{"id":"https://openalex.org/W2804893940","doi":"https://doi.org/10.1145/3205455.3205572","title":"Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference","display_name":"Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference","publication_year":2018,"publication_date":"2018-07-02","ids":{"openalex":"https://openalex.org/W2804893940","doi":"https://doi.org/10.1145/3205455.3205572","mag":"2804893940"},"language":"en","primary_location":{"id":"doi:10.1145/3205455.3205572","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3205455.3205572","pdf_url":null,"source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.manchester.ac.uk/portal/en/publications/dominance-epsilon-and-hypervolume-local-optimal-sets-in-multiobjective-optimization-and-how-to-tell-the-difference(2664c1cf-9e0b-427b-bb5d-03e3c2125086).html","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004181293","display_name":"Arnaud Liefooghe","orcid":"https://orcid.org/0000-0003-3283-3122"},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Arnaud Liefooghe","raw_affiliation_strings":["Univ. Lille, Lille, France"],"affiliations":[{"raw_affiliation_string":"Univ. Lille, Lille, France","institution_ids":["https://openalex.org/I2279609970"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014676600","display_name":"Manuel L\u00f3pez\u2010Ib\u00e1\u00f1ez","orcid":"https://orcid.org/0000-0001-9974-1295"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Manuel L\u00f3pez-Ib\u00e1\u00f1ez","raw_affiliation_strings":["University of Manchester, Manchester, UK","University of Manchester [Manchester] (Oxford Rd, Manchester M13 9PL - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"University of Manchester, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"University of Manchester [Manchester] (Oxford Rd, Manchester M13 9PL - United Kingdom)","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","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":false,"raw_author_name":"Lu\u00eds Paquete","raw_affiliation_strings":["University of Coimbra, Coimbra, Portugal","UC - University of Coimbra [Portugal] (Portugal)"],"affiliations":[{"raw_affiliation_string":"University of Coimbra, Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"UC - University of Coimbra [Portugal] (Portugal)","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078220546","display_name":"Seb\u00e1stien V\u00e9rel","orcid":"https://orcid.org/0000-0003-1661-4093"},"institutions":[{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S\u00e9bastien Verel","raw_affiliation_strings":["Univ. Littoral C\u00f4te d'Opale, Calais, France"],"affiliations":[{"raw_affiliation_string":"Univ. Littoral C\u00f4te d'Opale, Calais, France","institution_ids":["https://openalex.org/I2802487185"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004181293"],"corresponding_institution_ids":["https://openalex.org/I2279609970"],"apc_list":null,"apc_paid":null,"fwci":1.8308,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85035211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"324","last_page":"331"},"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":0.9980999827384949,"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/T10969","display_name":"Water resources management and optimization","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/mathematics","display_name":"Mathematics","score":0.6977762579917908},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6222255229949951},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5976048707962036},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5477244257926941},{"id":"https://openalex.org/keywords/dominance","display_name":"Dominance (genetics)","score":0.4740067422389984},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47153574228286743},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.45699140429496765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4471408426761627},{"id":"https://openalex.org/keywords/preference-relation","display_name":"Preference relation","score":0.4328634440898895},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4151528477668762},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.356334924697876},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25538718700408936},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16789424419403076},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07991549372673035}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6977762579917908},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6222255229949951},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5976048707962036},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5477244257926941},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.4740067422389984},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47153574228286743},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.45699140429496765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4471408426761627},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.4328634440898895},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4151528477668762},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.356334924697876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25538718700408936},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16789424419403076},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07991549372673035},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/3205455.3205572","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3205455.3205572","pdf_url":null,"source":{"id":"https://openalex.org/S4363608932","display_name":"Proceedings of the Genetic and Evolutionary Computation Conference","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Genetic and Evolutionary Computation Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:publications/2664c1cf-9e0b-427b-bb5d-03e3c2125086","is_oa":true,"landing_page_url":null,"pdf_url":"https://www.research.manchester.ac.uk/portal/en/publications/dominance-epsilon-and-hypervolume-local-optimal-sets-in-multiobjective-optimization-and-how-to-tell-the-difference(2664c1cf-9e0b-427b-bb5d-03e3c2125086).html","source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.atira.dk:publications/2664c1cf-9e0b-427b-bb5d-03e3c2125086","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/2664c1cf-9e0b-427b-bb5d-03e3c2125086","pdf_url":"https://www.research.manchester.ac.uk/portal/en/publications/dominance-epsilon-and-hypervolume-local-optimal-sets-in-multiobjective-optimization-and-how-to-tell-the-difference(2664c1cf-9e0b-427b-bb5d-03e3c2125086).html","source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Liefooghe, A, Lopez-Ibanez, M, Paquete, L & Verel, S 2018, Dominance, Epsilon, and Hypervolume Local Optimal Sets in Multi-objective Optimization, and How to Tell the Difference. in Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2018 . https://doi.org/10.1145/3205455.3205572","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-01823666v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01823666","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"GECCO 2018 - Genetic and Evolutionary Computation Conference, Jul 2018, Kyoto, Japan. pp.324-331, &#x27E8;10.1145/3205455.3205572&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:lilloa.univ-lille.fr:20.500.12210/22961","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12210/22961","pdf_url":null,"source":{"id":"https://openalex.org/S4306402203","display_name":"LillOA (Universit\u00e9 de Lille (University Of Lille))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210123514","host_organization_name":"Centre d'Etudes en Civilisations, Langues et Litt\u00e9ratures Etrang\u00e8res","host_organization_lineage":["https://openalex.org/I4210123514"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/2664c1cf-9e0b-427b-bb5d-03e3c2125086","is_oa":true,"landing_page_url":null,"pdf_url":"https://www.research.manchester.ac.uk/portal/en/publications/dominance-epsilon-and-hypervolume-local-optimal-sets-in-multiobjective-optimization-and-how-to-tell-the-difference(2664c1cf-9e0b-427b-bb5d-03e3c2125086).html","source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2804893940.pdf","grobid_xml":"https://content.openalex.org/works/W2804893940.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1522860708","https://openalex.org/W1976513030","https://openalex.org/W1991817987","https://openalex.org/W1995780467","https://openalex.org/W2005184489","https://openalex.org/W2034694420","https://openalex.org/W2073819677","https://openalex.org/W2105291362","https://openalex.org/W2118028531","https://openalex.org/W2133275519","https://openalex.org/W2517235705","https://openalex.org/W3097975330","https://openalex.org/W3100012702"],"related_works":["https://openalex.org/W2485961789","https://openalex.org/W4205262062","https://openalex.org/W2408137423","https://openalex.org/W2022533988","https://openalex.org/W2096290915","https://openalex.org/W2790208073","https://openalex.org/W2016410556","https://openalex.org/W1595663582","https://openalex.org/W3122913338","https://openalex.org/W4232816123"],"abstract_inverted_index":{"Local":[0],"search":[1],"algorithms":[2],"have":[3,143],"shown":[4],"good":[5],"performance":[6],"for":[7,146],"several":[8],"multi-objective":[9,68,147],"combinatorial":[10],"optimization":[11],"problems.":[12],"These":[13,141],"approaches":[14],"naturally":[15],"stop":[16],"at":[17],"a":[18,152,177],"local":[19,148],"optimal":[20],"set":[21,53],"(LO-set)":[22],"under":[23,51,103,107,115,119,123,129,136,139,170],"given":[24],"definitions":[25],"of":[26,33,80,93,100],"neighborhood":[27],"and":[28,88,110,112,162],"preference":[29,54,76],"relation":[30],"among":[31],"subsets":[32],"solutions,":[34],"such":[35],"as":[36],"set-based":[37],"dominance":[38],"relation,":[39,77],"hypervolume":[40],"or":[41,172],"epsilon":[42,109,124,137,171],"indicator.":[43],"It":[44],"is":[45,180],"an":[46,63,168],"open":[47],"question":[48],"how":[49],"LO-sets":[50,81,99,106,114,118,122,128,135],"different":[52],"relations":[55],"relate":[56],"to":[57,134,166,182,188],"each":[58],"other.":[59],"This":[60],"paper":[61],"reports":[62],"in-depth":[64],"experimental":[65],"analysis":[66],"on":[67],"nk-landscapes.":[69],"Our":[70],"results":[71],"reveal":[72],"that,":[73],"whatever":[74],"the":[75,78,85,91,175],"number":[79,92],"typically":[82],"increases":[83],"with":[84,90,155],"problem":[86],"non-linearity,":[87],"decreases":[89],"objectives.":[94],"We":[95],"observe":[96],"that":[97,113],"strict":[98],"bounded":[101,156],"cardinality":[102],"set-dominance":[104,130],"are":[105,117,125,131],"both":[108],"hypervolume,":[111],"hyper-volume":[116],"set-dominance,":[120],"whereas":[121],"not.":[126],"Nonetheless,":[127],"more":[132,159,184],"similar":[133],"than":[138],"hypervolume.":[140,173],"findings":[142],"important":[144],"implications":[145],"search.":[149],"For":[150],"instance,":[151],"dominance-based":[153],"approach":[154,179],"archive":[157],"gets":[158],"easily":[160],"trapped":[161],"might":[163],"experience":[164],"difficulty":[165],"identify":[167],"LO-set":[169],"On":[174],"contrary,":[176],"hypervolume-based":[178],"expected":[181],"perform":[183],"steps":[185],"before":[186],"converging":[187],"better":[189],"approximations.":[190]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
