{"id":"https://openalex.org/W4317910477","doi":"https://doi.org/10.1007/s40747-022-00965-6","title":"A two-stage adaptive penalty method based on co-evolution for constrained evolutionary optimization","display_name":"A two-stage adaptive penalty method based on co-evolution for constrained evolutionary optimization","publication_year":2023,"publication_date":"2023-01-25","ids":{"openalex":"https://openalex.org/W4317910477","doi":"https://doi.org/10.1007/s40747-022-00965-6"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-022-00965-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00965-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00965-6.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00965-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040076424","display_name":"Bing-Chuan Wang","orcid":"https://orcid.org/0000-0002-0234-2843"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bing-Chuan Wang","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100511531","display_name":"Jing-Jing Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing-Jing Guo","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042888574","display_name":"Pei-Qiu Huang","orcid":"https://orcid.org/0000-0001-6278-4566"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pei-Qiu Huang","raw_affiliation_strings":["School of Automation, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046710292","display_name":"Xian-Bing Meng","orcid":"https://orcid.org/0000-0003-2674-7295"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xian-Bing Meng","raw_affiliation_strings":["School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040076424"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":2.5737,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91263857,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"9","issue":"4","first_page":"4615","last_page":"4627"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.8518991470336914},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.6941684484481812},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.663481593132019},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6217734813690186},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6091246008872986},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.5374370813369751},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.535545825958252},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.523944616317749},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4807531535625458},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46518248319625854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28624212741851807},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20550617575645447}],"concepts":[{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.8518991470336914},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.6941684484481812},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.663481593132019},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6217734813690186},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6091246008872986},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.5374370813369751},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.535545825958252},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.523944616317749},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4807531535625458},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46518248319625854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28624212741851807},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20550617575645447},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s40747-022-00965-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00965-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00965-6.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4837ed8cad5a4159a7e8cf7a5bb03e86","is_oa":true,"landing_page_url":"https://doaj.org/article/4837ed8cad5a4159a7e8cf7a5bb03e86","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complex & Intelligent Systems, Vol 9, Iss 4, Pp 4615-4627 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s40747-022-00965-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00965-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00965-6.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1477544716","display_name":null,"funder_award_id":"Guangdong","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1709975844","display_name":null,"funder_award_id":"2022A1515011","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2118832652","display_name":null,"funder_award_id":"51501131","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3237826631","display_name":null,"funder_award_id":"62106287","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4488680036","display_name":null,"funder_award_id":"2022A15","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6746433303","display_name":null,"funder_award_id":"62006081","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7939324287","display_name":null,"funder_award_id":"2022A1515011317","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321514","display_name":"Central South University","ror":"https://ror.org/00f1zfq44"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4317910477.pdf"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1975680103","https://openalex.org/W1980750007","https://openalex.org/W1987748061","https://openalex.org/W1990607231","https://openalex.org/W1996545838","https://openalex.org/W2006291708","https://openalex.org/W2007351764","https://openalex.org/W2015808650","https://openalex.org/W2034988449","https://openalex.org/W2038984515","https://openalex.org/W2039355869","https://openalex.org/W2056665801","https://openalex.org/W2063524584","https://openalex.org/W2069650035","https://openalex.org/W2071226973","https://openalex.org/W2088500424","https://openalex.org/W2096524645","https://openalex.org/W2097754344","https://openalex.org/W2110368321","https://openalex.org/W2145418868","https://openalex.org/W2145479420","https://openalex.org/W2146713522","https://openalex.org/W2151339633","https://openalex.org/W2312408522","https://openalex.org/W2345178486","https://openalex.org/W2604750196","https://openalex.org/W2606717649","https://openalex.org/W2726495777","https://openalex.org/W2730641013","https://openalex.org/W2783674097","https://openalex.org/W2788586783","https://openalex.org/W2802384355","https://openalex.org/W2892336140","https://openalex.org/W2899649886","https://openalex.org/W2901888116","https://openalex.org/W2934819789","https://openalex.org/W2947657698","https://openalex.org/W2950241207","https://openalex.org/W2972396893","https://openalex.org/W3011126835","https://openalex.org/W3027210649","https://openalex.org/W3104512810","https://openalex.org/W3118408813","https://openalex.org/W3130995516","https://openalex.org/W3146654090","https://openalex.org/W3184980526","https://openalex.org/W3186351520","https://openalex.org/W3206559824","https://openalex.org/W3210984283","https://openalex.org/W4206391756","https://openalex.org/W4212923664","https://openalex.org/W4232244061","https://openalex.org/W4238076109","https://openalex.org/W4280629418"],"related_works":["https://openalex.org/W2394392475","https://openalex.org/W1996828931","https://openalex.org/W2069937987","https://openalex.org/W2076297169","https://openalex.org/W1571424162","https://openalex.org/W2090436135","https://openalex.org/W2015132550","https://openalex.org/W3168391725","https://openalex.org/W3006802988","https://openalex.org/W2235797280"],"abstract_inverted_index":{"Abstract":[0],"Penalty":[1],"function":[2],"method":[3],"is":[4,12,49,57,115,158,174],"popular":[5],"for":[6,20],"constrained":[7,22],"evolutionary":[8,153],"optimization.":[9],"However,":[10],"it":[11],"non-trivial":[13],"to":[14,31,117,176],"set":[15],"a":[16,21,38,60,104,171],"proper":[17],"penalty":[18,34,41,61,72,79,109],"factor":[19,35,110],"optimization":[23],"problem.":[24],"This":[25],"paper":[26],"takes":[27],"advantage":[28],"of":[29,55,66,71,167,191],"co-evolution":[30,45,65,113],"adjust":[32],"the":[33,44,47,64,69,83,96,107,112,119,124,143,151,155,178,183,189,192],"and":[36,106],"proposes":[37],"two-stage":[39,152],"adaptive":[40],"method.":[42,194],"In":[43,95,121,150],"stage,":[46,98],"population":[48,105,179],"divided":[50],"into":[51,103],"multiple":[52],"subpopulations,":[53,68],"each":[54],"which":[56],"associated":[58],"with":[59],"factor.":[62],"Through":[63],"these":[67,139],"performance":[70],"factors":[73,80],"can":[74,92,129,134],"be":[75,93,130,135,147],"evaluated.":[76],"Since":[77],"different":[78,88],"are":[81,101],"used,":[82],"subpopulations":[84,100,128],"will":[85],"evolve":[86],"along":[87],"directions.":[89],"Thus,":[90],"exploration":[91],"enhanced.":[94],"shuffle":[97],"all":[99],"merged":[102],"best":[108],"from":[111],"stage":[114],"used":[116],"guide":[118],"evolution.":[120,169],"this":[122],"manner,":[123],"information":[125],"interaction":[126],"among":[127],"facilitated;":[131],"thus,":[132],"exploitation":[133],"promoted.":[136],"By":[137],"executing":[138],"two":[140,162],"stages":[141],"iteratively,":[142],"feasible":[144],"optimum":[145],"could":[146],"obtained":[148],"finally.":[149],"process,":[154],"search":[156],"algorithm":[157],"designed":[159,175],"based":[160],"on":[161],"trial":[163],"vector":[164],"generation":[165],"strategies":[166],"differential":[168],"Additionally,":[170],"restart":[172],"mechanism":[173],"help":[177],"avoid":[180],"stagnating":[181],"in":[182],"infeasible":[184],"region.":[185],"Extensive":[186],"experiments":[187],"demonstrate":[188],"effectiveness":[190],"proposed":[193]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}