{"id":"https://openalex.org/W2963753818","doi":"https://doi.org/10.1109/mci.2019.2919398","title":"Diversity Assessment of Multi-Objective Evolutionary Algorithms: Performance Metric and Benchmark Problems [Research Frontier]","display_name":"Diversity Assessment of Multi-Objective Evolutionary Algorithms: Performance Metric and Benchmark Problems [Research Frontier]","publication_year":2019,"publication_date":"2019-07-17","ids":{"openalex":"https://openalex.org/W2963753818","doi":"https://doi.org/10.1109/mci.2019.2919398","mag":"2963753818"},"language":"en","primary_location":{"id":"doi:10.1109/mci.2019.2919398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mci.2019.2919398","pdf_url":null,"source":{"id":"https://openalex.org/S104797584","display_name":"IEEE Computational Intelligence Magazine","issn_l":"1556-603X","issn":["1556-603X","1556-6048"],"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 Computational Intelligence Magazine","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/A5058755242","display_name":"Ye Tian","orcid":"https://orcid.org/0000-0002-3487-5126"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]},{"id":"https://openalex.org/I2802624667","display_name":"Hefei Institutes of Physical Science","ror":"https://ror.org/046n57345","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I2802624667"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Tian","raw_affiliation_strings":["Institutes of Physical Science and Information Technology, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutes of Physical Science and Information Technology, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143","https://openalex.org/I2802624667"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004036087","display_name":"Ran Cheng","orcid":"https://orcid.org/0000-0001-9410-8263"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Cheng","raw_affiliation_strings":["Shenzhen Key Laboratory of Computational Intelligence, Southern University of Science and Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Computational Intelligence, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028634381","display_name":"Xingyi Zhang","orcid":"https://orcid.org/0000-0002-5052-000X"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingyi Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Northeastern University, Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036335232","display_name":"Miqing Li","orcid":"https://orcid.org/0000-0002-8607-9607"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Miqing Li","raw_affiliation_strings":["School of Computer Science, University of Birmingham, Birmingham, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham, Birmingham, U.K","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032314861","display_name":"Yaochu Jin","orcid":"https://orcid.org/0000-0003-1100-0631"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaochu Jin","raw_affiliation_strings":["Department of Computer Science, Southern University of Science and Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.2512,"has_fulltext":false,"cited_by_count":182,"citation_normalized_percentile":{"value":0.98972475,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"14","issue":"3","first_page":"61","last_page":"74"},"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":0.9962000250816345,"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":0.991599977016449,"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/benchmark","display_name":"Benchmark (surveying)","score":0.8489826917648315},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7440505623817444},{"id":"https://openalex.org/keywords/test-suite","display_name":"Test suite","score":0.7283816933631897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6648842096328735},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.6386321783065796},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5838756561279297},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5432544350624084},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.5399776101112366},{"id":"https://openalex.org/keywords/evolutionary-computation","display_name":"Evolutionary computation","score":0.4836665093898773},{"id":"https://openalex.org/keywords/performance-metric","display_name":"Performance metric","score":0.4828358292579651},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.442960262298584},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3664219081401825},{"id":"https://openalex.org/keywords/test-case","display_name":"Test case","score":0.29750263690948486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23971399664878845},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07607829570770264}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.8489826917648315},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7440505623817444},{"id":"https://openalex.org/C151552104","wikidata":"https://www.wikidata.org/wiki/Q7705809","display_name":"Test suite","level":4,"score":0.7283816933631897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6648842096328735},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.6386321783065796},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5838756561279297},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5432544350624084},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.5399776101112366},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.4836665093898773},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.4828358292579651},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.442960262298584},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3664219081401825},{"id":"https://openalex.org/C128942645","wikidata":"https://www.wikidata.org/wiki/Q1568346","display_name":"Test case","level":3,"score":0.29750263690948486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23971399664878845},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07607829570770264},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"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/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/mci.2019.2919398","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mci.2019.2919398","pdf_url":null,"source":{"id":"https://openalex.org/S104797584","display_name":"IEEE Computational Intelligence Magazine","issn_l":"1556-603X","issn":["1556-603X","1556-6048"],"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 Computational Intelligence Magazine","raw_type":"journal-article"},{"id":"pmh:oai:alma.44SUR_INST:11139895290002346","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335661","display_name":"State Key Laboratory of Synthetical Automation for Process Industries","ror":null},{"id":"https://openalex.org/F4320335790","display_name":"Shenzhen Peacock Plan","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1137530","https://openalex.org/W96550542","https://openalex.org/W1522538275","https://openalex.org/W1542437639","https://openalex.org/W1588375755","https://openalex.org/W1595498733","https://openalex.org/W1662894842","https://openalex.org/W1833634424","https://openalex.org/W1965667693","https://openalex.org/W1976159118","https://openalex.org/W1984675190","https://openalex.org/W1985357653","https://openalex.org/W1997053037","https://openalex.org/W2001591765","https://openalex.org/W2020320008","https://openalex.org/W2022485595","https://openalex.org/W2024008934","https://openalex.org/W2038420231","https://openalex.org/W2058142975","https://openalex.org/W2081939577","https://openalex.org/W2085507535","https://openalex.org/W2102365077","https://openalex.org/W2107845038","https://openalex.org/W2117396633","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2128357515","https://openalex.org/W2135293965","https://openalex.org/W2140886193","https://openalex.org/W2143185749","https://openalex.org/W2143381319","https://openalex.org/W2146446525","https://openalex.org/W2152551290","https://openalex.org/W2153654820","https://openalex.org/W2183043622","https://openalex.org/W2283268937","https://openalex.org/W2343601797","https://openalex.org/W2379909386","https://openalex.org/W2404080558","https://openalex.org/W2466060750","https://openalex.org/W2510493362","https://openalex.org/W2513211214","https://openalex.org/W2573114156","https://openalex.org/W2599937626","https://openalex.org/W2738689687","https://openalex.org/W2750985671","https://openalex.org/W2751605210","https://openalex.org/W2764251381","https://openalex.org/W2783781089","https://openalex.org/W2897783557","https://openalex.org/W2994964425","https://openalex.org/W3100195331","https://openalex.org/W4285719527","https://openalex.org/W4292408320","https://openalex.org/W6631460888","https://openalex.org/W6681822056","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W1485837041","https://openalex.org/W3204955359","https://openalex.org/W2801693842","https://openalex.org/W4297582752","https://openalex.org/W4285805405","https://openalex.org/W85101999","https://openalex.org/W2391924736","https://openalex.org/W3133779647","https://openalex.org/W4291270682","https://openalex.org/W1560122427"],"abstract_inverted_index":{"Diversity":[0],"preservation":[1],"plays":[2],"an":[3],"important":[4],"role":[5],"in":[6],"the":[7,14,39,51,68,71,100,105,117],"design":[8],"of":[9,18,42,55,70,107],"multi-objective":[10,35],"evolutionary":[11,44],"algorithms,":[12],"but":[13],"diversity":[15,40,106,133],"performance":[16,31],"assessment":[17,41],"these":[19],"algorithms":[20,89,128],"remains":[21],"challenging.":[22],"To":[23],"address":[24],"this":[25,27],"issue,":[26],"paper":[28],"proposes":[29],"a":[30,34,56,63,92,108],"metric":[32,48,102],"and":[33,53,66,116],"test":[36,77,119],"suite":[37,78,120],"for":[38,87],"multiobjective":[43],"algorithms.":[45],"The":[46,75],"proposed":[47,76,101,118],"assesses":[49],"both":[50],"evenness":[52],"spread":[54],"solution":[57,73,94,109],"set":[58,110],"by":[59],"projecting":[60],"it":[61],"to":[62,90,124,131],"lower-dimensional":[64],"hypercube":[65],"calculating":[67],"\"volume\"":[69],"projected":[72],"set.":[74,95],"contains":[79],"eight":[80],"benchmark":[81],"problems,":[82],"which":[83],"pose":[84],"stiff":[85],"challenges":[86],"existing":[88,114],"obtain":[91],"diverse":[93],"Experimental":[96],"studies":[97],"demonstrate":[98],"that":[99],"can":[103,121],"assess":[104],"more":[111],"precisely":[112],"than":[113],"ones,":[115],"be":[122],"used":[123],"effectively":[125],"distinguish":[126],"between":[127],"with":[129],"respect":[130],"their":[132],"performance.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":39},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":33},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
