{"id":"https://openalex.org/W3087341323","doi":"https://doi.org/10.1109/tcyb.2020.3013950","title":"A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization","display_name":"A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization","publication_year":2020,"publication_date":"2020-09-16","ids":{"openalex":"https://openalex.org/W3087341323","doi":"https://doi.org/10.1109/tcyb.2020.3013950","mag":"3087341323","pmid":"https://pubmed.ncbi.nlm.nih.gov/32936757"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.3013950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3013950","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Abhishek Kumar","orcid":"https://orcid.org/0000-0003-1940-0234"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Abhishek Kumar","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Varanasi, Varanasi, India"],"raw_orcid":"https://orcid.org/0000-0003-1940-0234","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Varanasi, Varanasi, India","institution_ids":["https://openalex.org/I56404289"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000078546","display_name":"Swagatam Das","orcid":"https://orcid.org/0000-0001-6843-4508"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Swagatam Das","raw_affiliation_strings":["Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India"],"raw_orcid":"https://orcid.org/0000-0001-6843-4508","affiliations":[{"raw_affiliation_string":"Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043565079","display_name":"Rammohan Mallipeddi","orcid":"https://orcid.org/0000-0001-9071-1145"},"institutions":[{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Rammohan Mallipeddi","raw_affiliation_strings":["Department of Artificial Intelligence, College of IT Engineering, Kyungpook National University, Daegu, South Korea"],"raw_orcid":"https://orcid.org/0000-0001-9071-1145","affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, College of IT Engineering, Kyungpook National University, Daegu, South Korea","institution_ids":["https://openalex.org/I31419693"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5201,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.94062514,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"52","issue":"5","first_page":"3696","last_page":"3709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9987999796867371,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cma-es","display_name":"CMA-ES","score":0.9338876008987427},{"id":"https://openalex.org/keywords/evolution-strategy","display_name":"Evolution strategy","score":0.8163657784461975},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7063631415367126},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5704767107963562},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5653997659683228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.556844174861908},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.55080246925354},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5336637496948242},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47125816345214844},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4620627164840698},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.4502262473106384},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.443962961435318},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4390348494052887},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4103556275367737},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32798123359680176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30684947967529297},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17406216263771057}],"concepts":[{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.9338876008987427},{"id":"https://openalex.org/C207002847","wikidata":"https://www.wikidata.org/wiki/Q2912857","display_name":"Evolution strategy","level":3,"score":0.8163657784461975},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7063631415367126},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5704767107963562},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5653997659683228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.556844174861908},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.55080246925354},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5336637496948242},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47125816345214844},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4620627164840698},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.4502262473106384},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.443962961435318},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4390348494052887},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4103556275367737},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32798123359680176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30684947967529297},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17406216263771057},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2020.3013950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3013950","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:32936757","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32936757","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W166726813","https://openalex.org/W1581875179","https://openalex.org/W1582016163","https://openalex.org/W1780343103","https://openalex.org/W1880731561","https://openalex.org/W1964857088","https://openalex.org/W1977822596","https://openalex.org/W1980750007","https://openalex.org/W1988833288","https://openalex.org/W2003143905","https://openalex.org/W2014759149","https://openalex.org/W2023910014","https://openalex.org/W2039355869","https://openalex.org/W2041760348","https://openalex.org/W2042594698","https://openalex.org/W2048810930","https://openalex.org/W2050774998","https://openalex.org/W2056665801","https://openalex.org/W2071569138","https://openalex.org/W2086421124","https://openalex.org/W2099197461","https://openalex.org/W2102428266","https://openalex.org/W2103191065","https://openalex.org/W2110368321","https://openalex.org/W2111761631","https://openalex.org/W2113123876","https://openalex.org/W2120248756","https://openalex.org/W2122670988","https://openalex.org/W2126105956","https://openalex.org/W2141684176","https://openalex.org/W2145479420","https://openalex.org/W2146713522","https://openalex.org/W2161029074","https://openalex.org/W2164655924","https://openalex.org/W2165109867","https://openalex.org/W2170338867","https://openalex.org/W2236623899","https://openalex.org/W2288517616","https://openalex.org/W2312408522","https://openalex.org/W2345178486","https://openalex.org/W2419306226","https://openalex.org/W2564599202","https://openalex.org/W2579361096","https://openalex.org/W2591313086","https://openalex.org/W2592891920","https://openalex.org/W2606717649","https://openalex.org/W2726495777","https://openalex.org/W2729115982","https://openalex.org/W2730641013","https://openalex.org/W2730907139","https://openalex.org/W2732972480","https://openalex.org/W2734823962","https://openalex.org/W2765056174","https://openalex.org/W2766293931","https://openalex.org/W2790343644","https://openalex.org/W2802384355","https://openalex.org/W2810095338","https://openalex.org/W2845268560","https://openalex.org/W2890957380","https://openalex.org/W2895627188","https://openalex.org/W2895914958","https://openalex.org/W2896508930","https://openalex.org/W2901888116","https://openalex.org/W2921913446","https://openalex.org/W2926551842","https://openalex.org/W2962757795","https://openalex.org/W3008773008","https://openalex.org/W3015290284","https://openalex.org/W3100570467","https://openalex.org/W3104621635","https://openalex.org/W3106485406","https://openalex.org/W6731140402"],"related_works":["https://openalex.org/W1579744901","https://openalex.org/W1492325323","https://openalex.org/W2510724351","https://openalex.org/W3087341323","https://openalex.org/W3119219900","https://openalex.org/W2102869784","https://openalex.org/W2926551842","https://openalex.org/W2022594112","https://openalex.org/W4211082860","https://openalex.org/W2116954712"],"abstract_inverted_index":{"During":[0],"the":[1,5,17,33,39,46,51,60,68,71,80,88,102,114,130,134,140,146,151,167,176,181,186,205,230,245],"last":[2],"two":[3,190],"decades,":[4],"notion":[6],"of":[7,70,82,113,119,153,195,244,251],"multiobjective":[8],"optimization":[9,20,93,147],"(MOO)":[10],"has":[11],"been":[12],"successfully":[13],"adopted":[14],"to":[15,74,128,174,178,222],"solve":[16,98],"nonconvex":[18],"constrained":[19,240],"problems":[21,200],"(COPs)":[22],"in":[23,137,155,242],"their":[24],"most":[25,115],"general":[26],"forms.":[27],"However,":[28],"such":[29,44],"works":[30],"mainly":[31],"utilized":[32],"Pareto":[34],"dominance-based":[35],"MOO":[36,42,73,158],"framework":[37],"while":[38],"other":[40,238],"successful":[41],"frameworks,":[43],"as":[45],"reference":[47],"vector":[48],"(RV)":[49],"and":[50,96,132,170,197,213],"decomposition-based":[52],"ones,":[53],"have":[54],"not":[55],"drawn":[56],"sufficient":[57],"attention":[58],"from":[59,180,204],"COP":[61,89],"researchers.":[62],"In":[63],"this":[64],"article,":[65],"we":[66],"utilize":[67],"concepts":[69],"RV-based":[72,125,157],"design":[75],"a":[76,83,91,156,163,171,218,248],"ranking":[77,126],"strategy":[78,107,127,173],"for":[79,166],"solutions":[81,169],"COP.":[84],"We":[85,122,160,184],"first":[86],"transform":[87],"into":[90],"biobjective":[92],"problem":[94,220],"(BOP)":[95],"then":[97],"it":[99],"by":[100],"using":[101],"covariance":[103,135],"matrix":[104,136],"adaptation":[105],"evolution":[106],"(CMA-ES),":[108],"which":[109],"is":[110,142],"arguably":[111],"one":[112],"competitive":[116],"evolutionary":[117],"algorithms":[118],"current":[120],"interest.":[121],"propose":[123,162],"an":[124],"calculate":[129],"mean":[131],"update":[133],"CMA-ES.":[138],"Besides,":[139],"RV":[141],"explicitly":[143],"tuned":[144],"during":[145],"process":[148],"based":[149],"on":[150,189,209,247],"characteristics":[152],"COPs":[154],"framework.":[159],"also":[161],"repair":[164],"mechanism":[165],"infeasible":[168,182],"restart":[172],"facilitate":[175],"population":[177],"escape":[179],"region.":[183],"test":[185,199],"proposal":[187],"extensively":[188],"well-known":[191],"benchmark":[192],"suites":[193],"comprised":[194],"36":[196],"112":[198],"(at":[201],"different":[202],"scales)":[203],"IEEE":[206],"CEC":[207],"(Congress":[208],"Evolutionary":[210],"Computation)":[211],"2010":[212],"2017":[214],"competitions":[215],"along":[216],"with":[217],"real-world":[219],"related":[221],"power":[223],"flow.":[224],"Our":[225],"experimental":[226],"results":[227],"suggest":[228],"that":[229],"proposed":[231],"algorithm":[232],"can":[233],"meet":[234],"or":[235],"beat":[236],"several":[237],"state-of-the-art":[239],"optimizers":[241],"terms":[243],"performance":[246],"wide":[249],"variety":[250],"problems.":[252]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}