{"id":"https://openalex.org/W2338399048","doi":"https://doi.org/10.1162/evco_a_00182","title":"Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations","display_name":"Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations","publication_year":2016,"publication_date":"2016-04-12","ids":{"openalex":"https://openalex.org/W2338399048","doi":"https://doi.org/10.1162/evco_a_00182","mag":"2338399048","pmid":"https://pubmed.ncbi.nlm.nih.gov/27070282"},"language":"en","primary_location":{"id":"doi:10.1162/evco_a_00182","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00182","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","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":"https://openalex.org/A5032711214","display_name":"Ali Ahrari","orcid":"https://orcid.org/0000-0001-7232-7967"},"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":true,"raw_author_name":"Ali Ahrari","raw_affiliation_strings":["Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"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":true,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062774048","display_name":"Mike Preu\u00df","orcid":"https://orcid.org/0000-0003-4681-1346"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mike Preuss","raw_affiliation_strings":["Department of Computer Science, TU Dortmund University, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, TU Dortmund University, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032711214","https://openalex.org/A5062774048","https://openalex.org/A5088394271"],"corresponding_institution_ids":["https://openalex.org/I200332995","https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":10.956,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.9797648,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"25","issue":"3","first_page":"439","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9843999743461609,"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":0.9653000235557556,"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/cma-es","display_name":"CMA-ES","score":0.8376649618148804},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7060271501541138},{"id":"https://openalex.org/keywords/evolution-strategy","display_name":"Evolution strategy","score":0.6183918714523315},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.614231288433075},{"id":"https://openalex.org/keywords/mahalanobis-distance","display_name":"Mahalanobis distance","score":0.5958056449890137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5423442125320435},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5168893337249756},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4460759460926056},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.4334966242313385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39535486698150635},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3188180923461914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2837265431880951},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.23652520775794983}],"concepts":[{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.8376649618148804},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7060271501541138},{"id":"https://openalex.org/C207002847","wikidata":"https://www.wikidata.org/wiki/Q2912857","display_name":"Evolution strategy","level":3,"score":0.6183918714523315},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.614231288433075},{"id":"https://openalex.org/C1921717","wikidata":"https://www.wikidata.org/wiki/Q1334846","display_name":"Mahalanobis distance","level":2,"score":0.5958056449890137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5423442125320435},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5168893337249756},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4460759460926056},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.4334966242313385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39535486698150635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3188180923461914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2837265431880951},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.23652520775794983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false}],"locations_count":4,"locations":[{"id":"doi:10.1162/evco_a_00182","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00182","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},{"id":"pmid:27070282","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27070282","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":"Evolutionary computation","raw_type":null},{"id":"pmh:oai:openaccess.leidenuniv.nl:1887/76707","is_oa":false,"landing_page_url":"http://hdl.handle.net/1887/76707","pdf_url":null,"source":{"id":"https://openalex.org/S4306400850","display_name":"Leiden Repository (Leiden University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121797337","host_organization_name":"Leiden University","host_organization_lineage":["https://openalex.org/I121797337"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25","raw_type":"Article / Letter to editor"},{"id":"pmh:oai:scholarlypublications.universiteitleiden.nl:item_2973375","is_oa":false,"landing_page_url":"https://hdl.handle.net/1887/76707","pdf_url":null,"source":{"id":"https://openalex.org/S4306400850","display_name":"Leiden Repository (Leiden University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121797337","host_organization_name":"Leiden University","host_organization_lineage":["https://openalex.org/I121797337"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Evolutionary Computation","raw_type":"Article / Letter to editor"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W206440355","https://openalex.org/W621499772","https://openalex.org/W1492325323","https://openalex.org/W1499983649","https://openalex.org/W1502374754","https://openalex.org/W1503296932","https://openalex.org/W1536965992","https://openalex.org/W1556539685","https://openalex.org/W1559287602","https://openalex.org/W1572960541","https://openalex.org/W1585335425","https://openalex.org/W1595498733","https://openalex.org/W1605438009","https://openalex.org/W1672197616","https://openalex.org/W1755390828","https://openalex.org/W1763200058","https://openalex.org/W1963974395","https://openalex.org/W1967331490","https://openalex.org/W1968005908","https://openalex.org/W1976606874","https://openalex.org/W1981015742","https://openalex.org/W1985599680","https://openalex.org/W1988383064","https://openalex.org/W1993377828","https://openalex.org/W2011733579","https://openalex.org/W2012996711","https://openalex.org/W2015776612","https://openalex.org/W2021726697","https://openalex.org/W2030639039","https://openalex.org/W2038262647","https://openalex.org/W2042476863","https://openalex.org/W2054878539","https://openalex.org/W2056311241","https://openalex.org/W2062960021","https://openalex.org/W2067401702","https://openalex.org/W2071638958","https://openalex.org/W2073992654","https://openalex.org/W2084792706","https://openalex.org/W2092221803","https://openalex.org/W2092765586","https://openalex.org/W2096590200","https://openalex.org/W2097263684","https://openalex.org/W2099129608","https://openalex.org/W2100671879","https://openalex.org/W2102559904","https://openalex.org/W2108398740","https://openalex.org/W2110335153","https://openalex.org/W2112036188","https://openalex.org/W2118007687","https://openalex.org/W2126926002","https://openalex.org/W2131579134","https://openalex.org/W2132147811","https://openalex.org/W2142619464","https://openalex.org/W2145088232","https://openalex.org/W2146584320","https://openalex.org/W2151883550","https://openalex.org/W2152100799","https://openalex.org/W2156166258","https://openalex.org/W2159325678","https://openalex.org/W2161876146","https://openalex.org/W2165687335","https://openalex.org/W2170436854","https://openalex.org/W2174170216","https://openalex.org/W2215853505","https://openalex.org/W2480545803","https://openalex.org/W2527572108","https://openalex.org/W4231461647","https://openalex.org/W4285719527","https://openalex.org/W4300766842"],"related_works":["https://openalex.org/W1579744901","https://openalex.org/W1492325323","https://openalex.org/W2510724351","https://openalex.org/W3087341323","https://openalex.org/W2465356436","https://openalex.org/W3119219900","https://openalex.org/W2926551842","https://openalex.org/W2022594112","https://openalex.org/W2075948845","https://openalex.org/W4211082860"],"abstract_inverted_index":{"During":[0],"the":[1,27,33,60,83,89,106,112,126,132,139,143,150,167,170,184,200,239,248,258,267,271,274,281,292],"recent":[2],"decades,":[3],"many":[4],"niching":[5,179,215],"methods":[6,216],"have":[7],"been":[8],"proposed":[9,84,147,178],"and":[10,30,50,59,111,210,273,287],"empirically":[11],"verified":[12],"on":[13,21,217,266],"some":[14,22],"available":[15,272],"test":[16,220],"problems.":[17,43],"They":[18],"often":[19],"rely":[20],"particular":[23],"assumptions":[24],"associated":[25],"with":[26,204],"distribution,":[28],"shape,":[29],"size":[31],"of":[32,79,95,108,142,152,154,160,169,238,242,250,260],"basins,":[34,115],"which":[35,74,116,233],"can":[36],"seldom":[37],"be":[38],"made":[39],"in":[40,64,92],"practical":[41],"optimization":[42,194],"This":[44],"study":[45],"utilizes":[46],"several":[47,86,213],"existing":[48],"concepts":[49],"techniques,":[51],"such":[52],"as":[53,119,280],"taboo":[54,120,123,144],"points,":[55],"normalized":[56],"Mahalanobis":[57],"distance,":[58],"Ursem's":[61],"hill-valley":[62],"function":[63],"order":[65],"to":[66,100,105,128,131,137,148,174,212,247],"develop":[67],"a":[68,96,102,161,191,218,235],"new":[69],"tool":[70],"for":[71,222,228],"multimodal":[72,223],"optimization,":[73],"does":[75],"not":[76],"make":[77],"any":[78],"these":[80],"assumptions.":[81],"In":[82],"method,":[85,198],"subpopulations":[87,110,206],"explore":[88],"search":[90],"space":[91],"parallel.":[93],"Offspring":[94],"subpopulation":[97,127,171],"are":[98,117,289],"forced":[99],"maintain":[101],"sufficient":[103],"distance":[104],"center":[107],"fitter":[109],"previously":[113],"identified":[114],"marked":[118],"points.":[121],"The":[122,157,177,196],"points":[124,145],"repel":[125],"prevent":[129],"convergence":[130],"same":[133,293],"basin.":[134,176],"A":[135],"strategy":[136,180,189],"update":[138],"repelling":[140,205],"power":[141],"is":[146,163,181,208,231,253],"address":[149],"challenge":[151],"basins":[153],"dissimilar":[155],"size.":[156],"local":[158],"shape":[159],"basin":[162],"also":[164,254],"approximated":[165],"by":[166,256],"distribution":[168],"members":[172],"converging":[173],"that":[175],"incorporated":[182],"into":[183],"covariance":[185,201],"matrix":[186,202],"self-adaptation":[187,203],"evolution":[188],"(CMSA-ES),":[190],"potent":[192],"global":[193],"method.":[195],"resultant":[197],"called":[199],"(RS-CMSA),":[207],"assessed":[209],"compared":[211],"state-of-the-art":[214],"standard":[219],"suite":[221],"optimization.":[224],"An":[225],"organized":[226],"procedure":[227],"parameter":[229],"setting":[230],"followed":[232],"assumes":[234],"rough":[236],"estimation":[237,252],"desired/expected":[240],"number":[241],"minima":[243],"available.":[244],"Performance":[245],"sensitivity":[246],"accuracy":[249],"this":[251],"studied":[255],"introducing":[257],"concept":[259],"robust":[261],"mean":[262],"peak":[263],"ratio.":[264],"Based":[265],"numerical":[268],"results":[269],"using":[270],"introduced":[275],"performance":[276],"measures,":[277],"RS-CMSA":[278],"emerges":[279],"most":[282],"successful":[283],"method":[284],"when":[285],"robustness":[286],"efficiency":[288],"considered":[290],"at":[291],"time.":[294]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}