{"id":"https://openalex.org/W2883636246","doi":"https://doi.org/10.1109/tsmc.2018.2852798","title":"Solving Nonlinear Equations System With Dynamic Repulsion-Based Evolutionary Algorithms","display_name":"Solving Nonlinear Equations System With Dynamic Repulsion-Based Evolutionary Algorithms","publication_year":2018,"publication_date":"2018-07-17","ids":{"openalex":"https://openalex.org/W2883636246","doi":"https://doi.org/10.1109/tsmc.2018.2852798","mag":"2883636246"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2018.2852798","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2018.2852798","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","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/A5027300195","display_name":"Zuowen Liao","orcid":"https://orcid.org/0000-0002-4436-6878"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuowen Liao","raw_affiliation_strings":["School of Computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-4436-6878","affiliations":[{"raw_affiliation_string":"School of Computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013105439","display_name":"Wenyin Gong","orcid":"https://orcid.org/0000-0003-1610-6865"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenyin Gong","raw_affiliation_strings":["School of Computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-1610-6865","affiliations":[{"raw_affiliation_string":"School of Computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000789681","display_name":"Xuesong Yan","orcid":"https://orcid.org/0000-0003-3333-1466"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuesong Yan","raw_affiliation_strings":["School of Computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067621763","display_name":"Ling Wang","orcid":"https://orcid.org/0000-0003-1226-2801"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Wang","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1226-2801","affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014548453","display_name":"Chengyu Hu","orcid":"https://orcid.org/0000-0001-8226-5747"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengyu Hu","raw_affiliation_strings":["School of Computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3881,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":{"value":0.9720858,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"50","issue":"4","first_page":"1590","last_page":"1601"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9959999918937683,"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":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6471826434135437},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6342119574546814},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.6103976368904114},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6015859842300415},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.5392045378684998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5245371460914612},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5008368492126465},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4263899326324463},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.423414945602417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35532957315444946},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14091846346855164}],"concepts":[{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6471826434135437},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6342119574546814},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6103976368904114},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6015859842300415},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.5392045378684998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5245371460914612},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5008368492126465},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4263899326324463},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.423414945602417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35532957315444946},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14091846346855164},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/tsmc.2018.2852798","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2018.2852798","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2157992925","display_name":null,"funder_award_id":"CUG160603","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G364181133","display_name":null,"funder_award_id":"2016YFB0901900","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8614762644","display_name":null,"funder_award_id":"61573324","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G998439987","display_name":null,"funder_award_id":"61673354","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"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W955312132","https://openalex.org/W1091026910","https://openalex.org/W1522440472","https://openalex.org/W1560154065","https://openalex.org/W1565317970","https://openalex.org/W1590211757","https://openalex.org/W1785500154","https://openalex.org/W1968005908","https://openalex.org/W1968294505","https://openalex.org/W1976905195","https://openalex.org/W1981194975","https://openalex.org/W1987878867","https://openalex.org/W1990180092","https://openalex.org/W1992419399","https://openalex.org/W1997949764","https://openalex.org/W1998405574","https://openalex.org/W1999672677","https://openalex.org/W2007354815","https://openalex.org/W2021027064","https://openalex.org/W2022209280","https://openalex.org/W2024382394","https://openalex.org/W2024540804","https://openalex.org/W2030495919","https://openalex.org/W2038653969","https://openalex.org/W2046526480","https://openalex.org/W2049193681","https://openalex.org/W2051423735","https://openalex.org/W2063657280","https://openalex.org/W2075950107","https://openalex.org/W2076132030","https://openalex.org/W2082231574","https://openalex.org/W2082483165","https://openalex.org/W2101961546","https://openalex.org/W2117000100","https://openalex.org/W2131613989","https://openalex.org/W2137340504","https://openalex.org/W2144051602","https://openalex.org/W2146713522","https://openalex.org/W2146879413","https://openalex.org/W2153724273","https://openalex.org/W2155529731","https://openalex.org/W2157557172","https://openalex.org/W2158308038","https://openalex.org/W2162145193","https://openalex.org/W2171052646","https://openalex.org/W2343113774","https://openalex.org/W2432517183","https://openalex.org/W2502271158","https://openalex.org/W2517876334","https://openalex.org/W2527572108","https://openalex.org/W2559382422","https://openalex.org/W2564007649","https://openalex.org/W2564330218","https://openalex.org/W2566539043","https://openalex.org/W2590939681","https://openalex.org/W2595753752","https://openalex.org/W2600551228","https://openalex.org/W2622727889","https://openalex.org/W2727024192","https://openalex.org/W2733302305","https://openalex.org/W2742416090","https://openalex.org/W3098226728","https://openalex.org/W6739574402"],"related_works":["https://openalex.org/W2003904901","https://openalex.org/W2767141225","https://openalex.org/W2394392475","https://openalex.org/W2069937987","https://openalex.org/W1571424162","https://openalex.org/W2035908454","https://openalex.org/W2015132550","https://openalex.org/W3006802988","https://openalex.org/W2235797280","https://openalex.org/W1825560194"],"abstract_inverted_index":{"Nonlinear":[0],"equations":[1],"system":[2],"(NES)":[3],"arises":[4],"commonly":[5],"in":[6,53,111],"science":[7],"and":[8,47,63,74,128,133,168],"engineering.":[9],"Repulsion":[10],"techniques":[11,132],"are":[12,173],"considered":[13],"to":[14,19,31,80,124,214],"be":[15,32,108,137],"the":[16,27,35,38,70,92,99,116,119,125,146,159,176,191,197,200,209],"effective":[17],"methods":[18],"locate":[20],"different":[21,130,134],"roots":[22,104],"of":[23,87,105,118,148,199],"NES.":[24,83],"In":[25,162],"general,":[26],"repulsive":[28,93,206],"radius":[29,94],"needs":[30],"given":[33],"by":[34],"user":[36],"before":[37],"run.":[39],"However,":[40],"its":[41],"optimal":[42],"parameter":[43],"setting":[44],"is":[45,78,95,121,180,212],"difficult":[46],"problem-dependent.":[48],"To":[49,143],"alleviate":[50],"this":[51,54,141],"drawback,":[52],"paper,":[55],"we":[56,151],"first":[57],"propose":[58],"a":[59,65,112],"dynamic":[60,71,192],"repulsion":[61,72,131,193,202],"technique,":[62],"then":[64],"general":[66],"framework":[67,89],"based":[68],"on":[69],"technique":[73,194,203],"evolutionary":[75,100],"algorithms":[76],"(EAs)":[77],"presented":[79],"effectively":[81],"solve":[82],"The":[84],"major":[85],"advantages":[86],"our":[88,149],"are:":[90],"1)":[91],"controlled":[96],"dynamically":[97],"during":[98],"process;":[101],"2)":[102],"multiple":[103],"NES":[106],"can":[107,136,195],"simultaneously":[109],"located":[110],"single":[113],"run;":[114],"3)":[115],"diversity":[117],"population":[120,126],"preserved":[122],"due":[123],"reinitialization;":[127],"4)":[129],"EAs":[135],"readily":[138],"integrated":[139],"into":[140,175],"framework.":[142,177],"extensively":[144],"evaluate":[145],"performance":[147,198],"framework,":[150],"choose":[152],"42":[153],"problems":[154],"with":[155,183,204,219],"diverse":[156],"features":[157],"as":[158],"test":[160],"suite.":[161],"addition,":[163],"some":[164],"representative":[165],"differential":[166],"evolution":[167],"particle":[169],"swarm":[170],"optimization":[171],"variants":[172],"incorporated":[174],"Our":[178],"method":[179,211],"also":[181],"compared":[182,218],"other":[184,220],"state-of-the-art":[185],"methods.":[186,221],"Experimental":[187],"results":[188,217],"indicate":[189],"that":[190],"improve":[196],"original":[201],"static":[205],"radius.":[207],"Moreover,":[208],"proposed":[210],"able":[213],"yield":[215],"better":[216]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
