{"id":"https://openalex.org/W1980750007","doi":"https://doi.org/10.1109/tevc.2010.2093582","title":"Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems","display_name":"Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems","publication_year":2012,"publication_date":"2012-01-11","ids":{"openalex":"https://openalex.org/W1980750007","doi":"https://doi.org/10.1109/tevc.2010.2093582","mag":"1980750007"},"language":"en","primary_location":{"id":"doi:10.1109/tevc.2010.2093582","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2010.2093582","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/A5100424366","display_name":"Yong Wang","orcid":"https://orcid.org/0000-0001-7670-3958"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong Wang","raw_affiliation_strings":["School of Information Science and Engineering, Central South University, Changsha, China","[School of Information Science and Engineering, Central South University, ChangSha, China]"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"[School of Information Science and Engineering, Central South University, ChangSha, China]","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101440146","display_name":"Zixing Cai","orcid":"https://orcid.org/0000-0003-1809-9590"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zixing Cai","raw_affiliation_strings":["School of Information Science and Engineering, Central South University, Changsha, China","[School of Information Science and Engineering, Central South University, ChangSha, China]"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"[School of Information Science and Engineering, Central South University, ChangSha, China]","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100424366"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":41.5473,"has_fulltext":false,"cited_by_count":291,"citation_normalized_percentile":{"value":0.99850693,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"16","issue":"1","first_page":"117","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":1.0,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998000264167786,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9958000183105469,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.7175229787826538},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6996160745620728},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6964547038078308},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.6887156367301941},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6753298044204712},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.596007227897644},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.581338107585907},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.5658868551254272},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.5100536942481995},{"id":"https://openalex.org/keywords/continuous-optimization","display_name":"Continuous optimization","score":0.45753055810928345},{"id":"https://openalex.org/keywords/meta-optimization","display_name":"Meta-optimization","score":0.4334535300731659},{"id":"https://openalex.org/keywords/constrained-optimization-problem","display_name":"Constrained optimization problem","score":0.41027718782424927},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.35692307353019714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2823314666748047}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7175229787826538},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6996160745620728},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6964547038078308},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.6887156367301941},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6753298044204712},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.596007227897644},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.581338107585907},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.5658868551254272},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.5100536942481995},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.45753055810928345},{"id":"https://openalex.org/C4935549","wikidata":"https://www.wikidata.org/wiki/Q6822261","display_name":"Meta-optimization","level":3,"score":0.4334535300731659},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.41027718782424927},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.35692307353019714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2823314666748047},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tevc.2010.2093582","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2010.2093582","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":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W47058917","https://openalex.org/W103896449","https://openalex.org/W113753875","https://openalex.org/W1508684207","https://openalex.org/W1595159159","https://openalex.org/W1907005258","https://openalex.org/W1998674867","https://openalex.org/W2003143905","https://openalex.org/W2014935608","https://openalex.org/W2023458593","https://openalex.org/W2031506230","https://openalex.org/W2038984515","https://openalex.org/W2098392363","https://openalex.org/W2102343719","https://openalex.org/W2102504690","https://openalex.org/W2103055617","https://openalex.org/W2103427656","https://openalex.org/W2103508798","https://openalex.org/W2106536441","https://openalex.org/W2106980278","https://openalex.org/W2113123876","https://openalex.org/W2117640392","https://openalex.org/W2118004793","https://openalex.org/W2127205708","https://openalex.org/W2127616106","https://openalex.org/W2128010900","https://openalex.org/W2140796089","https://openalex.org/W2141001839","https://openalex.org/W2145178363","https://openalex.org/W2145479420","https://openalex.org/W2149815769","https://openalex.org/W2151339633","https://openalex.org/W2161447745","https://openalex.org/W2164655924","https://openalex.org/W2166409353","https://openalex.org/W2167580870","https://openalex.org/W2169143828","https://openalex.org/W2170338867","https://openalex.org/W2348980703","https://openalex.org/W2994964425","https://openalex.org/W3137715965","https://openalex.org/W4241130836","https://openalex.org/W4285719527","https://openalex.org/W6601885039","https://openalex.org/W6676112274","https://openalex.org/W6678901102","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W2376444000","https://openalex.org/W2356516493","https://openalex.org/W2908708533","https://openalex.org/W3102725223","https://openalex.org/W2355999325","https://openalex.org/W2166409353","https://openalex.org/W2063870188","https://openalex.org/W2762521228","https://openalex.org/W3164164302","https://openalex.org/W2206584386"],"abstract_inverted_index":{"During":[0],"the":[1,36,57,67,89,108,126,130,136,171],"past":[2],"decade,":[3],"solving":[4],"constrained":[5,30,82,174],"optimization":[6,31,75,83,122],"problems":[7],"with":[8,76,81,125,165],"evolutionary":[9,32,175],"algorithms":[10],"has":[11,47],"received":[12],"considerable":[13],"attention":[14],"among":[15],"researchers":[16],"and":[17,20,135],"practitioners.":[18],"Cai":[19],"Wang's":[21],"method":[22],"(abbreviated":[23],"as":[24,107],"CW":[25,68],"method)":[26],"is":[27,42,95,123,144,152,157],"a":[28,44,113],"recent":[29],"algorithm":[33],"proposed":[34],"by":[35],"authors.":[37],"However,":[38],"its":[39,86],"main":[40],"shortcoming":[41],"that":[43,155],"trial-and-error":[45],"process":[46],"to":[48,51,79],"be":[49],"used":[50],"choose":[52],"suitable":[53],"parameters.":[54],"To":[55],"overcome":[56],"above":[58],"shortcoming,":[59],"this":[60],"paper":[61],"proposes":[62],"an":[63],"improved":[64],"version":[65],"of":[66,91,128,142,159,173],"method,":[69],"called":[70],"CMODE,":[71,102],"which":[72],"combines":[73],"multiobjective":[74,99,121],"differential":[77,104],"evolution":[78,105],"deal":[80],"problems.":[84],"Like":[85],"predecessor":[87],"CW,":[88],"comparison":[90],"individuals":[92],"in":[93,170],"CMODE":[94,143,156],"also":[96],"based":[97,119],"on":[98,120,146],"optimization.":[100,176],"In":[101,111],"however,":[103],"serves":[106],"search":[109],"engine.":[110],"addition,":[112],"novel":[114],"infeasible":[115],"solution":[116],"replacement":[117],"mechanism":[118],"proposed,":[124],"purpose":[127],"guiding":[129],"population":[131],"toward":[132],"promising":[133],"solutions":[134],"feasible":[137],"region":[138],"simultaneously.":[139],"The":[140],"performance":[141],"evaluated":[145],"24":[147],"benchmark":[148],"test":[149],"functions.":[150],"It":[151],"shown":[153],"empirically":[154],"capable":[158],"producing":[160],"highly":[161],"competitive":[162],"results":[163],"compared":[164],"some":[166],"other":[167],"state-of-the-art":[168],"approaches":[169],"community":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":31},{"year":2015,"cited_by_count":42},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":20},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
