{"id":"https://openalex.org/W4385453677","doi":"https://doi.org/10.1109/tnnls.2023.3297624","title":"Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints","display_name":"Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4385453677","doi":"https://doi.org/10.1109/tnnls.2023.3297624","pmid":"https://pubmed.ncbi.nlm.nih.gov/37527320"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3297624","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3297624","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5100430528","display_name":"Yajie Zhang","orcid":"https://orcid.org/0000-0003-1357-1278"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yajie Zhang","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Computer Science and Technology, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0003-1357-1278","affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Computer Science and Technology, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029561912","display_name":"Hao Jiang","orcid":"https://orcid.org/0000-0001-9853-3398"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Jiang","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058755242","display_name":"Ye Tian","orcid":"https://orcid.org/0000-0002-3487-5126"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Tian","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-3487-5126","affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101569394","display_name":"Haiping Ma","orcid":"https://orcid.org/0000-0002-3115-6855"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiping Ma","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-3115-6855","affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028634381","display_name":"Xingyi Zhang","orcid":"https://orcid.org/0000-0002-5052-000X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingyi Zhang","raw_affiliation_strings":["Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-5052-000X","affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Artificial Intelligence, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":null,"apc_paid":null,"fwci":5.5071,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.96797997,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"35","issue":"3","first_page":"2956","last_page":"2968"},"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9962999820709229,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9866999983787537,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.7535748481750488},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7492321729660034},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.692579448223114},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6194996237754822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5613235235214233},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.5374176502227783},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.513270378112793},{"id":"https://openalex.org/keywords/fitness-landscape","display_name":"Fitness landscape","score":0.4453076124191284},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.41915053129196167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30128955841064453}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.7535748481750488},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7492321729660034},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.692579448223114},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6194996237754822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5613235235214233},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.5374176502227783},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.513270378112793},{"id":"https://openalex.org/C91852762","wikidata":"https://www.wikidata.org/wiki/Q3307742","display_name":"Fitness landscape","level":3,"score":0.4453076124191284},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.41915053129196167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30128955841064453},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3297624","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3297624","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:37527320","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37527320","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2089016108","display_name":null,"funder_award_id":"PAL-N201805","funder_id":"https://openalex.org/F4320335661","funder_display_name":"State Key Laboratory of Synthetical Automation for Process Industries"},{"id":"https://openalex.org/G2757623951","display_name":null,"funder_award_id":"U21A20512","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G61320532","display_name":null,"funder_award_id":"1908085QF271","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G7077130566","display_name":null,"funder_award_id":"2018AAA0100105","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335661","display_name":"State Key Laboratory of Synthetical Automation for Process Industries","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1514363319","https://openalex.org/W1553373771","https://openalex.org/W1553573873","https://openalex.org/W1967157470","https://openalex.org/W1968258027","https://openalex.org/W1980750007","https://openalex.org/W1986130186","https://openalex.org/W2048685544","https://openalex.org/W2085507535","https://openalex.org/W2096369439","https://openalex.org/W2105245738","https://openalex.org/W2111526171","https://openalex.org/W2112912151","https://openalex.org/W2126105956","https://openalex.org/W2153654820","https://openalex.org/W2419199839","https://openalex.org/W2432516117","https://openalex.org/W2517882440","https://openalex.org/W2546299924","https://openalex.org/W2582113504","https://openalex.org/W2611669764","https://openalex.org/W2757342969","https://openalex.org/W2764251381","https://openalex.org/W2775524044","https://openalex.org/W2785722638","https://openalex.org/W2801550761","https://openalex.org/W2891186800","https://openalex.org/W2895700336","https://openalex.org/W2911994132","https://openalex.org/W2914106598","https://openalex.org/W2914821612","https://openalex.org/W2962947982","https://openalex.org/W2963115819","https://openalex.org/W2963371534","https://openalex.org/W3008435677","https://openalex.org/W3012133843","https://openalex.org/W3036925570","https://openalex.org/W3114546550","https://openalex.org/W3120662490","https://openalex.org/W3127290989","https://openalex.org/W3134125492","https://openalex.org/W3134254543","https://openalex.org/W3138501233","https://openalex.org/W3153328918","https://openalex.org/W3176681481","https://openalex.org/W3189216291","https://openalex.org/W6717764351","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W4297582752","https://openalex.org/W4285805405","https://openalex.org/W1634842376","https://openalex.org/W2652238734","https://openalex.org/W2391924736","https://openalex.org/W3133779647","https://openalex.org/W4293363729","https://openalex.org/W1995118269","https://openalex.org/W4225799919","https://openalex.org/W1560122427"],"abstract_inverted_index":{"Multiobjective":[0],"optimization":[1],"problems":[2,200],"(MOPs)":[3],"with":[4],"expensive":[5,30],"constraints":[6,31],"pose":[7],"stiff":[8],"challenges":[9],"to":[10,23,70,155,208],"existing":[11,39],"surrogate-assisted":[12],"evolutionary":[13,123],"algorithms":[14,124],"(SAEAs)":[15],"in":[16,46,100,112,142],"a":[17,47,75,117,147,195],"very":[18],"limited":[19],"computational":[20,106],"cost,":[21],"due":[22],"the":[24,27,52,62,79,94,127,137,140,143,157,161,169,178,181,191,203],"fact":[25],"that":[26,89,202],"number":[28,197],"of":[29,64,81,90,130,139,180,198],"for":[32,122],"an":[33,184],"MOP":[34],"is":[35,66,133,152,188,206],"often":[36,67],"large.":[37],"For":[38],"SAEAs,":[40],"they":[41],"always":[42],"approximate":[43],"constraint":[44,53,59,83,95,131,165],"functions":[45,96],"single":[48],"granularity,":[49],"namely,":[50],"approximating":[51,92],"violation":[54],"(CV,":[55],"coarse-grained)":[56],"or":[57],"each":[58,82],"(fine-grained).":[60],"However,":[61],"landscape":[63],"CV":[65],"too":[68],"complex":[69],"be":[71,86],"accurately":[72],"approximated":[73],"by":[74,136,164],"surrogate":[76,119],"model.":[77],"Although":[78],"modeling":[80,120],"function":[84],"may":[85,98],"simpler":[87],"than":[88],"CV,":[91],"all":[93],"independently":[97],"result":[99],"tremendous":[101],"cumulative":[102],"errors":[103,162],"and":[104,167,190],"high":[105],"costs.":[107],"To":[108,176],"address":[109],"this":[110,113],"issue,":[111],"article,":[114],"we":[115],"develop":[116],"multigranularity":[118],"framework":[121,205],"(EAs),":[125],"where":[126],"approximation":[128],"granularity":[129],"surrogates":[132,166],"adaptively":[134],"determined":[135],"position":[138],"population":[141,170],"fitness":[144],"landscape.":[145],"Moreover,":[146],"dedicated":[148],"model":[149],"management":[150],"strategy":[151],"also":[153],"developed":[154],"reduce":[156],"impact":[158],"resulting":[159],"from":[160,171],"introduced":[163],"prevent":[168],"trapping":[172],"into":[173],"local":[174],"optima.":[175],"evaluate":[177],"performance":[179],"proposed":[182,204],"framework,":[183],"implementation":[185],"called":[186],"K-MGSAEA":[187],"proposed,":[189],"experimental":[192],"results":[193],"on":[194],"large":[196],"test":[199],"show":[201],"superior":[207],"seven":[209],"state-of-the-art":[210],"competitors.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":13}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
