007.892759"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2020.3034180"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2013.2281535"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcyb.2018.2849403"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcyb.2015.2403849"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2017.2744674"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcyb.2019.2931434"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2014.2350995"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2011.2166159"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1162\/evco_a_00009"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2017.2749619"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2016.2519378"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2013.2281533"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-017-0039-7"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2019.2898456"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106592"},{"key":"e_1_2_9_21_2","volume-title":"Advances in Artificial Intelligence","author":"Jiang S.","year":"2011"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1162\/evco_a_00038"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2014.05.019"},{"key":"e_1_2_9_24_2","article-title":"MOEA\/D with adaptive weight adjustment","volume":"22","author":"Qi Y.","year":"2013","journal-title":"Evolutionary Computation"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105731"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.01.049"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2737554"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2737519"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2020.06.028"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.07.012"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2019.06.009"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2013.2281534"},{"key":"e_1_2_9_33_2","doi-asserted-by":"crossref","unstructured":"LiuQ. 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Adaptation of reference vectors for evolutionary many-objective optimization of problems with irregular pareto fronts Proceedings of the 2019 IEEE Congress on Evolutionary Computation (CEC) June 2019 Wellington New Zealand 1726\u20131733.","DOI":"10.1109\/CEC.2019.8790214"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcyb.2020.3020630"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2020.100776"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2018.2882166"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2016.2521175"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/mci.2017.2742868"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.797969"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1109\/tevc.2003.810761"},{"key":"e_1_2_9_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2018.08.017"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8870356.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/8870356.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/8870356","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:56:46Z","timestamp":1723240606000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/8870356"}},"subtitle":[],"editor":[{"given":"In\u00e9s P.","family":"Mari\u00f1o","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/8870356"],"URL":"https:\/\/doi.org\/10.1155\/2021\/8870356","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-09-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-10-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-11-17","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8870356"}}