{"id":"https://openalex.org/W1983370583","doi":"https://doi.org/10.1109/cec.2009.4983076","title":"Constructing test problems for bilevel evolutionary multi-objective optimization","display_name":"Constructing test problems for bilevel evolutionary multi-objective optimization","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W1983370583","doi":"https://doi.org/10.1109/cec.2009.4983076","mag":"1983370583"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2009.4983076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983076","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Congress on 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/A5088394271","display_name":"Kalyanmoy Deb","orcid":"https://orcid.org/0000-0001-7402-9939"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Business Technology, Helsinki School of Economics, Helsinki, Finland","Department of Business Technology, Helsinki School of Economics, PO Box 1210, FIN-00101, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Business Technology, Helsinki School of Economics, Helsinki, Finland","institution_ids":[]},{"raw_affiliation_string":"Department of Business Technology, Helsinki School of Economics, PO Box 1210, FIN-00101, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018720209","display_name":"Ankur Sinha","orcid":"https://orcid.org/0000-0002-0464-6736"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Ankur Sinha","raw_affiliation_strings":["Department of Business Technology, Helsinki School of Economics, Helsinki, Finland","Department of Business Technology, Helsinki School of Economics, PO Box 1210, FIN-00101, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Business Technology, Helsinki School of Economics, Helsinki, Finland","institution_ids":[]},{"raw_affiliation_string":"Department of Business Technology, Helsinki School of Economics, PO Box 1210, FIN-00101, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088394271"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":2.4815,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.88217221,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1153","last_page":"1160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9674000144004822,"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":0.9635999798774719,"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/bilevel-optimization","display_name":"Bilevel optimization","score":0.9531916379928589},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7449148297309875},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6615868806838989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6123431324958801},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5855094790458679},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5220541954040527},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48985525965690613},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4735153019428253},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4301730692386627},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.41206127405166626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2589402198791504},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.11342212557792664},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10376110672950745}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.9531916379928589},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7449148297309875},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6615868806838989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6123431324958801},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5855094790458679},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5220541954040527},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48985525965690613},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4735153019428253},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4301730692386627},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.41206127405166626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2589402198791504},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.11342212557792664},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10376110672950745},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2009.4983076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983076","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W225560312","https://openalex.org/W1523483560","https://openalex.org/W1595498733","https://openalex.org/W1604175135","https://openalex.org/W1990676004","https://openalex.org/W2020430967","https://openalex.org/W2033330109","https://openalex.org/W2054118322","https://openalex.org/W2058637990","https://openalex.org/W2079868696","https://openalex.org/W2084575232","https://openalex.org/W2102365077","https://openalex.org/W2103259510","https://openalex.org/W2124659975","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2163194391","https://openalex.org/W2170631832","https://openalex.org/W2259507927","https://openalex.org/W2913544278","https://openalex.org/W4236995599","https://openalex.org/W6608886761","https://openalex.org/W6636147571","https://openalex.org/W6664990241"],"related_works":["https://openalex.org/W2550138382","https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W2161149697","https://openalex.org/W2090178682","https://openalex.org/W2001591765","https://openalex.org/W2884337142","https://openalex.org/W4241467429","https://openalex.org/W3090200643","https://openalex.org/W1994436307"],"abstract_inverted_index":{"Many":[0],"real-world":[1],"problems":[2,29,61,135,156],"demand":[3],"a":[4,37,73,85,110,126,138,177],"feasible":[5],"solution":[6,75],"to":[7,23,76,95,114,172,194,198],"satisfy":[8],"physical":[9],"equilibrium,":[10],"stability,":[11],"or":[12],"certain":[13],"properties":[14],"which":[15,49,125,157,169],"require":[16],"an":[17],"additional":[18,63],"lower":[19,68,90],"level":[20,69,79,91,98],"optimization":[21,60,144],"problem":[22,179,184],"be":[24],"solved.":[25],"Although":[26],"such":[27,116,134],"bilevel":[28,127,143,178],"are":[30,44,53,158],"studied":[31],"somewhat":[32],"in":[33,40,48,55,132,160],"the":[34,77,96,106,123,149,196],"context":[35],"of":[36,88,102,162,164,176],"single":[38],"objective":[39],"each":[41,56],"level,":[42],"there":[43],"not":[45,66],"many":[46],"studies":[47,104],"multiple":[50],"conflicting":[51],"objectives":[52],"considered":[54],"level.":[57],"Bilevel":[58],"multi-objective":[59],"offer":[62],"complexities,":[64],"as":[65],"every":[67],"Pareto-optimal":[70,80],"front":[71,81],"has":[72],"representative":[74],"upper":[78,97],"and":[82,136,166,168,189],"that":[83],"only":[84],"tiny":[86],"fraction":[87],"participating":[89],"fronts":[92],"make":[93],"it":[94],"front.":[99],"A":[100],"couple":[101],"recent":[103],"by":[105],"authors":[107],"have":[108],"suggested":[109,150],"viable":[111],"EMO":[112,128],"method":[113],"handle":[115],"problems.":[117,146,202],"In":[118],"this":[119],"paper,":[120],"we":[121,152],"analyze":[122],"difficulties":[124],"procedure":[129,141,186],"may":[130,190],"face":[131],"handling":[133],"present":[137],"systematic":[139],"construction":[140,185],"for":[142],"test":[145,155,183,201],"Based":[147],"on":[148],"principles,":[151],"propose":[153],"five":[154],"scalable":[159],"terms":[161],"number":[163],"variables":[165],"objectives,":[167],"enable":[170],"researchers":[171,193],"evaluate":[173],"different":[174],"phases":[175],"solving":[180],"task.":[181],"The":[182],"is":[187],"interesting":[188],"motivate":[191],"other":[192],"extend":[195],"idea":[197],"develop":[199],"further":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-28T09:10:13.091523","created_date":"2025-10-10T00:00:00"}