{"id":"https://openalex.org/W2018712218","doi":"https://doi.org/10.1109/tevc.2012.2185847","title":"Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms","display_name":"Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms","publication_year":2012,"publication_date":"2012-02-10","ids":{"openalex":"https://openalex.org/W2018712218","doi":"https://doi.org/10.1109/tevc.2012.2185847","mag":"2018712218"},"language":"en","primary_location":{"id":"doi:10.1109/tevc.2012.2185847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2012.2185847","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"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 Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5043795281","display_name":"Dhish Kumar Saxena","orcid":"https://orcid.org/0000-0001-7809-7744"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dhish Kumar Saxena","raw_affiliation_strings":["Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","Dept. of Manuf., Cranfield Univ., Cranfield, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","institution_ids":["https://openalex.org/I82284825"]},{"raw_affiliation_string":"Dept. of Manuf., Cranfield Univ., Cranfield, UK","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073367317","display_name":"Jo\u00e3o A. Duro","orcid":"https://orcid.org/0000-0002-7684-4707"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o A. Duro","raw_affiliation_strings":["Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","Dept. of Manuf., Cranfield Univ., Cranfield, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","institution_ids":["https://openalex.org/I82284825"]},{"raw_affiliation_string":"Dept. of Manuf., Cranfield Univ., Cranfield, UK","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066657755","display_name":"Ashutosh Tiwari","orcid":"https://orcid.org/0000-0002-6197-1519"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ashutosh Tiwari","raw_affiliation_strings":["Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","Dept. of Manuf., Cranfield Univ., Cranfield, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Manufacturing, Cranfield University, Cranfield, Bedfordshire, UK","institution_ids":["https://openalex.org/I82284825"]},{"raw_affiliation_string":"Dept. of Manuf., Cranfield Univ., Cranfield, UK","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088394271","display_name":"Kalyanmoy Deb","orcid":"https://orcid.org/0000-0001-7402-9939"},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kalyanmoy Deb","raw_affiliation_strings":["Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Kanpur, India","Dept. of Mech. Eng., Indian Inst. of Technol. Kanpur, Kanpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]},{"raw_affiliation_string":"Dept. of Mech. Eng., Indian Inst. of Technol. Kanpur, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000546219","display_name":"Qingfu Zhang","orcid":"https://orcid.org/0000-0003-0786-0671"},"institutions":[{"id":"https://openalex.org/I110002522","display_name":"University of Essex","ror":"https://ror.org/02nkf1q06","country_code":"GB","type":"education","lineage":["https://openalex.org/I110002522"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Qingfu Zhang","raw_affiliation_strings":["School of Computer Science and Electronic Engineering, University of Essex, Colchester, UK","[Sch. of Comput. Sci. & Electron. Eng., Univ. of Essex, Colchester, UK]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Electronic Engineering, University of Essex, Colchester, UK","institution_ids":["https://openalex.org/I110002522"]},{"raw_affiliation_string":"[Sch. of Comput. Sci. & Electron. Eng., Univ. of Essex, Colchester, UK]","institution_ids":["https://openalex.org/I110002522"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":27.199,"has_fulltext":false,"cited_by_count":297,"citation_normalized_percentile":{"value":0.99811837,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"17","issue":"1","first_page":"77","last_page":"99"},"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9927999973297119,"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"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9909999966621399,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6427949666976929},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6092317700386047},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5693955421447754},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5298635363578796},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5261263847351074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5008959770202637},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.4781649708747864},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.4417823851108551},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4204399585723877},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41285955905914307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3963736593723297},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1499100923538208}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6427949666976929},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6092317700386047},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5693955421447754},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5298635363578796},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5261263847351074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5008959770202637},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.4781649708747864},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.4417823851108551},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4204399585723877},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41285955905914307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3963736593723297},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1499100923538208},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tevc.2012.2185847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2012.2185847","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"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 Evolutionary Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W216586509","https://openalex.org/W1484287363","https://openalex.org/W1494252918","https://openalex.org/W1503648602","https://openalex.org/W1504943474","https://openalex.org/W1519778441","https://openalex.org/W1533748389","https://openalex.org/W1555148682","https://openalex.org/W1568794265","https://openalex.org/W1569986015","https://openalex.org/W1575601714","https://openalex.org/W1583275772","https://openalex.org/W1588375755","https://openalex.org/W1591635931","https://openalex.org/W1595205399","https://openalex.org/W1605170913","https://openalex.org/W1605810911","https://openalex.org/W1607221389","https://openalex.org/W1799158580","https://openalex.org/W1842155679","https://openalex.org/W1967073510","https://openalex.org/W1980591224","https://openalex.org/W1987958230","https://openalex.org/W1999613943","https://openalex.org/W2025525377","https://openalex.org/W2037124948","https://openalex.org/W2053900989","https://openalex.org/W2063375245","https://openalex.org/W2073317560","https://openalex.org/W2074308169","https://openalex.org/W2097536098","https://openalex.org/W2100830227","https://openalex.org/W2102365077","https://openalex.org/W2105511939","https://openalex.org/W2107031757","https://openalex.org/W2110828487","https://openalex.org/W2116858902","https://openalex.org/W2120269552","https://openalex.org/W2126105956","https://openalex.org/W2129318555","https://openalex.org/W2139196352","https://openalex.org/W2140095548","https://openalex.org/W2140886193","https://openalex.org/W2143185749","https://openalex.org/W2143381319","https://openalex.org/W2148933727","https://openalex.org/W2150046657","https://openalex.org/W2151879717","https://openalex.org/W2153654820","https://openalex.org/W2154693991","https://openalex.org/W2162478582","https://openalex.org/W2166898117","https://openalex.org/W2490736661","https://openalex.org/W2994964425","https://openalex.org/W3013880646","https://openalex.org/W4245973528","https://openalex.org/W4285719527","https://openalex.org/W4298199339","https://openalex.org/W4300870773","https://openalex.org/W6635433731","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W1997381757","https://openalex.org/W3201550974","https://openalex.org/W4239294646","https://openalex.org/W2236365751","https://openalex.org/W2763601085","https://openalex.org/W2372680517","https://openalex.org/W2058142975","https://openalex.org/W1967991081","https://openalex.org/W1999564523","https://openalex.org/W2100916763"],"abstract_inverted_index":{"The":[0,159],"difficulties":[1,37],"faced":[2],"by":[3,38,83],"existing":[4,85],"multiobjective":[5],"evolutionary":[6],"algorithms":[7,233,255],"(MOEAs)":[8],"in":[9,25,169,179,213],"handling":[10],"many-objective":[11],"problems":[12,187,268],"relate":[13],"to":[14,34,52,59,73,183,194,209,221,271],"the":[15,40,43,47,61,66,78,84,102,109,113,120,167,170,174,201,211,223,231,235,240,243,250,253],"inefficiency":[16],"of":[17,27,42,68,112,129,162,173,181,186,191,217,225,230,242,249,252,266],"selection":[18,45],"operators,":[19,46],"high":[20],"computational":[21,123],"cost,":[22,124],"and":[23,125,131,145,153,204,239,246,274],"difficulty":[24],"visualization":[26],"objective":[28,48,90,133,155],"space.":[29],"While":[30],"many":[31],"approaches":[32,135],"aim":[33],"counter":[35],"these":[36],"increasing":[39],"fidelity":[41],"standard":[44],"reduction":[49,91,134,156],"approach":[50],"attempts":[51],"eliminate":[53],"objectives":[54,70,104],"that":[55,89,198],"are":[56,105],"not":[57],"essential":[58,69,103],"describe":[60],"Pareto-optimal":[62],"front":[63],"(POF).":[64],"If":[65],"number":[67],"is":[71],"found":[72],"be":[74,81],"two":[75,275],"or":[76,107],"three,":[77],"problem":[79,98,114],"could":[80,92],"solved":[82],"MOEAs.":[86],"It":[87],"implies":[88],"make":[93],"an":[94,218],"otherwise":[95],"unsolvable":[96],"(many-objective)":[97],"solvable.":[99],"Even":[100],"when":[101],"four":[106],"more,":[108],"reduced":[110],"representation":[111],"will":[115],"have":[116],"favorable":[117],"impact":[118],"on":[119,206,262],"search":[121],"efficiency,":[122],"decision-making.":[126],"Hence,":[127],"development":[128],"generic":[130],"robust":[132],"becomes":[136],"important.":[137],"This":[138],"paper":[139,164],"presents":[140],"a":[141,184,263],"principal":[142],"component":[143],"analysis":[144,229],"maximum":[146],"variance":[147],"unfolding":[148],"based":[149,260],"framework":[150,175],"for":[151,176,234],"linear":[152],"nonlinear":[154],"algorithms,":[157,261],"respectively.":[158],"major":[160],"contribution":[161],"this":[163],"includes:":[165],"1)":[166],"enhancements":[168],"core":[171],"components":[172],"higher":[177],"robustness":[178],"terms":[180],"applicability":[182],"range":[185,265],"with":[188],"disparate":[189],"degree":[190],"redundancy;":[192],"mechanisms":[193],"handle":[195],"input":[196,244],"data":[197],"poorly":[199],"approximates":[200],"true":[202],"POF;":[203],"dependence":[205],"fewer":[207],"parameters":[208],"minimize":[210],"variability":[212],"performance;":[214],"2)":[215],"proposition":[216],"error":[219],"measure":[220],"assess":[222],"quality":[224],"results;":[226],"3)":[227],"sensitivity":[228],"proposed":[232,254],"critical":[236],"parameter":[237],"involved,":[238],"characteristics":[241],"data;":[245],"4)":[247],"study":[248],"performance":[251],"vis-\u00e0-vis":[256],"dominance":[257],"relation":[258],"preservation":[259],"wide":[264],"test":[267],"(scaled":[269],"up":[270],"50":[272],"objectives)":[273],"real-world":[276],"problems.":[277]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":28},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":30},{"year":2016,"cited_by_count":30},{"year":2015,"cited_by_count":30},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
