{"id":"https://openalex.org/W2062166073","doi":"https://doi.org/10.1109/cec.2013.6557739","title":"Many-objective and many-variable test problems for visual examination of multiobjective search","display_name":"Many-objective and many-variable test problems for visual examination of multiobjective search","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2062166073","doi":"https://doi.org/10.1109/cec.2013.6557739","mag":"2062166073"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2013.6557739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557739","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":"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/A5035595838","display_name":"Hisao Ishibuchi","orcid":"https://orcid.org/0000-0001-9186-6472"},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hisao Ishibuchi","raw_affiliation_strings":["Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","institution_ids":["https://openalex.org/I15807432"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057582529","display_name":"Masakazu Yamane","orcid":null},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masakazu Yamane","raw_affiliation_strings":["Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","institution_ids":["https://openalex.org/I15807432"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022311020","display_name":"Naoya Akedo","orcid":null},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Naoya Akedo","raw_affiliation_strings":["Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","institution_ids":["https://openalex.org/I15807432"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004957967","display_name":"Yusuke Nojima","orcid":"https://orcid.org/0000-0003-4853-1305"},"institutions":[{"id":"https://openalex.org/I15807432","display_name":"Osaka Prefecture University","ror":"https://ror.org/02cf1je33","country_code":"JP","type":"education","lineage":["https://openalex.org/I15807432"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yusuke Nojima","raw_affiliation_strings":["Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai, Osaka, Japan","institution_ids":["https://openalex.org/I15807432"]},{"raw_affiliation_string":"Dept. of Comput. Sci. & Intell. Syst., Osaka Prefecture Univ., Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035595838"],"corresponding_institution_ids":["https://openalex.org/I15807432"],"apc_list":null,"apc_paid":null,"fwci":5.0756,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.95632062,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.989300012588501,"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":0.9837999939918518,"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/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6782153844833374},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5716648101806641},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5474855899810791},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4686198830604553},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4598442316055298},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4414314925670624},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4402645528316498},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.43575894832611084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39529672265052795},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3484717011451721}],"concepts":[{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6782153844833374},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5716648101806641},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5474855899810791},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4686198830604553},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4598442316055298},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4414314925670624},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4402645528316498},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.43575894832611084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39529672265052795},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3484717011451721},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2013.6557739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557739","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":[{"id":"https://metadata.un.org/sdg/16","score":0.4399999976158142,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W69831977","https://openalex.org/W1484287363","https://openalex.org/W1496927484","https://openalex.org/W1500125712","https://openalex.org/W1502374754","https://openalex.org/W1503648602","https://openalex.org/W1519778441","https://openalex.org/W1575601714","https://openalex.org/W1581487892","https://openalex.org/W1583993532","https://openalex.org/W1585939719","https://openalex.org/W1595498733","https://openalex.org/W1605170913","https://openalex.org/W1607221389","https://openalex.org/W1976656630","https://openalex.org/W1980729457","https://openalex.org/W1987958230","https://openalex.org/W1990057974","https://openalex.org/W2020320008","https://openalex.org/W2025525377","https://openalex.org/W2038420231","https://openalex.org/W2050914643","https://openalex.org/W2106334424","https://openalex.org/W2108968575","https://openalex.org/W2118693290","https://openalex.org/W2126105956","https://openalex.org/W2126273906","https://openalex.org/W2143381319","https://openalex.org/W2148933727","https://openalex.org/W2162974421","https://openalex.org/W6602830933","https://openalex.org/W6629608623","https://openalex.org/W6630373516","https://openalex.org/W6631285064","https://openalex.org/W6634933633","https://openalex.org/W6635097213","https://openalex.org/W6656537966"],"related_works":["https://openalex.org/W3094456605","https://openalex.org/W2744462909","https://openalex.org/W4287635425","https://openalex.org/W3127946984","https://openalex.org/W3097111480","https://openalex.org/W2029959045","https://openalex.org/W2111219748","https://openalex.org/W2394981641","https://openalex.org/W1534737284","https://openalex.org/W1994436307"],"abstract_inverted_index":{"In":[0,159],"the":[1,19,24,31,44,58,68,100,122,132,137,140,155,164,174,207,227,236,245],"development":[2],"of":[3,21,67,83,103,114,134,142,147,166,173,209,229,239,247],"evolutionary":[4],"multiobjective":[5,69],"optimization":[6],"(EMO)":[7],"algorithms,":[8],"it":[9],"is":[10,38,71,128,136,191],"important":[11],"to":[12,40,97,244],"implement":[13],"a":[14,41,64,112,117,178,198,232],"good":[15],"balancing":[16],"mechanism":[17],"between":[18],"convergence":[20],"solutions":[22,53],"towards":[23],"Pareto":[25,32],"front":[26],"and":[27],"their":[28],"diversity":[29,246],"over":[30],"front.":[33],"When":[34],"an":[35,129,201,217],"EMO":[36,104,148,210,240],"algorithm":[37],"applied":[39],"two-objective":[42],"problem,":[43],"balance":[45],"can":[46,150],"be":[47,151],"easily":[48],"visualized":[49],"by":[50,111,193],"showing":[51],"all":[52],"at":[54],"each":[55,126],"generation":[56],"in":[57,94,116,154,177,200],"two-dimensional":[59,118,156],"objective":[60],"space.":[61,158,181,204],"However,":[62],"such":[63,216],"visual":[65,171],"examination":[66,172],"search":[70,101,145,175,237],"difficult":[72],"for":[73,170],"many-objective":[74,84,167],"problems":[75,86,108,169],"with":[76,87,188,242],"four":[77],"or":[78],"more":[79],"objectives.":[80],"The":[81,144],"use":[82,165],"test":[85,107,168,186,220],"two":[88],"decision":[89,119,157,180,203],"variables":[90,190,230],"has":[91,231],"been":[92],"proposed":[93],"some":[95],"studies":[96],"visually":[98,152],"examine":[99,206],"behavior":[102,146,176,208,238],"algorithms.":[105],"Such":[106],"are":[109],"defined":[110],"number":[113,133,141,228],"points":[115,196],"space":[120],"where":[121],"distance":[123],"minimization":[124],"from":[125],"point":[127],"objective.":[130],"Thus":[131],"objectives":[135],"same":[138],"as":[139],"points.":[143],"algorithms":[149,211,241],"examined":[153],"this":[160],"paper,":[161],"we":[162],"propose":[163],"high-dimensional":[179],"More":[182],"specifically,":[183],"our":[184],"m-objective":[185,218],"problem":[187],"n":[189],"generated":[192],"specifying":[194],"m":[195],"on":[197,215,235],"plane":[199],"n-dimensional":[202],"We":[205],"through":[212],"computational":[213],"experiments":[214],"n-variable":[219],"problem.":[221],"Our":[222],"experimental":[223],"results":[224],"show":[225],"that":[226],"large":[233],"effect":[234],"respect":[243],"solutions.":[248]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}