{"id":"https://openalex.org/W2508723547","doi":"https://doi.org/10.1109/tevc.2016.2606577","title":"Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms","display_name":"Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2508723547","doi":"https://doi.org/10.1109/tevc.2016.2606577","mag":"2508723547"},"language":"en","primary_location":{"id":"doi:10.1109/tevc.2016.2606577","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2016.2606577","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100610638","display_name":"Hai\u2010Lin Liu","orcid":"https://orcid.org/0000-0003-2276-1938"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai-Lin Liu","raw_affiliation_strings":["Guangdong University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-2276-1938","affiliations":[{"raw_affiliation_string":"Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333550","display_name":"Lei Chen","orcid":"https://orcid.org/0000-0003-1423-3481"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Chen","raw_affiliation_strings":["Guangdong University of Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088394271","display_name":"Kalyanmoy Deb","orcid":"https://orcid.org/0000-0001-7402-9939"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Electrical and Computer Engineering and BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034853476","display_name":"Erik D. Goodman","orcid":"https://orcid.org/0000-0002-2419-0692"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erik Goodman","raw_affiliation_strings":["Department of Electrical and Computer Engineering and BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.2379,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.98517182,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6764802932739258},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6640477180480957},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.5492510795593262},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5242281556129456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5154879689216614},{"id":"https://openalex.org/keywords/diversity","display_name":"Diversity (politics)","score":0.48950374126434326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4312267303466797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38490062952041626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3725622892379761}],"concepts":[{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6764802932739258},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6640477180480957},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.5492510795593262},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5242281556129456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5154879689216614},{"id":"https://openalex.org/C2781316041","wikidata":"https://www.wikidata.org/wiki/Q1230584","display_name":"Diversity (politics)","level":2,"score":0.48950374126434326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4312267303466797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38490062952041626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3725622892379761},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tevc.2016.2606577","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2016.2606577","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Evolutionary Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2735605540","display_name":null,"funder_award_id":"61673121","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W225560312","https://openalex.org/W764325004","https://openalex.org/W1491287429","https://openalex.org/W1525375343","https://openalex.org/W1559956479","https://openalex.org/W1581562576","https://openalex.org/W1585939719","https://openalex.org/W1588375755","https://openalex.org/W1595498733","https://openalex.org/W1601556876","https://openalex.org/W1605170913","https://openalex.org/W1662894842","https://openalex.org/W1905847227","https://openalex.org/W1979908631","https://openalex.org/W1980272771","https://openalex.org/W2022485595","https://openalex.org/W2024008934","https://openalex.org/W2038420231","https://openalex.org/W2045750029","https://openalex.org/W2058142975","https://openalex.org/W2067544246","https://openalex.org/W2098907614","https://openalex.org/W2102248717","https://openalex.org/W2106334424","https://openalex.org/W2108968575","https://openalex.org/W2109865546","https://openalex.org/W2126105956","https://openalex.org/W2127459836","https://openalex.org/W2129392074","https://openalex.org/W2136827689","https://openalex.org/W2140066605","https://openalex.org/W2143381319","https://openalex.org/W2145479420","https://openalex.org/W2147968712","https://openalex.org/W2152551290","https://openalex.org/W2156221357","https://openalex.org/W2156262512","https://openalex.org/W2156622046","https://openalex.org/W2193409108","https://openalex.org/W2271389764","https://openalex.org/W2313094906","https://openalex.org/W2314267498","https://openalex.org/W2326149522","https://openalex.org/W2343897395","https://openalex.org/W2415637909","https://openalex.org/W2432516117","https://openalex.org/W2615258659","https://openalex.org/W3023175681","https://openalex.org/W3037787799","https://openalex.org/W3103451854","https://openalex.org/W4302557773","https://openalex.org/W6608886761","https://openalex.org/W6631406560","https://openalex.org/W6635097213","https://openalex.org/W6635433731","https://openalex.org/W6675537533","https://openalex.org/W6680838134","https://openalex.org/W6717764351"],"related_works":["https://openalex.org/W4297582752","https://openalex.org/W4285805405","https://openalex.org/W2391924736","https://openalex.org/W3133779647","https://openalex.org/W2887328214","https://openalex.org/W1560122427","https://openalex.org/W2021957875","https://openalex.org/W2802808995","https://openalex.org/W2787833928","https://openalex.org/W2593449396"],"abstract_inverted_index":{"There":[0],"are":[1,39,156,173],"two":[2],"main":[3],"tasks":[4],"involved":[5],"in":[6,62,104],"addressing":[7],"a":[8,75,150],"multiobjective":[9,15,129,182,184],"optimization":[10],"problem":[11],"(MOP)":[12],"by":[13,90,181],"evolutionary":[14,130,138],"(EMO)":[16],"algorithms:":[17],"1)":[18],"make":[19],"the":[20,25,43,96,99,177,190,199,203,207,217,221],"population":[21,32,191],"converge":[22],"close":[23],"to":[24,69,175,183],"Pareto-optimal":[26],"front":[27],"and":[28,46,81,94,114,142,149,198],"2)":[29],"maintain":[30],"adequate":[31],"diversity.":[33],"However,":[34],"most":[35],"state-of-the-art":[36],"EMO":[37,57,101,122,146,164,204],"algorithms":[38,58,165],"designed":[40],"based":[41,132],"on":[42,133,211],"\u201cconvergence":[44],"first":[45],"diversity":[47,79],"second\u201d":[48],"principle.":[49],"It":[50,159],"has":[51],"been":[52,60],"observed":[53],"that":[54,73,162,188],"although":[55],"these":[56,163,168],"have":[59],"successful":[61,200],"optimizing":[63],"many":[64],"real-world":[65],"MOPs,":[66],"they":[67,172],"fail":[68],"solve":[70,167,176],"certain":[71],"problems":[72,178,215],"feature":[74],"severe":[76],"imbalance":[77],"between":[78],"preservation":[80],"achieving":[82],"convergence.":[83],"This":[84],"paper":[85],"characterizes":[86],"an":[87,186],"imbalanced":[88,111,169],"MOP":[89],"clearly":[91],"defining":[92],"properties":[93],"indicating":[95],"reasons":[97],"for":[98],"existing":[100,121],"algorithms'":[102],"difficulties":[103],"solving":[105],"them.":[106],"We":[107],"then":[108,157],"present":[109],"14":[110],"problems,":[112,170],"with":[113,206],"without":[115],"constraints.":[116],"Computational":[117],"results":[118,197],"using":[119,220],"four":[120],"algorithms-elitist":[123],"non-dominated":[124],"sorting":[125],"genetic":[126,154],"algorithm":[127,131,139,147,155],"(NSGA-II),":[128],"decomposition":[134],"(MOEA/D),":[135],"strength":[136],"Pareto":[137],"2":[140],"(SPEA2),":[141],"S":[143],"metric":[144],"selection":[145],"(SMS-EMOA)":[148],"proposed":[151],"generalized":[152],"vector-evaluated":[153],"presented.":[158],"is":[160],"seen":[161],"cannot":[166],"but":[171],"able":[174],"when":[179],"augmented":[180],"(M2M),":[185],"approach":[187,209],"decomposes":[189],"into":[192],"several":[193],"interacting":[194],"subpopulations.":[195],"These":[196],"application":[201],"of":[202,219],"methods":[205],"M2M":[208,222],"even":[210],"standard":[212],"so-called":[213],"balanced":[214],"indicate":[216],"usefulness":[218],"approach.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}