{"id":"https://openalex.org/W2921913446","doi":"https://doi.org/10.1109/tcyb.2020.2979821","title":"Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization","display_name":"Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization","publication_year":2020,"publication_date":"2020-03-27","ids":{"openalex":"https://openalex.org/W2921913446","doi":"https://doi.org/10.1109/tcyb.2020.2979821","mag":"2921913446","pmid":"https://pubmed.ncbi.nlm.nih.gov/32224478"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.2979821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.2979821","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":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.04886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100385896","display_name":"Tao Xu","orcid":"https://orcid.org/0000-0001-8574-7768"},"institutions":[{"id":"https://openalex.org/I16038530","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889","country_code":"GB","type":"education","lineage":["https://openalex.org/I16038530"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Tao Xu","raw_affiliation_strings":["Department of Computer Science, Aberystwyth University, Aberystwyth, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aberystwyth University, Aberystwyth, U.K","institution_ids":["https://openalex.org/I16038530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100639998","display_name":"Jun He","orcid":"https://orcid.org/0000-0002-5616-4691"},"institutions":[{"id":"https://openalex.org/I52590639","display_name":"Nottingham Trent University","ror":"https://ror.org/04xyxjd90","country_code":"GB","type":"education","lineage":["https://openalex.org/I52590639"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jun He","raw_affiliation_strings":["School of Science and Technology, Nottingham Trent University, Nottingham, U.K"],"affiliations":[{"raw_affiliation_string":"School of Science and Technology, Nottingham Trent University, Nottingham, U.K","institution_ids":["https://openalex.org/I52590639"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039652471","display_name":"Changjing Shang","orcid":"https://orcid.org/0000-0001-6375-6276"},"institutions":[{"id":"https://openalex.org/I16038530","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889","country_code":"GB","type":"education","lineage":["https://openalex.org/I16038530"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Changjing Shang","raw_affiliation_strings":["Department of Computer Science, Aberystwyth University, Aberystwyth, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aberystwyth University, Aberystwyth, U.K","institution_ids":["https://openalex.org/I16038530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100385896"],"corresponding_institution_ids":["https://openalex.org/I16038530"],"apc_list":null,"apc_paid":null,"fwci":1.7327,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87697803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"1","first_page":"240","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9926999807357788,"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/computer-science","display_name":"Computer science","score":0.46502089500427246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4486090838909149},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.440408855676651},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22965887188911438}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46502089500427246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4486090838909149},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.440408855676651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22965887188911438}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1109/tcyb.2020.2979821","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.2979821","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:32224478","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32224478","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},{"id":"pmh:oai:irep.ntu.ac.uk:39513","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400559","display_name":"Nottingham Trent University's Institutional Repository (Nottingham Trent Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I52590639","host_organization_name":"Nottingham Trent University","host_organization_lineage":["https://openalex.org/I52590639"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1903.04886","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.04886","pdf_url":"https://arxiv.org/pdf/1903.04886","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:aber.ac.uk:publications/9774ea77-affc-4ba8-920d-bb160ebc2bc7","is_oa":true,"landing_page_url":"https://pure.aber.ac.uk/portal/en/publications/helper-and-equivalent-objectives(9774ea77-affc-4ba8-920d-bb160ebc2bc7).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401660","display_name":"Aberystwyth Research portal (Aberystwyth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16038530","host_organization_name":"Aberystwyth University","host_organization_lineage":["https://openalex.org/I16038530"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.04886","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.04886","pdf_url":"https://arxiv.org/pdf/1903.04886","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2283300546","display_name":null,"funder_award_id":"EP/I009809/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G305414047","display_name":"Evolutionary Approximation Algorithms for Optimisation: Algorithm Design and Complexity Analysis","funder_award_id":"EP/I009809/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W167027853","https://openalex.org/W1529988604","https://openalex.org/W1719846953","https://openalex.org/W1975680103","https://openalex.org/W1980750007","https://openalex.org/W1987213726","https://openalex.org/W2000609527","https://openalex.org/W2018299061","https://openalex.org/W2028261435","https://openalex.org/W2042253843","https://openalex.org/W2057775647","https://openalex.org/W2058518193","https://openalex.org/W2073297125","https://openalex.org/W2079557127","https://openalex.org/W2088500424","https://openalex.org/W2098392363","https://openalex.org/W2099934773","https://openalex.org/W2110368321","https://openalex.org/W2119001727","https://openalex.org/W2129057129","https://openalex.org/W2139747021","https://openalex.org/W2143381319","https://openalex.org/W2145479420","https://openalex.org/W2155529731","https://openalex.org/W2157816158","https://openalex.org/W2161447745","https://openalex.org/W2164655924","https://openalex.org/W2167580870","https://openalex.org/W2345178486","https://openalex.org/W2486699312","https://openalex.org/W2510693965","https://openalex.org/W2519112510","https://openalex.org/W2579361096","https://openalex.org/W2591313086","https://openalex.org/W2606717649","https://openalex.org/W2726495777","https://openalex.org/W2730641013","https://openalex.org/W2730907139","https://openalex.org/W2732972480","https://openalex.org/W2747525273","https://openalex.org/W2798936903","https://openalex.org/W2884225201","https://openalex.org/W2888418128","https://openalex.org/W2895914958","https://openalex.org/W2896508930","https://openalex.org/W2901888116","https://openalex.org/W2920893828","https://openalex.org/W2950241207","https://openalex.org/W2959336812","https://openalex.org/W2963372016","https://openalex.org/W3007812559","https://openalex.org/W3099645121","https://openalex.org/W3103451854","https://openalex.org/W3103982436","https://openalex.org/W4233868968","https://openalex.org/W4248462665","https://openalex.org/W6606754508"],"related_works":["https://openalex.org/W122341662","https://openalex.org/W2098490153","https://openalex.org/W2945790020","https://openalex.org/W2111888732","https://openalex.org/W2128089710","https://openalex.org/W181374404","https://openalex.org/W2148472017","https://openalex.org/W4388279573","https://openalex.org/W2902675733","https://openalex.org/W3104770499"],"abstract_inverted_index":{"Numerous":[0],"multiobjective":[1,29,46,91],"evolutionary":[2],"algorithms":[3,20],"(EAs)":[4],"have":[5],"been":[6],"designed":[7],"for":[8,48,184],"constrained":[9,24,49,81,220],"optimization":[10,25,30,92],"over":[11],"the":[12,75,80,102,126,130,172,176],"past":[13],"two":[14,156],"decades.":[15],"The":[16,197],"idea":[17],"behind":[18],"these":[19],"is":[21,74,94,195,205],"to":[22,116,153],"transform":[23],"problems":[26,31],"(COPs)":[27],"into":[28,57,96],"without":[32],"any":[33],"constraint,":[34],"and":[35,62,132,167,192],"then":[36],"solve":[37],"them.":[38],"In":[39,143],"this":[40,90],"article,":[41],"we":[42],"propose":[43],"a":[44,55,58,84,97,117,137,144,181],"new":[45],"method":[47,135],"optimization,":[50],"which":[51],"works":[52],"by":[53],"converting":[54],"COP":[56],"problem":[59,82,93,118,139],"with":[60,119,190,210],"helper":[61,85,131,166,191],"equivalent":[63,66,121,133,168,193],"objectives.":[64],"An":[65,188],"objective":[67,86,134],"means":[68],"that":[69,78,111,164,201],"its":[70,202],"optimal":[71],"solution":[72],"set":[73],"same":[76],"as":[77],"of":[79,99,129,174],"but":[83],"does":[87],"not.":[88],"Then,":[89],"decomposed":[95],"group":[98],"subproblems":[100],"using":[101,165],"weighted":[103],"sum":[104],"approach.":[105],"Weights":[106],"are":[107],"dynamically":[108],"adjusted":[109],"so":[110],"each":[112],"subproblem":[113],"eventually":[114],"tends":[115],"an":[120,148],"objective.":[122],"We":[123,162,179],"theoretically":[124],"analyze":[125],"computational":[127],"time":[128,152,173],"on":[136,215],"hard":[138],"called":[140],"\"wide":[141],"gap.\"":[142],"wide":[145,160,177],"gap":[146],"problem,":[147],"algorithm":[149,189],"needs":[150],"exponential":[151],"cross":[154],"between":[155],"fitness":[157],"levels":[158],"(a":[159],"gap).":[161],"prove":[163],"objectives":[169,194],"can":[170],"shorten":[171],"crossing":[175],"gap.":[178],"conduct":[180],"case":[182],"study":[183],"validating":[185],"our":[186],"method.":[187],"implemented.":[196],"experimental":[198],"results":[199],"show":[200],"overall":[203],"performance":[204],"ranked":[206],"first":[207],"when":[208],"compared":[209],"other":[211],"eight":[212],"state-of-the-art":[213],"EAs":[214],"IEEE":[216],"CEC2017":[217],"benchmarks":[218],"in":[219],"optimization.":[221]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
