{"id":"https://openalex.org/W2161886616","doi":"https://doi.org/10.1109/cec.2009.4983090","title":"An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion","display_name":"An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2161886616","doi":"https://doi.org/10.1109/cec.2009.4983090","mag":"2161886616"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2009.4983090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 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/A5042326416","display_name":"Luis Mart\u00ed","orcid":"https://orcid.org/0000-0003-2789-5062"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Luis Marti","raw_affiliation_strings":["Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100653268","display_name":"Jes\u00fas Garc\u0131\u0301a","orcid":"https://orcid.org/0000-0003-1768-2688"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jesus Garcia","raw_affiliation_strings":["Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079499955","display_name":"Antonio Berlanga","orcid":"https://orcid.org/0000-0002-5564-399X"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonio Berlanga","raw_affiliation_strings":["Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059583924","display_name":"Jos\u00e9 M. Molina","orcid":"https://orcid.org/0000-0002-7484-7357"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jose M. Molina","raw_affiliation_strings":["Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, Group of Applied Artificial Intelligence, Universidad Carlos III de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042326416"],"corresponding_institution_ids":["https://openalex.org/I50357001"],"apc_list":null,"apc_paid":null,"fwci":5.8273,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.96611943,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1263","last_page":"1270"},"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9988999962806702,"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":0.9948999881744385,"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":0.6588778495788574},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6552332639694214},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5806295871734619},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.563869833946228},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.56020587682724},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4844372570514679},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47880348563194275},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.44076448678970337},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43769487738609314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25031137466430664},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.20779532194137573},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1727743148803711}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6588778495788574},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6552332639694214},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5806295871734619},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.563869833946228},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.56020587682724},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4844372570514679},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47880348563194275},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.44076448678970337},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43769487738609314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25031137466430664},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.20779532194137573},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1727743148803711},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2009.4983090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2009.4983090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322835","display_name":"Ministry of Economic Affairs","ror":"https://ror.org/042ge0913"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W42649658","https://openalex.org/W140906297","https://openalex.org/W1500356961","https://openalex.org/W1502761295","https://openalex.org/W1559536185","https://openalex.org/W1571947545","https://openalex.org/W1575601714","https://openalex.org/W1587435968","https://openalex.org/W1980272771","https://openalex.org/W1992580876","https://openalex.org/W2036109172","https://openalex.org/W2069135014","https://openalex.org/W2098907614","https://openalex.org/W2102365077","https://openalex.org/W2105934661","https://openalex.org/W2137904150","https://openalex.org/W2150881546","https://openalex.org/W2222230941","https://openalex.org/W2615258659","https://openalex.org/W2941281702","https://openalex.org/W3020888050","https://openalex.org/W3029591682","https://openalex.org/W6605721000","https://openalex.org/W6630035506","https://openalex.org/W6675537533","https://openalex.org/W6689236931"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2760382975","https://openalex.org/W2349716249","https://openalex.org/W2120941928","https://openalex.org/W3191856393","https://openalex.org/W2146909562","https://openalex.org/W2745986669","https://openalex.org/W4206770590","https://openalex.org/W2379462184","https://openalex.org/W1611787488"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"put":[4],"forward":[5],"a":[6,21,38,57,77,139],"comprehensive":[7],"study":[8],"on":[9],"the":[10,30,63,71,74,93,111,134],"design":[11],"of":[12,69,73,92],"global":[13],"stopping":[14,23,64],"criteria":[15,112],"for":[16,45,62,84,117],"multi-objective":[17],"optimization.":[18],"We":[19],"describe":[20],"novel":[22],"criterion,":[24],"denominated":[25],"MGBM":[26],"criterion":[27],"that":[28,42],"combines":[29],"mutual":[31],"domination":[32],"rate":[33],"(MDR)":[34],"improvement":[35,136],"indicator":[36],"with":[37,76,100,138],"simplified":[39],"Kalman":[40],"filter":[41],"is":[43,53,56,67,95],"used":[44],"evidence":[46],"gathering":[47],"process.":[48],"The":[49,90],"MDR":[50],"indicator,":[51],"which":[52],"introduced":[54],"along,":[55],"special":[58],"purpose":[59],"solution":[60],"meant":[61,116],"task.":[65],"It":[66,105],"capable":[68],"gauging":[70],"progress":[72],"optimization":[75],"low":[78],"computational":[79],"cost":[80],"and":[81,119],"therefore":[82],"suitable":[83,140],"solving":[85],"complex":[86],"or":[87,129],"many-objective":[88],"problems.":[89],"viability":[91],"proposal":[94],"established":[96],"by":[97,132],"comparing":[98],"it":[99],"some":[101],"other":[102,127],"possible":[103],"alternatives.":[104],"should":[106],"be":[107,123],"noted":[108],"that,":[109],"although":[110],"discussed":[113],"here":[114],"are":[115],"MOPs":[118],"MOEAs,":[120],"they":[121],"could":[122],"easily":[124],"adapted":[125],"to":[126],"softcomputing":[128],"numerical":[130],"methods":[131],"substituting":[133],"local":[135],"metric":[137],"one.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}