{"id":"https://openalex.org/W1965667693","doi":"https://doi.org/10.1109/cec.2013.6557960","title":"Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique","display_name":"Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W1965667693","doi":"https://doi.org/10.1109/cec.2013.6557960","mag":"1965667693"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2013.6557960","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-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/A5012143052","display_name":"Christian Dom\u00ednguez-Medina","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090124","display_name":"Tecnol\u00f3gico Nacional de M\u00e9xico","ror":"https://ror.org/00davry38","country_code":"MX","type":"funder","lineage":["https://openalex.org/I1302736544","https://openalex.org/I4210090124","https://openalex.org/I4413696010"]},{"id":"https://openalex.org/I59361560","display_name":"Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34","country_code":"MX","type":"education","lineage":["https://openalex.org/I59361560"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Christian Dominguez-Medina","raw_affiliation_strings":["Computer Research Center, National Polytechnic Institute, Mexico, Distrito Federal, Mexico","Comput. Res. Center, Nat. Polytech. Inst., Mexico City, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Research Center, National Polytechnic Institute, Mexico, Distrito Federal, Mexico","institution_ids":["https://openalex.org/I4210090124","https://openalex.org/I59361560"]},{"raw_affiliation_string":"Comput. Res. Center, Nat. Polytech. Inst., Mexico City, Mexico","institution_ids":["https://openalex.org/I4210090124"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062851293","display_name":"G\u00fcnter Rudolph","orcid":"https://orcid.org/0000-0003-4223-5257"},"institutions":[{"id":"https://openalex.org/I1323252656","display_name":"Information Technology University","ror":"https://ror.org/00ngv8j44","country_code":"PK","type":"education","lineage":["https://openalex.org/I1323252656"]},{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE","PK"],"is_corresponding":false,"raw_author_name":"Gunter Rudolph","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Informatik, Technical University Dortmund, Dortmund, Germany","Fak. fur Inf., Tech. Univ. Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Informatik, Technical University Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Fak. fur Inf., Tech. Univ. Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I1323252656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050431536","display_name":"Oliver Sch\u00fctze","orcid":"https://orcid.org/0000-0002-8867-6878"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Oliver Schutze","raw_affiliation_strings":["Computer Science Department, CINVESTAV-IPN, Mexico, Distrito Federal, Mexico","Computer Science Department, CINVESTAV-IPN, Mexico City Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, CINVESTAV-IPN, Mexico, Distrito Federal, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Computer Science Department, CINVESTAV-IPN, Mexico City Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084825454","display_name":"Heike Trautmann","orcid":"https://orcid.org/0000-0002-9788-8282"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Heike Trautmann","raw_affiliation_strings":["Information Systems and Statistics, University of M\u00fcnster, Munster, Germany","Inf. Syst. & Stat., Univ. of Munster, Munster, Germany"],"affiliations":[{"raw_affiliation_string":"Information Systems and Statistics, University of M\u00fcnster, Munster, Germany","institution_ids":["https://openalex.org/I22465464"]},{"raw_affiliation_string":"Inf. Syst. & Stat., Univ. of Munster, Munster, Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012143052"],"corresponding_institution_ids":["https://openalex.org/I4210090124","https://openalex.org/I59361560"],"apc_list":null,"apc_paid":null,"fwci":3.6254,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92631996,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"3190","last_page":"3197"},"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":0.9973999857902527,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.7281370759010315},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.7210299968719482},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6300569176673889},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.621211051940918},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.5923953652381897},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5415601134300232},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5335674285888672},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5091912150382996},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.45750948786735535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4435851275920868},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.41222649812698364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4037335216999054},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2442747950553894},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13345718383789062},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07170763611793518}],"concepts":[{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.7281370759010315},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.7210299968719482},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6300569176673889},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.621211051940918},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.5923953652381897},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5415601134300232},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5335674285888672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5091912150382996},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.45750948786735535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4435851275920868},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.41222649812698364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4037335216999054},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2442747950553894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13345718383789062},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07170763611793518},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2013.6557960","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2013.6557960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1137530","https://openalex.org/W49351470","https://openalex.org/W96550542","https://openalex.org/W1521316934","https://openalex.org/W1595498733","https://openalex.org/W1607104331","https://openalex.org/W1846834309","https://openalex.org/W1976159118","https://openalex.org/W1994769619","https://openalex.org/W2038420231","https://openalex.org/W2055025427","https://openalex.org/W2098907614","https://openalex.org/W2126105956","https://openalex.org/W2143381319","https://openalex.org/W2148615815","https://openalex.org/W6648849640"],"related_works":["https://openalex.org/W2886349793","https://openalex.org/W1144450175","https://openalex.org/W4297582752","https://openalex.org/W2031465436","https://openalex.org/W4285805405","https://openalex.org/W2906115061","https://openalex.org/W1512585147","https://openalex.org/W2977596624","https://openalex.org/W85101999","https://openalex.org/W2145877535"],"abstract_inverted_index":{"Here":[0],"we":[1,53,78],"address":[2],"the":[3,12,33,42,50,71,84,87],"problem":[4],"of":[5,11,15,21,66,86],"computing":[6],"finite":[7],"size":[8],"Hausdorff":[9,43],"approximations":[10,37],"Pareto":[13,34,51],"front":[14,35,52],"four-objective":[16],"optimization":[17],"problems":[18],"by":[19],"means":[20],"evolutionary":[22,57],"computing.":[23],"Since":[24],"many":[25],"applications":[26],"desire":[27],"an":[28],"approximation":[29],"evenly":[30,47],"spread":[31,48],"along":[32,49],"and":[36,73],"that":[38,62],"are":[39,45,68],"good":[40],"in":[41],"sense":[44],"typically":[46],"consider":[54],"three":[55],"different":[56],"multi-objective":[58],"algorithms":[59],"tailored":[60],"to":[61],"purpose,":[63],"where":[64],"two":[65],"them":[67],"based":[69],"on":[70],"Part":[72],"Selection":[74],"Algorithm":[75],"(PSA).":[76],"Finally,":[77],"present":[79],"some":[80],"numerical":[81],"results":[82],"indicating":[83],"strength":[85],"novel":[88],"methods.":[89]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}