{"id":"https://openalex.org/W3138369982","doi":"https://doi.org/10.1109/tcyb.2021.3061420","title":"A Three-Level Radial Basis Function Method for Expensive Optimization","display_name":"A Three-Level Radial Basis Function Method for Expensive Optimization","publication_year":2021,"publication_date":"2021-03-22","ids":{"openalex":"https://openalex.org/W3138369982","doi":"https://doi.org/10.1109/tcyb.2021.3061420","mag":"3138369982","pmid":"https://pubmed.ncbi.nlm.nih.gov/33750724"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2021.3061420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3061420","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/A5001176258","display_name":"Genghui Li","orcid":"https://orcid.org/0000-0002-9950-9848"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Genghui Li","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Hong Kong","City University of Hong Kong, Shenzhen Research Institute, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"City University of Hong Kong, Shenzhen Research Institute, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000546219","display_name":"Qingfu Zhang","orcid":"https://orcid.org/0000-0003-0786-0671"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210105229","display_name":"City University of Hong Kong, Shenzhen Research Institute","ror":"https://ror.org/00xc0ma20","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105229"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Qingfu Zhang","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Hong Kong","City University of Hong Kong, Shenzhen Research Institute, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"City University of Hong Kong, Shenzhen Research Institute, Shenzhen, China","institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066935890","display_name":"Qiuzhen Lin","orcid":"https://orcid.org/0000-0003-2415-0401"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuzhen Lin","raw_affiliation_strings":["College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047167952","display_name":"Weifeng Gao","orcid":"https://orcid.org/0000-0003-3853-0771"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weifeng Gao","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi’an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi’an, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001176258"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I4210105229"],"apc_list":null,"apc_paid":null,"fwci":6.4382,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.9709552,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"52","issue":"7","first_page":"5720","last_page":"5731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9995999932289124,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.7307305335998535},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6306162476539612},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6296573877334595},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4872538149356842},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.47563862800598145},{"id":"https://openalex.org/keywords/local-search","display_name":"Local search (optimization)","score":0.4699673354625702},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4444364309310913},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.444333553314209},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.41760244965553284},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3964952826499939},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37865495681762695},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19171541929244995},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.08025050163269043}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7307305335998535},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6306162476539612},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6296573877334595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4872538149356842},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.47563862800598145},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.4699673354625702},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4444364309310913},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.444333553314209},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.41760244965553284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3964952826499939},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37865495681762695},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19171541929244995},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08025050163269043},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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":2,"locations":[{"id":"doi:10.1109/tcyb.2021.3061420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3061420","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:33750724","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33750724","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":[{"id":"https://openalex.org/G6667768056","display_name":null,"funder_award_id":"61876163","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1507162258","https://openalex.org/W1539307555","https://openalex.org/W1555684898","https://openalex.org/W1573878755","https://openalex.org/W1670967200","https://openalex.org/W1790284589","https://openalex.org/W1834439319","https://openalex.org/W1988945200","https://openalex.org/W1989011358","https://openalex.org/W1997869834","https://openalex.org/W2005337722","https://openalex.org/W2027120741","https://openalex.org/W2054352980","https://openalex.org/W2074959697","https://openalex.org/W2076332286","https://openalex.org/W2076569421","https://openalex.org/W2082228576","https://openalex.org/W2095769364","https://openalex.org/W2097812610","https://openalex.org/W2104815732","https://openalex.org/W2105245738","https://openalex.org/W2113076747","https://openalex.org/W2131612655","https://openalex.org/W2146713522","https://openalex.org/W2155529731","https://openalex.org/W2187133804","https://openalex.org/W2295710326","https://openalex.org/W2556761448","https://openalex.org/W2557306121","https://openalex.org/W2567368484","https://openalex.org/W2591927365","https://openalex.org/W2679717297","https://openalex.org/W2727814428","https://openalex.org/W2736848882","https://openalex.org/W2778065156","https://openalex.org/W2785988364","https://openalex.org/W2788953516","https://openalex.org/W2791362611","https://openalex.org/W2794706240","https://openalex.org/W2796139399","https://openalex.org/W2801960628","https://openalex.org/W3006649997","https://openalex.org/W3083389730","https://openalex.org/W3091956744","https://openalex.org/W6609450013","https://openalex.org/W6647628012"],"related_works":["https://openalex.org/W2350737211","https://openalex.org/W3182909153","https://openalex.org/W4230482078","https://openalex.org/W2783540637","https://openalex.org/W2020667009","https://openalex.org/W2571293944","https://openalex.org/W2373554757","https://openalex.org/W2778065156","https://openalex.org/W2186293978","https://openalex.org/W4386913846"],"abstract_inverted_index":{"This":[0],"article":[1],"proposes":[2],"a":[3,31,35,42,57,66,81,85,117],"three-level":[4],"radial":[5],"basis":[6],"function":[7,39,64],"(TLRBF)-assisted":[8],"optimization":[9,121],"algorithm":[10,125],"for":[11,128],"expensive":[12,114,129],"optimization.":[13,130],"It":[14],"consists":[15],"of":[16,93],"three":[17],"search":[18,27,48,53,77],"procedures":[19],"at":[20],"each":[21],"iteration:":[22],"1)":[23],"the":[24,46,51,74,91,94],"global":[25,36],"exploration":[26],"is":[28,54,78],"to":[29,41,55,79],"find":[30],"solution":[32,58,82],"by":[33,59,69,83],"optimizing":[34],"RBF":[37,62,87],"approximation":[38,63,88],"subject":[40],"distance":[43],"constraint":[44],"in":[45,65,90],"whole":[47],"space;":[49],"2)":[50],"subregion":[52,67],"generate":[56,80],"minimizing":[60],"an":[61],"determined":[68],"fuzzy":[70],"clustering;":[71],"and":[72,116],"3)":[73],"local":[75,86],"exploitation":[76],"solving":[84],"model":[89],"neighborhood":[92],"current":[95],"best":[96],"solution.":[97],"Compared":[98],"with":[99],"some":[100],"other":[101],"state-of-the-art":[102],"algorithms":[103],"on":[104],"five":[105],"commonly":[106],"used":[107],"scalable":[108],"benchmark":[109],"problems,":[110,115],"ten":[111],"CEC2015":[112],"computationally":[113],"real-world":[118],"airfoil":[119],"design":[120],"problem,":[122],"our":[123],"proposed":[124],"performs":[126],"well":[127]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}