{"id":"https://openalex.org/W2086859315","doi":"https://doi.org/10.1145/2739480.2754701","title":"Characterizing Pareto Front Approximations in Many-objective Optimization","display_name":"Characterizing Pareto Front Approximations in Many-objective Optimization","publication_year":2015,"publication_date":"2015-07-07","ids":{"openalex":"https://openalex.org/W2086859315","doi":"https://doi.org/10.1145/2739480.2754701","mag":"2086859315"},"language":"en","primary_location":{"id":"doi:10.1145/2739480.2754701","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2739480.2754701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 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/A5014752949","display_name":"Md Asafuddoula","orcid":"https://orcid.org/0000-0003-4102-6349"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Md Asafuddoula","raw_affiliation_strings":["UNSW, Canberra, Australia"],"affiliations":[{"raw_affiliation_string":"UNSW, Canberra, Australia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061883146","display_name":"Tapabrata Ray","orcid":"https://orcid.org/0000-0003-1950-5917"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tapabrata Ray","raw_affiliation_strings":["UNSW, Canberra, Australia"],"affiliations":[{"raw_affiliation_string":"UNSW, Canberra, Australia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077555584","display_name":"Hemant Kumar Singh","orcid":"https://orcid.org/0000-0003-1653-232X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hemant Kumar Singh","raw_affiliation_strings":["UNSW, Canberra, Australia"],"affiliations":[{"raw_affiliation_string":"UNSW, Canberra, Australia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014752949"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.701,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73365625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"607","last_page":"614"},"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":0.9980000257492065,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6669220924377441},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6652304530143738},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5538248419761658},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5225181579589844},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49724486470222473},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.49063196778297424},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4740181565284729},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4422231614589691},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4285180866718292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4078867733478546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3692704439163208},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10840892791748047}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6669220924377441},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6652304530143738},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5538248419761658},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5225181579589844},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49724486470222473},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.49063196778297424},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4740181565284729},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4422231614589691},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4285180866718292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4078867733478546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3692704439163208},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10840892791748047},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2739480.2754701","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2739480.2754701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W87936626","https://openalex.org/W1504943474","https://openalex.org/W1506010655","https://openalex.org/W1571017796","https://openalex.org/W1612556207","https://openalex.org/W1846834309","https://openalex.org/W1976159118","https://openalex.org/W2001591765","https://openalex.org/W2022485595","https://openalex.org/W2024008934","https://openalex.org/W2049862811","https://openalex.org/W2058923947","https://openalex.org/W2065371917","https://openalex.org/W2081939577","https://openalex.org/W2085830763","https://openalex.org/W2106334424","https://openalex.org/W2109643392","https://openalex.org/W2118028531","https://openalex.org/W2120482366","https://openalex.org/W2125015761","https://openalex.org/W2126105956","https://openalex.org/W2143381319","https://openalex.org/W2156679542","https://openalex.org/W2265976285","https://openalex.org/W3025907391","https://openalex.org/W3029591682","https://openalex.org/W4293860453"],"related_works":["https://openalex.org/W2918702815","https://openalex.org/W2980744436","https://openalex.org/W2292688905","https://openalex.org/W4240078139","https://openalex.org/W2762096397","https://openalex.org/W2027494127","https://openalex.org/W2584277547","https://openalex.org/W4313304367","https://openalex.org/W2320193650","https://openalex.org/W3011561584"],"abstract_inverted_index":{"A":[0],"Pareto":[1,165],"Optimal":[2],"Front":[3],"(POF)":[4],"provides":[5,238,253],"the":[6,18,29,39,63,78,81,127,130,174,183,204,209,217,221,225,235,241,244,251,256,259],"set":[7,168],"of":[8,17,31,38,61,65,80,85,97,126,129,141,150,156,169,185,193,247,258,269],"optimal":[9],"trade-off":[10],"solutions":[11,67,202,233],"formulti-objective":[12],"optimization":[13,56,151],"problems.":[14],"The":[15,72,158,261],"characteristics":[16],"POF,":[19],"e.g.":[20],"continuity,":[21],"convexity,":[22],"spread":[23,172],"and":[24,34,83,116,212,230],"uniformity":[25],"are":[26,89,264],"important":[27],"in":[28,124,234],"context":[30],"decision":[32],"making":[33],"performance":[35],"assessment.":[36],"Most":[37],"existing":[40,106],"metrics":[41,73,263],"(hypervolume,":[42],"inverted":[43],"generational":[44],"distance,":[45],"coverage":[46],"etc.)":[47],"were":[48],"originally":[49],"designed":[50],"for":[51,92,108,146],"two":[52],"or":[53],"three":[54,104],"objective":[55],"problems":[57,93,100,152,271],"with":[58,101,153,176,203],"an":[59,137],"aim":[60],"assessing":[62],"quality":[64],"non-dominated":[66],"delivered":[68],"by":[69],"various":[70],"algorithms.":[71],"provide":[74],"little":[75],"information":[76,123,239,254],"about":[77,240,255],"nature":[79,128],"front":[82,237],"some":[84],"them":[86],"(e.g.":[87],"hypervolume)":[88],"computationally":[90],"expensive":[91],"involving":[94,272],"large":[95],"number":[96,155,268],"objectives.":[98,157,276],"For":[99],"more":[102],"than":[103],"objectives,":[105],"tools":[107],"visualization":[109],"such":[110,186],"as":[111],"parallel":[112],"plots,":[113],"spider/radar":[114],"plots":[115,118],"scatter":[117],"also":[119,180],"offer":[120],"limited":[121],"useful":[122],"terms":[125],"front.":[131],"In":[132,219],"this":[133],"paper,":[134],"we":[135],"introduce":[136],"alternative":[138],"scalar":[139],"measure":[140],"diversity":[142,159],"that":[143,182],"is":[144,160,189],"suitable":[145],"characterizing":[147],"POF":[148],"approximations":[149],"high":[154],"measured":[161],"against":[162],"a":[163,167,187,190,267],"Reference":[164],"Front,":[166],"points":[170,215],"uniformly":[171,213,226],"on":[173,216],"hyperplane":[175,252],"unit":[177],"intercepts.":[178],"We":[179],"illustrate":[181],"computation":[184],"metric":[188],"natural":[191],"extension":[192],"decomposition":[194],"based":[195],"evolutionary":[196],"algorithms":[197],"which":[198],"attempt":[199],"to":[200,274],"align":[201],"reference":[205,228],"directions":[206,229],"constructed":[207],"using":[208,266],"Ideal":[210],"point":[211],"distributed":[214,227],"hyperplane.":[218],"particular,":[220],"perpendicular":[222],"distances":[223],"between":[224],"their":[231],"closest":[232],"nondominated":[236],"diversity,":[242],"while":[243],"shortest":[245],"distance":[246],"every":[248],"solution":[249],"from":[250],"convexity":[257],"POF.":[260],"proposed":[262],"illustrated":[265],"test":[270],"up":[273],"fifteen":[275]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
