{"id":"https://openalex.org/W3139497286","doi":"https://doi.org/10.1109/tcyb.2021.3061551","title":"Solving Bilevel Optimization Problems Using Kriging Approximations","display_name":"Solving Bilevel Optimization Problems Using Kriging Approximations","publication_year":2021,"publication_date":"2021-03-22","ids":{"openalex":"https://openalex.org/W3139497286","doi":"https://doi.org/10.1109/tcyb.2021.3061551","mag":"3139497286","pmid":"https://pubmed.ncbi.nlm.nih.gov/33750725"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2021.3061551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3061551","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":"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, Ahmedabad, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Production and Quantitative Methods, Indian Institute of Management Ahmedabad, Ahmedabad, India","institution_ids":["https://openalex.org/I150870154"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056765319","display_name":"Vaseem Shaikh","orcid":"https://orcid.org/0000-0002-2085-1940"},"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":false,"raw_author_name":"Vaseem Shaikh","raw_affiliation_strings":["Production and Quantitative Methods, Indian Institute of Management Ahmedabad, Ahmedabad, India"],"raw_orcid":"https://orcid.org/0000-0002-2085-1940","affiliations":[{"raw_affiliation_string":"Production and Quantitative Methods, Indian Institute of Management Ahmedabad, Ahmedabad, India","institution_ids":["https://openalex.org/I150870154"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018720209"],"corresponding_institution_ids":["https://openalex.org/I150870154"],"apc_list":null,"apc_paid":null,"fwci":4.4403,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.94880363,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"52","issue":"10","first_page":"10639","last_page":"10654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9979000091552734,"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":0.9958000183105469,"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":0.8705655336380005},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7526708841323853},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6635445952415466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4928557872772217},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.45518749952316284},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.44677048921585083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4341503977775574},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.0783551037311554}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8705655336380005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7526708841323853},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6635445952415466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4928557872772217},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.45518749952316284},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.44677048921585083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4341503977775574},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0783551037311554},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2021.3061551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3061551","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:33750725","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33750725","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}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W49793390","https://openalex.org/W55700729","https://openalex.org/W1484068505","https://openalex.org/W1518498522","https://openalex.org/W1555684898","https://openalex.org/W1588628884","https://openalex.org/W1598286983","https://openalex.org/W1650861223","https://openalex.org/W1762936176","https://openalex.org/W1972038842","https://openalex.org/W1974549991","https://openalex.org/W1974952991","https://openalex.org/W1976452842","https://openalex.org/W1979380639","https://openalex.org/W1988724314","https://openalex.org/W1990864994","https://openalex.org/W1991984686","https://openalex.org/W1994697143","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/W2009649383","https://openalex.org/W2013365934","https://openalex.org/W2016379082","https://openalex.org/W2018044188","https://openalex.org/W2030667419","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/W2064997474","https://openalex.org/W2065534296","https://openalex.org/W2069577676","https://openalex.org/W2071385623","https://openalex.org/W2074376561","https://openalex.org/W2078101422","https://openalex.org/W2084575232","https://openalex.org/W2095798353","https://openalex.org/W2099746148","https://openalex.org/W2101680187","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/W2156417353","https://openalex.org/W2162885967","https://openalex.org/W2163194391","https://openalex.org/W2168353587","https://openalex.org/W2259507927","https://openalex.org/W2330338143","https://openalex.org/W2481910659","https://openalex.org/W2501776475","https://openalex.org/W2521809336","https://openalex.org/W2557096003","https://openalex.org/W2558645170","https://openalex.org/W2587953039","https://openalex.org/W2614367549","https://openalex.org/W2732076076","https://openalex.org/W2794659965","https://openalex.org/W2795590041","https://openalex.org/W2807256486","https://openalex.org/W2896140431","https://openalex.org/W2952108774","https://openalex.org/W2954234207","https://openalex.org/W2980487008","https://openalex.org/W3044569448","https://openalex.org/W3121609094","https://openalex.org/W4241417870"],"related_works":["https://openalex.org/W4318070895","https://openalex.org/W3157915181","https://openalex.org/W2896140431","https://openalex.org/W3015956618","https://openalex.org/W3156147173","https://openalex.org/W2920493340","https://openalex.org/W2071082401","https://openalex.org/W1994436307","https://openalex.org/W2795565301","https://openalex.org/W4285677055"],"abstract_inverted_index":{"Bilevel":[0],"optimization":[1,9,29,36,59,128,177,198,256],"involves":[2],"two":[3,224],"levels":[4],"of":[5,18,27,35,91,102,136,146,163,167,174,183,195,226,235],"optimization,":[6],"where":[7,100,150],"one":[8,101],"problem":[10,20,178,202,231,284],"is":[11,76,171,208,244,260],"nested":[12],"within":[13],"the":[14,19,46,66,74,89,134,144,151,156,160,164,168,172,180,184,196,212,216,233,242,275,281,288],"other.":[15],"The":[16,41,200,258],"structure":[17,135],"often":[21,54,96],"requires":[22],"solving":[23,254,270],"a":[24,62,71,83,106,230],"large":[25],"number":[26],"inner":[28],"problems":[30,37,60,99,129,228],"that":[31,86,109,190,241,266],"make":[32],"these":[33,92,103,121,137],"kinds":[34],"expensive":[38],"to":[39,56,61,77,98,124,210,250,262],"solve.":[40],"reaction":[42],"set":[43],"mapping":[44,52],"and":[45,73,229,247],"lower":[47,185,282],"level":[48,186,283],"optimal":[49,187,218],"value":[50,188],"function":[51,189,278],"are":[53,68,95,141,267,285],"used":[55,204],"reduce":[57],"bilevel":[58,127,197,217,255,271],"single":[63],"level;":[64],"however,":[65],"mappings":[67,104,122],"not":[69],"known":[70,107],"priori,":[72],"need":[75],"be":[78],"estimated.":[79],"Though":[80],"there":[81],"exist":[82],"few":[84],"studies":[85],"rely":[87],"on":[88,133,223],"estimation":[90],"mappings,":[93],"they":[94],"applied":[97],"has":[105],"form,":[108],"is,":[110],"piecewise":[111],"linear,":[112],"convex,":[113],"etc.":[114],"In":[115],"this":[116],"article,":[117],"we":[118],"utilize":[119],"both":[120],"together":[123],"solve":[125],"general":[126],"without":[130],"any":[131],"assumptions":[132],"mappings.":[138],"Kriging":[139],"approximations":[140],"created":[142],"during":[143],"generations":[145],"an":[147,175,192],"evolutionary":[148,213],"algorithm,":[149],"population":[152],"members":[153],"serve":[154],"as":[155],"samples":[157],"for":[158,205,269,280],"creating":[159],"approximations.":[161],"One":[162],"important":[165],"features":[166],"proposed":[169,289],"algorithm":[170,214],"creation":[173],"auxiliary":[176,201],"using":[179],"Kriging-based":[181],"metamodel":[182],"solves":[191],"approximate":[193],"relaxation":[194],"problem.":[199],"when":[203,253],"local":[206],"search":[207],"able":[209,261],"accelerate":[211],"toward":[215],"solution.":[219],"We":[220],"perform":[221],"experiments":[222,239],"sets":[225],"test":[227],"from":[232],"domain":[234],"control":[236],"theory.":[237],"Our":[238],"suggest":[240],"approach":[243,259],"quite":[245],"promising":[246],"can":[248],"lead":[249],"substantial":[251,286],"savings":[252,276],"problems.":[257],"outperform":[263],"state-of-the-art":[264],"methods":[265],"available":[268],"problems,":[272],"in":[273,277],"particular,":[274],"evaluations":[279],"with":[287],"approach.":[290]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
