{"id":"https://openalex.org/W2604292605","doi":"https://doi.org/10.1145/3040718.3040730","title":"Hypervolume Subset Selection for Triangular and Inverted Triangular Pareto Fronts of Three-Objective Problems","display_name":"Hypervolume Subset Selection for Triangular and Inverted Triangular Pareto Fronts of Three-Objective Problems","publication_year":2017,"publication_date":"2017-01-12","ids":{"openalex":"https://openalex.org/W2604292605","doi":"https://doi.org/10.1145/3040718.3040730","mag":"2604292605"},"language":"en","primary_location":{"id":"doi:10.1145/3040718.3040730","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3040718.3040730","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms","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":["Osaka Prefecture University, Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Osaka Prefecture University, Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057108498","display_name":"Ryo Imada","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":"Ryo Imada","raw_affiliation_strings":["Osaka Prefecture University, Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Osaka Prefecture University, Sakai, Japan","institution_ids":["https://openalex.org/I15807432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072935373","display_name":"Yu Setoguchi","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":"Yu Setoguchi","raw_affiliation_strings":["Osaka Prefecture University, Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Osaka Prefecture University, 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":["Osaka Prefecture Univesity, Sakai, Japan"],"affiliations":[{"raw_affiliation_string":"Osaka Prefecture Univesity, 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":3.6338,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9387663,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"95","last_page":"110"},"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9933000206947327,"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/maximization","display_name":"Maximization","score":0.7827836275100708},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6941637992858887},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6788560748100281},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6516252756118774},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6363382935523987},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5981389284133911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.568244993686676},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.534919798374176},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.470625638961792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24605020880699158},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22917228937149048},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11410084366798401}],"concepts":[{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.7827836275100708},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6941637992858887},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6788560748100281},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6516252756118774},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6363382935523987},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5981389284133911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.568244993686676},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.534919798374176},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.470625638961792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24605020880699158},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22917228937149048},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11410084366798401},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3040718.3040730","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3040718.3040730","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms","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/W1480517346","https://openalex.org/W1558919105","https://openalex.org/W1562465485","https://openalex.org/W1564638059","https://openalex.org/W1846834309","https://openalex.org/W1985197628","https://openalex.org/W2008049315","https://openalex.org/W2025283589","https://openalex.org/W2038420231","https://openalex.org/W2072116998","https://openalex.org/W2085507535","https://openalex.org/W2098907614","https://openalex.org/W2108968575","https://openalex.org/W2117068724","https://openalex.org/W2143185749","https://openalex.org/W2144982506","https://openalex.org/W2148615815","https://openalex.org/W2156384963","https://openalex.org/W2275394662","https://openalex.org/W2336282002","https://openalex.org/W2343498104","https://openalex.org/W2434562129","https://openalex.org/W2466060750","https://openalex.org/W2559591803","https://openalex.org/W4301762632"],"related_works":["https://openalex.org/W2900864464","https://openalex.org/W2475480881","https://openalex.org/W2121723556","https://openalex.org/W2288977275","https://openalex.org/W54727051","https://openalex.org/W2783639087","https://openalex.org/W2155956102","https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2390244926"],"abstract_inverted_index":{"Hypervolume":[0],"subset":[1,39],"selection":[2,40],"is":[3,53,75,89,148,164,191,198,208],"to":[4,54,121,178,200],"find":[5],"a":[6,63,141],"pre-specified":[7],"number":[8],"of":[9,17,59,62,73,101,137,140,189],"solutions":[10,18,74,96,190],"for":[11,27,41,66],"hypervolume":[12,38,67],"maximization.":[13],"The":[14,186],"optimal":[15,71,146,187],"distribution":[16,72,147,188],"on":[19,69,98,144],"the":[20,31,57,60,70,86,92,99,102,113,135,138,145,157,167,195,201,210,214],"Pareto":[21,49,83,93,105,116,160,174,184,202,215],"front":[22,106,203],"has":[23],"been":[24],"theoretically":[25],"studied":[26],"two-objective":[28],"problems":[29,43,125,155,171,180],"in":[30,123],"literature.":[32],"In":[33],"this":[34],"paper,":[35],"we":[36],"discuss":[37],"three-objective":[42],"with":[44,126,156,172,181],"triangular":[45,48,79,82,104,115,159,173,183],"and":[46,80,153,213],"inverted":[47,81,103,182],"fronts.":[50,84,161,185],"Our":[51],"contribution":[52],"show":[55,133],"that":[56,134,169],"effect":[58,136],"location":[61,139,207],"reference":[64,87,142,196],"point":[65,88,143,197,212],"calculation":[68],"totally":[76,149],"different":[77,150],"between":[78,151,209],"When":[85],"far":[90],"from":[91],"front,":[94],"most":[95],"are":[97,109,176],"sides":[100],"while":[107],"they":[108],"evenly":[110],"distributed":[111],"over":[112],"entire":[114],"front.":[117],"These":[118],"properties":[119],"seem":[120],"hold":[122],"multiobjective":[124],"four":[127],"or":[128],"more":[129],"objectives.":[130],"We":[131],"also":[132,192],"maximization":[152,170],"minimization":[154,179],"same":[158],"This":[162],"property":[163],"supported":[165],"by":[166],"fact":[168],"fronts":[175],"equivalent":[177],"discussed":[193],"when":[194,205],"close":[199],"(i.e.,":[204],"its":[206],"nadir":[211],"front).":[216]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
