{"id":"https://openalex.org/W2896140431","doi":"https://doi.org/10.1109/cec.2018.8477763","title":"Bilevel Optimization Based on Kriging Approximations of Lower Level Optimal Value Function","display_name":"Bilevel Optimization Based on Kriging Approximations of Lower Level Optimal Value Function","publication_year":2018,"publication_date":"2018-07-01","ids":{"openalex":"https://openalex.org/W2896140431","doi":"https://doi.org/10.1109/cec.2018.8477763","mag":"2896140431"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2018.8477763","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2018.8477763","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Congress on Evolutionary Computation (CEC)","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/A5018720209","display_name":"Ankur Sinha","orcid":"https://orcid.org/0000-0002-0464-6736"},"institutions":[{"id":"https://openalex.org/I150870154","display_name":"Indian Institute of Management Ahmedabad","ror":"https://ror.org/02egcpy68","country_code":"IN","type":"education","lineage":["https://openalex.org/I150870154"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ankur Sinha","raw_affiliation_strings":["Production and Quantitative Methods, Indian Institute of Management, Ahmedabad, India"],"affiliations":[{"raw_affiliation_string":"Production and Quantitative Methods, Indian Institute of Management, Ahmedabad, India","institution_ids":["https://openalex.org/I150870154"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069819967","display_name":"Samish Bedi","orcid":null},"institutions":[{"id":"https://openalex.org/I74796645","display_name":"Birla Institute of Technology and Science, Pilani","ror":"https://ror.org/001p3jz28","country_code":"IN","type":"education","lineage":["https://openalex.org/I74796645"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Samish Bedi","raw_affiliation_strings":["Department of Computer Science, Birla Institute of Technology and Science, Pilani, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Birla Institute of Technology and Science, Pilani, India","institution_ids":["https://openalex.org/I74796645"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088394271","display_name":"Kalyanmoy Deb","orcid":"https://orcid.org/0000-0001-7402-9939"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Michigan State University, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Michigan State University, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018720209"],"corresponding_institution_ids":["https://openalex.org/I150870154"],"apc_list":null,"apc_paid":null,"fwci":1.6554,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.84996684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10969","display_name":"Water resources management and optimization","score":0.9955999851226807,"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"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9901999831199646,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.9698249697685242},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.783841609954834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6076406240463257},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.601296603679657},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.5198367238044739},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.514600396156311},{"id":"https://openalex.org/keywords/test-functions-for-optimization","display_name":"Test functions for optimization","score":0.501591682434082},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4337957203388214},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4167889952659607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34486478567123413},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.13461339473724365},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.09286192059516907}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.9698249697685242},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.783841609954834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6076406240463257},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.601296603679657},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.5198367238044739},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.514600396156311},{"id":"https://openalex.org/C150185637","wikidata":"https://www.wikidata.org/wiki/Q7705773","display_name":"Test functions for optimization","level":4,"score":0.501591682434082},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4337957203388214},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4167889952659607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34486478567123413},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.13461339473724365},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.09286192059516907},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2018.8477763","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2018.8477763","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W55700729","https://openalex.org/W1483357708","https://openalex.org/W1484068505","https://openalex.org/W1510052597","https://openalex.org/W1515826176","https://openalex.org/W1588628884","https://openalex.org/W1598286983","https://openalex.org/W1650861223","https://openalex.org/W1676470423","https://openalex.org/W1762936176","https://openalex.org/W1964765773","https://openalex.org/W1972038842","https://openalex.org/W1974952991","https://openalex.org/W1976452842","https://openalex.org/W1977398984","https://openalex.org/W1979380639","https://openalex.org/W1988724314","https://openalex.org/W1990864994","https://openalex.org/W1991984686","https://openalex.org/W1995153978","https://openalex.org/W2000152357","https://openalex.org/W2001759562","https://openalex.org/W2005629858","https://openalex.org/W2006911191","https://openalex.org/W2007103412","https://openalex.org/W2013365934","https://openalex.org/W2016379082","https://openalex.org/W2018044188","https://openalex.org/W2029002433","https://openalex.org/W2030667419","https://openalex.org/W2031264011","https://openalex.org/W2032195237","https://openalex.org/W2035893651","https://openalex.org/W2042943043","https://openalex.org/W2044241503","https://openalex.org/W2046542460","https://openalex.org/W2056468324","https://openalex.org/W2060743072","https://openalex.org/W2065534296","https://openalex.org/W2074376561","https://openalex.org/W2078101422","https://openalex.org/W2084575232","https://openalex.org/W2099746148","https://openalex.org/W2111240209","https://openalex.org/W2116765717","https://openalex.org/W2127587365","https://openalex.org/W2134230680","https://openalex.org/W2149960577","https://openalex.org/W2154062181","https://openalex.org/W2162885967","https://openalex.org/W2163194391","https://openalex.org/W2168353587","https://openalex.org/W2259507927","https://openalex.org/W2329255878","https://openalex.org/W2481910659","https://openalex.org/W2517278259","https://openalex.org/W2521809336","https://openalex.org/W2558645170","https://openalex.org/W2614367549","https://openalex.org/W2732076076","https://openalex.org/W2807256486","https://openalex.org/W2980487008","https://openalex.org/W3148840946","https://openalex.org/W4252848749","https://openalex.org/W4256439778","https://openalex.org/W4285719527","https://openalex.org/W4297925816","https://openalex.org/W6602247602","https://openalex.org/W6628981487","https://openalex.org/W6657754005","https://openalex.org/W6752096913"],"related_works":["https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W2161149697","https://openalex.org/W4388092588","https://openalex.org/W3090200643","https://openalex.org/W4287330080","https://openalex.org/W3127438322","https://openalex.org/W2216231335","https://openalex.org/W4297925816","https://openalex.org/W4214689360"],"abstract_inverted_index":{"A":[0],"large":[1],"number":[2,78,156,177],"of":[3,9,38,53,72,79,157,178,191,205,210,218],"application":[4],"problems":[5,21,27,43,75,161],"involve":[6],"two":[7,133],"levels":[8],"optimization,":[10],"where":[11],"one":[12],"optimization":[13,26,42,74,88,92,135],"task":[14,136],"is":[15,128,143],"nested":[16],"inside":[17],"the":[18,36,54,102,115,132,165,173,189,192,202,206,219],"other.":[19],"These":[20],"are":[22,44,60,184],"known":[23,45],"as":[24],"bilevel":[25,73,91,112,166,198,235],"and":[28,49,153],"have":[29],"been":[30,231],"widely":[31,232],"studied":[32],"by":[33,105],"researchers":[34],"in":[35,111,130,194,234],"area":[37],"mathematical":[39],"optimization.":[40,236],"Bilevel":[41],"to":[46,67,100,137,162],"be":[47],"difficult":[48],"computationally":[50,62],"demanding.":[51],"Most":[52],"solution":[55,212],"procedures":[56],"proposed":[57],"until":[58],"now":[59],"either":[61],"very":[63],"expensive":[64],"or":[65],"applicable":[66],"only":[68],"a":[69,86,155,176,211,226],"narrow":[70],"class":[71],"involving":[76],"small":[77],"variables.":[80],"In":[81,168],"this":[82,141,151],"paper,":[83],"we":[84,171],"propose":[85],"global":[87],"algorithm":[89],"for":[90],"using":[93,225],"Kriging":[94],"approximation":[95,217],"based":[96,214],"model":[97],"that":[98],"tries":[99],"reduce":[101],"computational":[103],"expense":[104],"iteratively":[106],"approximating":[107],"an":[108],"important":[109],"mapping":[110,152],"optimization;":[113],"namely,":[114],"lower":[116,123,221],"level":[117,124,134,160,222],"optimal":[118,125,220],"value":[119,126,223],"function":[120,127,142,224],"mapping.":[121],"The":[122,181],"useful":[129],"reducing":[131],"one;":[138],"however,":[139],"identifying":[140],"not":[144,230],"straightforward.":[145],"Our":[146],"approach":[147,193],"aims":[148],"at":[149,164],"meta-modeling":[150],"solving":[154,195],"auxiliary":[158],"single":[159],"arrive":[163],"optimum.":[167],"our":[169],"study,":[170],"test":[172,179,199],"methodology":[174],"on":[175,215],"problems.":[180],"preliminary":[182],"results":[183],"quite":[185],"promising":[186],"which":[187],"suggest":[188],"viability":[190],"more":[196],"complicated":[197],"problem.":[200],"To":[201],"best":[203],"knowledge":[204],"authors,":[207],"such":[208],"kind":[209],"procedure":[213],"iterative":[216],"stochastic":[227],"process":[228],"has":[229],"used":[233]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}