{"id":"https://openalex.org/W2434562129","doi":"https://doi.org/10.1162/evco_a_00188","title":"Greedy Hypervolume Subset Selection in Low Dimensions","display_name":"Greedy Hypervolume Subset Selection in Low Dimensions","publication_year":2016,"publication_date":"2016-06-15","ids":{"openalex":"https://openalex.org/W2434562129","doi":"https://doi.org/10.1162/evco_a_00188","mag":"2434562129","pmid":"https://pubmed.ncbi.nlm.nih.gov/27303786"},"language":"en","primary_location":{"id":"doi:10.1162/evco_a_00188","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00188","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5066470602","display_name":"Andreia P. Guerreiro","orcid":"https://orcid.org/0000-0003-0757-2709"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Andreia P. Guerreiro","raw_affiliation_strings":["CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038504776","display_name":"Carlos M. Fonseca","orcid":"https://orcid.org/0000-0001-5162-2457"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Carlos M. Fonseca","raw_affiliation_strings":["CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055996291","display_name":"Lu\u00eds Paquete","orcid":"https://orcid.org/0000-0001-7525-8901"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Lu\u00eds Paquete","raw_affiliation_strings":["CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CISUC, Department of Informatics Engineering, University of Coimbra, P\u00f3lo II, P-3030 290 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038504776","https://openalex.org/A5055996291","https://openalex.org/A5066470602"],"corresponding_institution_ids":["https://openalex.org/I76903346"],"apc_list":null,"apc_paid":null,"fwci":5.4069,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.95887312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"521","last_page":"544"},"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/T12072","display_name":"Machine Learning and Algorithms","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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.8452857732772827},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6568160653114319},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.6260181069374084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6199747323989868},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5937017202377319},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.541573166847229},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4891071915626526},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4868437647819519},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4791147708892822},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47418293356895447},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4649122655391693},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4633313715457916},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.45654797554016113},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.4347837567329407},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4295763671398163},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34335291385650635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31101781129837036},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10290512442588806},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08042958378791809}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.8452857732772827},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6568160653114319},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.6260181069374084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6199747323989868},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5937017202377319},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.541573166847229},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4891071915626526},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4868437647819519},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4791147708892822},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47418293356895447},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4649122655391693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4633313715457916},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.45654797554016113},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.4347837567329407},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4295763671398163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34335291385650635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31101781129837036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10290512442588806},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08042958378791809},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/evco_a_00188","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00188","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},{"id":"pmid:27303786","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27303786","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W86912879","https://openalex.org/W118842119","https://openalex.org/W166394191","https://openalex.org/W1491287429","https://openalex.org/W1558919105","https://openalex.org/W1595498733","https://openalex.org/W1599011794","https://openalex.org/W1680189815","https://openalex.org/W2008049315","https://openalex.org/W2025283589","https://openalex.org/W2038420231","https://openalex.org/W2050914643","https://openalex.org/W2100228661","https://openalex.org/W2108968575","https://openalex.org/W2117068724","https://openalex.org/W2127474646","https://openalex.org/W2132936405","https://openalex.org/W2148615815","https://openalex.org/W2154781286","https://openalex.org/W2187701960","https://openalex.org/W2260039808","https://openalex.org/W2615258659","https://openalex.org/W3118655244","https://openalex.org/W4302557773"],"related_works":["https://openalex.org/W4313349761","https://openalex.org/W2923536170","https://openalex.org/W2963059222","https://openalex.org/W2901206941","https://openalex.org/W2968699064","https://openalex.org/W4300407000","https://openalex.org/W2964314169","https://openalex.org/W2735578456","https://openalex.org/W4296167846","https://openalex.org/W4312724132"],"abstract_inverted_index":{"Given":[0],"a":[1,14,30,63,80,107,117,124],"nondominated":[2],"point":[3,17],"set":[4],"[Formula:":[5,10,18,34,84,95,99,120,131],"see":[6,11,19,35,85,96,100,121,132],"text]":[7,12,36,97,122],"of":[8,28,32,83,119,148],"size":[9,33],"and":[13,49,140,156],"suitable":[15],"reference":[16],"text],":[20],"the":[21,39,70,76,89,103,111,136,146,153],"Hypervolume":[22],"Subset":[23],"Selection":[24],"Problem":[25],"(HSSP)":[26],"consists":[27],"finding":[29],"subset":[31],"that":[37],"maximizes":[38],"hypervolume":[40,104],"indicator.":[41],"It":[42],"arises":[43],"in":[44,138],"connection":[45],"with":[46,62],"multiobjective":[47],"selection":[48],"archiving":[50],"strategies,":[51],"as":[52,54],"well":[53],"Pareto-front":[55],"approximation":[56,165],"postprocessing":[57],"for":[58,75,94,135,152,163],"visualization":[59],"and/or":[60],"interaction":[61],"decision":[64],"maker.":[65],"Efficient":[66],"algorithms":[67,134,151],"to":[68,116],"solve":[69],"HSSP":[71,112,137],"are":[72,143],"available":[73,93],"only":[74],"2-dimensional":[77,154],"case,":[78,155],"achieving":[79],"time":[81],"complexity":[82,147,161],"text].":[86,101],"In":[87,127],"contrast,":[88],"best":[90],"upper":[91],"bound":[92],"is":[98,106],"Since":[102],"indicator":[105],"monotone":[108],"submodular":[109],"function,":[110],"can":[113],"be":[114],"approximated":[115],"factor":[118],"using":[123],"greedy":[125,130],"strategy.":[126],"this":[128,164],"article,":[129],"text]-time":[133],"2":[139],"3":[141],"dimensions":[142],"proposed,":[144],"matching":[145],"current":[149],"exact":[150],"considerably":[157],"improving":[158],"upon":[159],"recent":[160],"results":[162],"problem.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}