{"id":"https://openalex.org/W3211644589","doi":"https://doi.org/10.1109/tcyb.2021.3125071","title":"Solution Set Augmentation for Knee Identification in Multiobjective Decision Analysis","display_name":"Solution Set Augmentation for Knee Identification in Multiobjective Decision Analysis","publication_year":2021,"publication_date":"2021-11-13","ids":{"openalex":"https://openalex.org/W3211644589","doi":"https://doi.org/10.1109/tcyb.2021.3125071","mag":"3211644589","pmid":"https://pubmed.ncbi.nlm.nih.gov/34767520"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2021.3125071","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3125071","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","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":null,"display_name":"Guo Yu","orcid":"https://orcid.org/0000-0003-2302-2010"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo Yu","raw_affiliation_strings":["Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-2302-2010","affiliations":[{"raw_affiliation_string":"Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032314861","display_name":"Yaochu Jin","orcid":"https://orcid.org/0000-0003-1100-0631"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Yaochu Jin","raw_affiliation_strings":["Chair of Nature Inspired Computing and Engineering, Faculty of Technology, Bielefeld University, Bielefeld, Germany","Department of Computer Science, University of Surrey, Guildford, Surrey, U.K"],"raw_orcid":"https://orcid.org/0000-0003-1100-0631","affiliations":[{"raw_affiliation_string":"Chair of Nature Inspired Computing and Engineering, Faculty of Technology, Bielefeld University, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"Department of Computer Science, University of Surrey, Guildford, Surrey, U.K","institution_ids":["https://openalex.org/I28290843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086755250","display_name":"Markus Olhofer","orcid":"https://orcid.org/0000-0002-3062-3829"},"institutions":[{"id":"https://openalex.org/I4210112253","display_name":"Honda (Germany)","ror":"https://ror.org/022c1xk47","country_code":"DE","type":"company","lineage":["https://openalex.org/I1283473643","https://openalex.org/I4210112253"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Olhofer","raw_affiliation_strings":["Honda Research Institute Europe GmbH, Offenbach/Main, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3062-3829","affiliations":[{"raw_affiliation_string":"Honda Research Institute Europe GmbH, Offenbach/Main, Germany","institution_ids":["https://openalex.org/I4210112253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042399424","display_name":"Qiqi Liu","orcid":"https://orcid.org/0000-0003-1587-5515"},"institutions":[{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Qiqi Liu","raw_affiliation_strings":["Department of Computer Science, University of Surrey, Guildford, U.K"],"raw_orcid":"https://orcid.org/0000-0003-1587-5515","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Surrey, Guildford, U.K","institution_ids":["https://openalex.org/I28290843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048267931","display_name":"Wenli Du","orcid":"https://orcid.org/0000-0002-2676-6341"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenli Du","raw_affiliation_strings":["Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2676-6341","affiliations":[{"raw_affiliation_string":"Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0133,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.80327747,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"4","first_page":"2480","last_page":"2493"},"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9976999759674072,"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":0.9878000020980835,"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/benchmark","display_name":"Benchmark (surveying)","score":0.7248339653015137},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6891859173774719},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.6240843534469604},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6191847920417786},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.61371910572052},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5949546694755554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5303930640220642},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45512884855270386},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41185176372528076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3490513563156128}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7248339653015137},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6891859173774719},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.6240843534469604},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6191847920417786},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.61371910572052},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5949546694755554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5303930640220642},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45512884855270386},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41185176372528076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3490513563156128},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcyb.2021.3125071","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3125071","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:34767520","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34767520","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":"IEEE transactions on cybernetics","raw_type":null},{"id":"pmh:oai:pub.uni-bielefeld.de:2960436","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2960436","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3578109697","display_name":null,"funder_award_id":"62103150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4427995887","display_name":null,"funder_award_id":"61725301","funder_id":"https://openalex.org/F4320336125","funder_display_name":"National Science Fund for Distinguished Young Scholars"},{"id":"https://openalex.org/G6128435363","display_name":null,"funder_award_id":"2021M691012","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6511873551","display_name":null,"funder_award_id":"62136003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F1991941565","display_name":"Honda Research Institute Europe","ror":"https://ror.org/028cc2127"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320336125","display_name":"National Science Fund for Distinguished Young Scholars","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W225560312","https://openalex.org/W763499377","https://openalex.org/W1486418736","https://openalex.org/W1506010655","https://openalex.org/W1507162258","https://openalex.org/W1553573873","https://openalex.org/W1695563742","https://openalex.org/W1879678483","https://openalex.org/W1920632974","https://openalex.org/W1967157470","https://openalex.org/W2003409240","https://openalex.org/W2008499862","https://openalex.org/W2011174137","https://openalex.org/W2020320008","https://openalex.org/W2040137081","https://openalex.org/W2040622444","https://openalex.org/W2072661909","https://openalex.org/W2075356520","https://openalex.org/W2086379452","https://openalex.org/W2089929273","https://openalex.org/W2090235798","https://openalex.org/W2105245738","https://openalex.org/W2106334424","https://openalex.org/W2111526171","https://openalex.org/W2119208341","https://openalex.org/W2131436844","https://openalex.org/W2136918060","https://openalex.org/W2146134063","https://openalex.org/W2146216407","https://openalex.org/W2170176908","https://openalex.org/W2333879426","https://openalex.org/W2546299924","https://openalex.org/W2559279975","https://openalex.org/W2588086554","https://openalex.org/W2588272390","https://openalex.org/W2599319023","https://openalex.org/W2739082215","https://openalex.org/W2744038038","https://openalex.org/W2747781258","https://openalex.org/W2752455195","https://openalex.org/W2755582626","https://openalex.org/W2763990018","https://openalex.org/W2764251381","https://openalex.org/W2772079570","https://openalex.org/W2785722638","https://openalex.org/W2798336324","https://openalex.org/W2883388603","https://openalex.org/W2891186800","https://openalex.org/W2895854944","https://openalex.org/W2914044793","https://openalex.org/W2956883339","https://openalex.org/W2962800945","https://openalex.org/W2964502788","https://openalex.org/W2969104687","https://openalex.org/W2994776571","https://openalex.org/W3016419690","https://openalex.org/W3037258640","https://openalex.org/W3043537770","https://openalex.org/W3123270512","https://openalex.org/W4241971694","https://openalex.org/W4249753629","https://openalex.org/W4388297464","https://openalex.org/W6609450013","https://openalex.org/W6640059419","https://openalex.org/W6702881703","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W2996366161","https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2001591765","https://openalex.org/W2073147994","https://openalex.org/W1588199609","https://openalex.org/W2384474142","https://openalex.org/W1550055091","https://openalex.org/W2744462909","https://openalex.org/W3083133203"],"abstract_inverted_index":{"In":[0],"multiobjective":[1],"decision":[2,120],"making,":[3],"most":[4],"knee":[5,24,78,162],"identification":[6],"algorithms":[7],"implicitly":[8],"assume":[9],"that":[10,63],"the":[11,34,42,45,52,65,77,81,109,113,119,123,134,141,147,150,159,165],"given":[12,142],"solutions":[13,104,130,163],"are":[14,96,105,131],"well":[15],"distributed":[16],"and":[17,93,116,138,182],"can":[18],"provide":[19],"sufficient":[20],"information":[21],"for":[22,158],"identifying":[23],"solutions.":[25],"However,":[26],"this":[27],"assumption":[28],"may":[29],"fail":[30],"to":[31,76,118,140,185],"hold":[32],"when":[33,41,164],"number":[35],"of":[36,44,80,125,149,161,173],"objectives":[37],"is":[38,48,87,156,169,175],"large":[39],"or":[40],"shape":[43],"Pareto":[46,66,82,167],"front":[47,67,168],"complex.":[49],"To":[50,145],"address":[51],"above":[53],"issues,":[54],"we":[55],"propose":[56],"a":[57,69,91,99,154,186],"knee-oriented":[58],"solution":[59,143,152],"augmentation":[60],"(KSA)":[61],"framework":[62],"converts":[64],"into":[68],"multimodal":[70],"auxiliary":[71,85],"function":[72,86],"whose":[73],"basins":[74,95,111],"correspond":[75],"regions":[79],"front.":[83],"The":[84,171],"then":[88,106],"approximated":[89],"using":[90],"surrogate":[92],"its":[94],"identified":[97],"by":[98,133],"peak":[100],"detection":[101],"method.":[102],"Additional":[103],"generated":[107],"in":[108,112],"detected":[110],"objective":[114,136],"space":[115,121],"mapped":[117],"with":[122],"help":[124],"an":[126],"inverse":[127],"model.":[128],"These":[129],"evaluated":[132],"original":[135],"functions":[137],"added":[139],"set.":[144],"assess":[146],"quality":[148],"augmented":[151],"set,":[153],"measurement":[155],"proposed":[157],"verification":[160],"true":[166],"unknown.":[170],"effectiveness":[172],"KSA":[174],"verified":[176],"on":[177],"widely":[178],"used":[179],"benchmark":[180],"problems":[181],"successfully":[183],"applied":[184],"hybrid":[187],"electric":[188],"vehicle":[189],"controller":[190],"design":[191],"problem.":[192]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
