{"id":"https://openalex.org/W2122297020","doi":"https://doi.org/10.1109/cec.2013.6557743","title":"A ranking method based on the R2 indicator for many-objective optimization","display_name":"A ranking method based on the R2 indicator for many-objective optimization","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2122297020","doi":"https://doi.org/10.1109/cec.2013.6557743","mag":"2122297020"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2013.6557743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5020421469","display_name":"Alan Diaz-Manr\u00edquez","orcid":"https://orcid.org/0000-0003-2847-8316"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Alan Diaz-Manriquez","raw_affiliation_strings":["Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","institution_ids":[]},{"raw_affiliation_string":"Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046224413","display_name":"Gregorio Toscano\u2010Pulido","orcid":"https://orcid.org/0000-0001-5311-8027"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Gregorio Toscano-Pulido","raw_affiliation_strings":["Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","institution_ids":[]},{"raw_affiliation_string":"Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085548317","display_name":"Carlos A. Coello Coello","orcid":"https://orcid.org/0000-0002-8435-680X"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Carlos A. Coello Coello","raw_affiliation_strings":["Departamento de Computaci\u00f3n, CINVESTAV-IPN, Mexico, MEXICO","Dept. de Comput., CINVESTAV - IPN, Mexico City, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Computaci\u00f3n, CINVESTAV-IPN, Mexico, MEXICO","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Dept. de Comput., CINVESTAV - IPN, Mexico City, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017248538","display_name":"Ricardo Landa Becerra","orcid":"https://orcid.org/0000-0003-2645-0942"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Ricardo Landa-Becerra","raw_affiliation_strings":["Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology Laboratory, CINVESTAV Tamaulipas, Ciudad Victoria, Tamaulipas, Mexico","institution_ids":[]},{"raw_affiliation_string":"Inf. Technol. Lab., Cinvestav Tamaulipas, Ciudad Victoria, Mexico","institution_ids":["https://openalex.org/I68368234"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1523","last_page":"1530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":1.0,"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":1.0,"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":0.9980000257492065,"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":0.9945999979972839,"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/ranking","display_name":"Ranking (information retrieval)","score":0.8492152690887451},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.8118476867675781},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6440379619598389},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.6411253213882446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6375212669372559},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6281862258911133},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5503770112991333},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5063050985336304},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4809236228466034},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4766681492328644},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.4175010919570923},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3712630867958069},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34462523460388184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22020354866981506},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18079474568367004}],"concepts":[{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.8492152690887451},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.8118476867675781},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6440379619598389},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6411253213882446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6375212669372559},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6281862258911133},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5503770112991333},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5063050985336304},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4809236228466034},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4766681492328644},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.4175010919570923},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3712630867958069},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34462523460388184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22020354866981506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18079474568367004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2013.6557743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 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":24,"referenced_works":["https://openalex.org/W225560312","https://openalex.org/W1504943474","https://openalex.org/W1519778441","https://openalex.org/W1522538275","https://openalex.org/W1575601714","https://openalex.org/W1588375755","https://openalex.org/W1595159159","https://openalex.org/W1976159118","https://openalex.org/W1980591224","https://openalex.org/W1987958230","https://openalex.org/W2035451851","https://openalex.org/W2038420231","https://openalex.org/W2048469132","https://openalex.org/W2102365077","https://openalex.org/W2108968575","https://openalex.org/W2118028531","https://openalex.org/W2125899728","https://openalex.org/W2135974394","https://openalex.org/W2142492189","https://openalex.org/W2143185749","https://openalex.org/W2160088187","https://openalex.org/W6631460888","https://openalex.org/W6635433731","https://openalex.org/W6645553445"],"related_works":["https://openalex.org/W1994686097","https://openalex.org/W4297582752","https://openalex.org/W4285805405","https://openalex.org/W2906115061","https://openalex.org/W2977596624","https://openalex.org/W2145877535","https://openalex.org/W2744730182","https://openalex.org/W2751605210","https://openalex.org/W3151104768","https://openalex.org/W2022485595"],"abstract_inverted_index":{"In":[0],"recent":[1,65],"years,":[2],"the":[3,21,25,69,86,102,137,143],"development":[4],"of":[5,71,93,104],"selection":[6],"mechanisms":[7],"based":[8,33],"on":[9,34],"performance":[10,73,132],"indicators":[11,74],"has":[12,23,62,75],"become":[13],"an":[14,81],"important":[15],"trend":[16],"in":[17,67,98,119,136,173,177],"algorithmic":[18],"design.":[19],"Hereof,":[20],"hypervolume":[22],"been":[24,76],"most":[26],"popular":[27],"choice.":[28],"Multi-objective":[29],"evolutionary":[30],"algorithms":[31,56],"(MOEAs)":[32],"this":[35],"indicator":[36,88],"seem":[37],"to":[38,84,89,100,113,149,160,191],"be":[39],"a":[40,90,105,193,197],"good":[41],"choice":[42],"for":[43],"dealing":[44],"with":[45,158],"many-objective":[46,174],"optimization":[47,175],"problems.":[48],"However,":[49],"their":[50],"main":[51,185],"drawback":[52],"is":[53,111,189],"that":[54,142,155],"such":[55],"are":[57,125,156],"typically":[58],"computationally":[59],"expensive.":[60],"This":[61],"motivated":[63],"some":[64],"research":[66],"which":[68,152,178],"use":[70],"other":[72],"explored.":[77],"Here,":[78],"we":[79,168],"propose":[80],"efficient":[82],"mechanism":[83],"integrate":[85],"R2":[87],"modified":[91],"version":[92],"Goldberg's":[94],"nondominated":[95],"sorting":[96],"method,":[97],"order":[99],"rank":[101],"individuals":[103],"MOEA.":[106],"Our":[107],"proposed":[108,144,180],"ranking":[109,145,181],"scheme":[110,182],"coupled":[112],"two":[114,120],"different":[115],"search":[116],"engines,":[117],"resulting":[118,171],"new":[121],"MOEAs.":[122,166],"These":[123],"MOEAs":[124,172],"validated":[126],"using":[127],"several":[128],"test":[129],"problems":[130],"and":[131],"measures":[133],"commonly":[134],"adopted":[135],"specialized":[138],"literature.":[139],"Results":[140],"indicate":[141],"approach":[146],"gives":[147],"rise":[148],"effective":[150],"MOEAs,":[151],"produce":[153],"results":[154],"competitive":[157],"respect":[159],"those":[161],"obtained":[162],"by":[163],"three":[164],"well-known":[165],"Additionally,":[167],"validate":[169],"our":[170,179],"problems,":[176],"shows":[183],"its":[184],"advantage,":[186],"since":[187],"it":[188],"able":[190],"outperform":[192],"hypervolume-based":[194],"MOEA,":[195],"requiring":[196],"much":[198],"lower":[199],"computational":[200],"time.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}