{"id":"https://openalex.org/W2008049315","doi":"https://doi.org/10.1145/2576768.2598276","title":"Two-dimensional subset selection for hypervolume and epsilon-indicator","display_name":"Two-dimensional subset selection for hypervolume and epsilon-indicator","publication_year":2014,"publication_date":"2014-07-11","ids":{"openalex":"https://openalex.org/W2008049315","doi":"https://doi.org/10.1145/2576768.2598276","mag":"2008049315"},"language":"en","primary_location":{"id":"doi:10.1145/2576768.2598276","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2576768.2598276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2014 Annual Conference on Genetic and 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/A5044394587","display_name":"Karl Bringmann","orcid":"https://orcid.org/0000-0003-1356-5177"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Karl Bringmann","raw_affiliation_strings":["Max Planck Institute for Informatics, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Informatics, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077389210","display_name":"Tobias Friedrich","orcid":"https://orcid.org/0000-0003-0076-6308"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Friedrich","raw_affiliation_strings":["Friedrich-Schiller-Universit\u00e4t Jena, Jena, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Schiller-Universit\u00e4t Jena, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043940262","display_name":"Patrick Klitzke","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Patrick Klitzke","raw_affiliation_strings":["Universit\u00e4t des Saarlandes, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t des Saarlandes, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044394587"],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":null,"apc_paid":null,"fwci":8.4085,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.9803734,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"589","last_page":"596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9976999759674072,"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":0.9939000010490417,"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/selection","display_name":"Selection (genetic algorithm)","score":0.6863281726837158},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6725299954414368},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5266801118850708},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5100551247596741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48507848381996155},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4715675711631775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46547171473503113},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4605511724948883},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42782413959503174},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4150159955024719},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4122583866119385},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3723064064979553},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12290215492248535},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07334211468696594}],"concepts":[{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6863281726837158},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6725299954414368},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5266801118850708},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5100551247596741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48507848381996155},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4715675711631775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46547171473503113},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4605511724948883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42782413959503174},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4150159955024719},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4122583866119385},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3723064064979553},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12290215492248535},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07334211468696594},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2576768.2598276","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2576768.2598276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:escidoc.org:escidoc:2073188","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0024-413F-F","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W21003870","https://openalex.org/W86912879","https://openalex.org/W118285713","https://openalex.org/W133511943","https://openalex.org/W1564638059","https://openalex.org/W1599011794","https://openalex.org/W1604295974","https://openalex.org/W1976093161","https://openalex.org/W2002682954","https://openalex.org/W2007928479","https://openalex.org/W2038420231","https://openalex.org/W2049864887","https://openalex.org/W2117068724","https://openalex.org/W2127474646","https://openalex.org/W2129143099","https://openalex.org/W2154781286","https://openalex.org/W2160088187","https://openalex.org/W4251391716"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2606073172","https://openalex.org/W2125356288","https://openalex.org/W2128302072","https://openalex.org/W2970622411","https://openalex.org/W2386767533","https://openalex.org/W2355215981","https://openalex.org/W2153798538","https://openalex.org/W2193130317","https://openalex.org/W2103427656"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,11,96,147,154],"bi-objective":[3,19],"optimization":[4],"is":[5,22,124],"to":[6,56],"find":[7],"a":[8,106,125,152],"small":[9],"set":[10,92],"good":[12],"compromise":[13],"solutions.":[14],"A":[15],"common":[16],"problem":[17,27],"for":[18,68,89,109,128,162],"evolutionary":[20],"algorithms":[21],"the":[23,36,51,63,76,86,110,129,144,148,159,169],"following":[24],"subset":[25],"selection":[26],"(SSP):":[28],"Given":[29],"n":[30,136],"solutions":[31,41],"P":[32,44],"\u2282":[33,94],"R2":[34,95],"in":[35],"objective":[37],"space,":[38],"select":[39,57],"k":[40,58],"P*":[42,60,83],"from":[43],"that":[45,61,84,168],"optimize":[46],"an":[47],"indicator":[48,65],"function.":[49],"In":[50],"hypervolume":[52,64,111],"SSP":[53,78,112,131],"we":[54],"want":[55],"points":[59],"maximize":[62],"IHYP(P*,":[66],"r)":[67],"some":[69,90],"reference":[70,91],"point":[71],"r":[72],"\u2208":[73],"R2.":[74],"Similarly,":[75],"\u03b5-indicator":[77,87,130],"aims":[79],"at":[80],"selecting":[81],"k~points":[82],"minimize":[85],"I\u03b5(P*,R)":[88],"R":[93],"size":[97],"m":[98,138],"(which":[99],"can":[100],"be":[101],"R=P).":[102],"We":[103],"first":[104],"present":[105],"new":[107,126,163],"algorithm":[108,127],"with":[113,132],"runtime":[114,133,176],"O(n":[115,134],"(k":[116],"+":[117,137],"log":[118,135,139],"n)).":[119],"Our":[120],"second":[121],"main":[122],"result":[123],"m).":[140],"Both":[141],"results":[142,171],"improve":[143],"current":[145],"state":[146],"art":[149],"runtimes":[150],"by":[151],"factor":[153],"(nearly)":[155],"$n$":[156],"and":[157],"make":[158],"problems":[160],"tractable":[161],"applications.":[164],"Preliminary":[165],"experiments":[166],"confirm":[167],"theoretical":[170],"translate":[172],"into":[173],"substantial":[174],"empirical":[175],"improvements.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
