{"id":"https://openalex.org/W1964413087","doi":"https://doi.org/10.1109/cec.2010.5586086","title":"Using an enhanced integer NSGA-II for solving the multiobjective Generalized Assignment Problem","display_name":"Using an enhanced integer NSGA-II for solving the multiobjective Generalized Assignment Problem","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W1964413087","doi":"https://doi.org/10.1109/cec.2010.5586086","mag":"1964413087"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2010.5586086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5586086","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-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/A5071506212","display_name":"Robert F. Subtil","orcid":null},"institutions":[{"id":"https://openalex.org/I96294087","display_name":"Companhia Energ\u00e9tica de Minas Gerais (Brazil)","ror":"https://ror.org/02kbrsj34","country_code":"BR","type":"company","lineage":["https://openalex.org/I96294087"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Robert F. Subtil","raw_affiliation_strings":["Devex Tecnologia S. A, Belo Horizonte, Minas Gerais, Brazil","Devex Tecnolog\u00eda S.A., Av. Afonso Pena. 3130 (7\u00b0 Andar), Belo Horizonte-MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Devex Tecnologia S. A, Belo Horizonte, Minas Gerais, Brazil","institution_ids":["https://openalex.org/I96294087"]},{"raw_affiliation_string":"Devex Tecnolog\u00eda S.A., Av. Afonso Pena. 3130 (7\u00b0 Andar), Belo Horizonte-MG, Brazil","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081008483","display_name":"Eduardo G. Carrano","orcid":"https://orcid.org/0000-0003-3368-4245"},"institutions":[{"id":"https://openalex.org/I4210136482","display_name":"Federal Center for Technological Education of Minas Gerais","ror":"https://ror.org/04ch49185","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210136482"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Eduardo G. Carrano","raw_affiliation_strings":["Department of Computer Engineering, Centro Federal de Educa\u00e7\u00e3o Tecnol\u00f3gica, Belo Horizonte, Minas Gerais, Brazil","Department of Computer Engineering, Centro Federal de Educa\u00e7\u00e0o Tecnol\u00f3gica, Av. Amazonas, 7675, Belo Horizonte-MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Centro Federal de Educa\u00e7\u00e3o Tecnol\u00f3gica, Belo Horizonte, Minas Gerais, Brazil","institution_ids":["https://openalex.org/I4210136482"]},{"raw_affiliation_string":"Department of Computer Engineering, Centro Federal de Educa\u00e7\u00e0o Tecnol\u00f3gica, Av. Amazonas, 7675, Belo Horizonte-MG, Brazil","institution_ids":["https://openalex.org/I4210136482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006915301","display_name":"Marcone Jamilson Freitas Souza","orcid":"https://orcid.org/0000-0002-7141-357X"},"institutions":[{"id":"https://openalex.org/I10824318","display_name":"Universidade Federal de Ouro Preto","ror":"https://ror.org/056s65p46","country_code":"BR","type":"education","lineage":["https://openalex.org/I10824318"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcone J. F. Souza","raw_affiliation_strings":["Department of Computing, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil","Department of Computing, Universidade Federal de Ouro Preto, Campus Universitario Morro do Cruzeiro, Ouro Preto-MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil","institution_ids":["https://openalex.org/I10824318"]},{"raw_affiliation_string":"Department of Computing, Universidade Federal de Ouro Preto, Campus Universitario Morro do Cruzeiro, Ouro Preto-MG, Brazil","institution_ids":["https://openalex.org/I10824318"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084933585","display_name":"Ricardo H. C. Takahashi","orcid":"https://orcid.org/0000-0003-0814-6314"},"institutions":[{"id":"https://openalex.org/I110200422","display_name":"Universidade Federal de Minas Gerais","ror":"https://ror.org/0176yjw32","country_code":"BR","type":"education","lineage":["https://openalex.org/I110200422"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ricardo H. C. Takahashi","raw_affiliation_strings":["Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil","Department of Mathematics, Universidade Federal de Minas G\u00e9rais, Av. Antonio Carlos, 6626, Belo Horizonte-MG, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil","institution_ids":["https://openalex.org/I110200422"]},{"raw_affiliation_string":"Department of Mathematics, Universidade Federal de Minas G\u00e9rais, Av. Antonio Carlos, 6626, Belo Horizonte-MG, Brazil","institution_ids":["https://openalex.org/I110200422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071506212"],"corresponding_institution_ids":["https://openalex.org/I96294087"],"apc_list":null,"apc_paid":null,"fwci":1.3381,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.7934892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9973000288009644,"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/T11053","display_name":"Process Optimization and Integration","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/mathematical-optimization","display_name":"Mathematical optimization","score":0.761002779006958},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.7586171627044678},{"id":"https://openalex.org/keywords/generalized-assignment-problem","display_name":"Generalized assignment problem","score":0.6554994583129883},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.6539789438247681},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6174160242080688},{"id":"https://openalex.org/keywords/assignment-problem","display_name":"Assignment problem","score":0.6045411825180054},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.591786801815033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.55497807264328},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5168759822845459},{"id":"https://openalex.org/keywords/weapon-target-assignment-problem","display_name":"Weapon target assignment problem","score":0.49754956364631653},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4747087061405182},{"id":"https://openalex.org/keywords/problem-statement","display_name":"Problem statement","score":0.45803478360176086},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.4531751275062561},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.41117459535598755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3254523277282715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2571067810058594},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07291018962860107}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.761002779006958},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.7586171627044678},{"id":"https://openalex.org/C194146004","wikidata":"https://www.wikidata.org/wiki/Q5532462","display_name":"Generalized assignment problem","level":3,"score":0.6554994583129883},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.6539789438247681},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6174160242080688},{"id":"https://openalex.org/C85044808","wikidata":"https://www.wikidata.org/wiki/Q620614","display_name":"Assignment problem","level":2,"score":0.6045411825180054},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.591786801815033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.55497807264328},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5168759822845459},{"id":"https://openalex.org/C30202268","wikidata":"https://www.wikidata.org/wiki/Q7978065","display_name":"Weapon target assignment problem","level":4,"score":0.49754956364631653},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4747087061405182},{"id":"https://openalex.org/C202532154","wikidata":"https://www.wikidata.org/wiki/Q4374193","display_name":"Problem statement","level":2,"score":0.45803478360176086},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.4531751275062561},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.41117459535598755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3254523277282715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2571067810058594},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07291018962860107},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2010.5586086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5586086","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1497697549","https://openalex.org/W1509898203","https://openalex.org/W1992447159","https://openalex.org/W1993062444","https://openalex.org/W2014617308","https://openalex.org/W2022065551","https://openalex.org/W2036109172","https://openalex.org/W2050274364","https://openalex.org/W2058233069","https://openalex.org/W2058324360","https://openalex.org/W2062822390","https://openalex.org/W2078765720","https://openalex.org/W2081725015","https://openalex.org/W2086190489","https://openalex.org/W2086917808","https://openalex.org/W2102201348","https://openalex.org/W2108203093","https://openalex.org/W2108219706","https://openalex.org/W2121365620","https://openalex.org/W2126105956","https://openalex.org/W2147758533","https://openalex.org/W2155078398","https://openalex.org/W2172122819","https://openalex.org/W6629907934","https://openalex.org/W6672155188"],"related_works":["https://openalex.org/W2937059810","https://openalex.org/W2760584304","https://openalex.org/W1586515950","https://openalex.org/W2358965113","https://openalex.org/W2379349345","https://openalex.org/W2382974548","https://openalex.org/W1976256054","https://openalex.org/W2113934189","https://openalex.org/W2311097448","https://openalex.org/W4387558585"],"abstract_inverted_index":{"The":[0,112,139],"traditional":[1],"Generalized":[2],"Assignment":[3],"Problem":[4],"(GAP)":[5],"problem":[6,54,70],"consists":[7],"of":[8,45,95,134,148,154,165],"assigning":[9],"n":[10],"different":[11,15],"tasks":[12,86],"to":[13,26,33,57,83,123,130,143],"m":[14],"agents,":[16],"while":[17],"minimizing":[18],"a":[19,34,58,109,145,169],"cost":[20,160],"function.":[21],"Additionally,":[22],"it":[23,80,120],"is":[24,31,48,55,66,74,81,104,121],"necessary":[25],"ensure":[27],"that":[28,40,119],"each":[29],"task":[30],"assigned":[32],"single":[35,136],"agent":[36],"(indivisible":[37],"task)":[38],"and":[39,161],"the":[41,46,53,69,85,89,96,131,135,149,152,166,176],"maximum":[42],"resource":[43],"capacity":[44],"agents":[47],"honored.":[49],"In":[50],"this":[51,116],"paper,":[52],"extended":[56],"bi-objective":[59],"formulation,":[60],"in":[61,68,78,175],"which":[62,79,126],"an":[63],"equilibrium":[64],"function":[65],"included":[67],"statement.":[71],"This":[72],"formulation":[73],"motivated":[75],"by":[76],"situations":[77],"important":[82],"distribute":[84],"uniformly":[87],"amongst":[88],"agents.":[90],"An":[91],"integer":[92],"enhanced":[93],"version":[94],"Non-dominated":[97],"Sorting":[98],"Genetic":[99],"Algorithm":[100],"II":[101],"(NSGA-II)":[102],"algorithm":[103,117],"proposed":[105],"for":[106],"solving":[107],"such":[108],"multiobjective":[110],"problem.":[111,138],"results":[113],"obtained":[114],"using":[115],"show":[118],"possible":[122],"find":[124],"solutions":[125,156],"are":[127],"very":[128],"close":[129],"exact":[132],"optimum":[133],"objective":[137],"approach":[140],"still":[141],"allows":[142],"perform":[144],"trade-off":[146,170],"analysis":[147],"objectives,":[150],"offering":[151],"possibility":[153],"choosing":[155],"with":[157],"slightly":[158],"higher":[159],"considerably":[162],"better":[163],"distribution":[164],"tasks.":[167],"Such":[168],"decision":[171],"cannot":[172],"be":[173],"performed":[174],"mono-objective":[177],"approaches.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}