{"id":"https://openalex.org/W2897783557","doi":"https://doi.org/10.1109/cec.2018.8477730","title":"Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems","display_name":"Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems","publication_year":2018,"publication_date":"2018-07-01","ids":{"openalex":"https://openalex.org/W2897783557","doi":"https://doi.org/10.1109/cec.2018.8477730","mag":"2897783557"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2018.8477730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2018.8477730","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"},"type":"conference-paper","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Tian","raw_affiliation_strings":["Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039480515","display_name":"Xiaoshu Xiang","orcid":"https://orcid.org/0000-0002-9107-1677"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoshu Xiang","raw_affiliation_strings":["Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"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/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingyi Zhang","raw_affiliation_strings":["Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Bio-inspired Intelligence and Mining Knowledge, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"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/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":"Ran Cheng","raw_affiliation_strings":["School of Computer Science, University of Birmingham, Birmingham, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham, Birmingham, United Kingdom","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/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yaochu Jin","raw_affiliation_strings":["Department of Computer Science, University of Surrey, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Surrey, United Kingdom","institution_ids":["https://openalex.org/I28290843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9905999898910522,"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/benchmark","display_name":"Benchmark (surveying)","score":0.778334379196167},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6945412158966064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6031739711761475},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5954617857933044},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5055534839630127},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5013644695281982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26823776960372925},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.058581918478012085}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.778334379196167},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6945412158966064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6031739711761475},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5954617857933044},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5055534839630127},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5013644695281982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26823776960372925},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.058581918478012085},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cec.2018.8477730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2018.8477730","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"},{"id":"pmh:oai:alma.44SUR_INST:11138864930002346","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":""},{"id":"pmh:oai:epubs.surrey.ac.uk:848905","is_oa":false,"landing_page_url":"http://epubs.surrey.ac.uk/848905/1/Sampling%20Reference%20Points%20on%20the%20Pareto%20Fronts%20of%20Benchmark%20Multi-Objective%20Optimization%20Problems.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400680","display_name":"Surrey Research Insight Open Access (The University of Surrey)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28290843","host_organization_name":"University of Surrey","host_organization_lineage":["https://openalex.org/I28290843"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},{"id":"pmh:oai:pub.uni-bielefeld.de:2978466","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2978466","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"http://purl.org/coar/resource_type/c_5794"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8448577284","display_name":null,"funder_award_id":"EP/M017869/1","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1522538275","https://openalex.org/W1542437639","https://openalex.org/W1595498733","https://openalex.org/W1662894842","https://openalex.org/W2015371402","https://openalex.org/W2016014758","https://openalex.org/W2020320008","https://openalex.org/W2022485595","https://openalex.org/W2024008934","https://openalex.org/W2072661909","https://openalex.org/W2085507535","https://openalex.org/W2102365077","https://openalex.org/W2116858902","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2140066605","https://openalex.org/W2143185749","https://openalex.org/W2146446525","https://openalex.org/W2153654820","https://openalex.org/W2343498104","https://openalex.org/W2343601797","https://openalex.org/W2513211214","https://openalex.org/W2559448781","https://openalex.org/W2563621803","https://openalex.org/W2583230990","https://openalex.org/W2599937626","https://openalex.org/W2751605210","https://openalex.org/W2764251381","https://openalex.org/W2994964425","https://openalex.org/W4285719527","https://openalex.org/W6631460888","https://openalex.org/W6680838134","https://openalex.org/W6743462582","https://openalex.org/W6771627385"],"related_works":["https://openalex.org/W2996366161","https://openalex.org/W4318426920","https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2001591765","https://openalex.org/W2080708212","https://openalex.org/W2055791821","https://openalex.org/W2073147994","https://openalex.org/W2162013778","https://openalex.org/W1588199609"],"abstract_inverted_index":{"The":[0],"effectiveness":[1],"of":[2,15,32,37,47,55,140,160],"evolutionary":[3,17,95],"algorithms":[4,18,161],"have":[5,19],"been":[6,20,64],"verified":[7],"on":[8,43,74,111],"multi-objective":[9,16,96],"optimization,":[10],"and":[11,115],"a":[12,35],"large":[13],"number":[14],"proposed":[21,100,153],"during":[22],"the":[23,30,44,53,68,120,129,147,152,158],"last":[24],"two":[25],"decades.":[26],"To":[27],"quantitatively":[28],"compare":[29],"performance":[31,57,121,159],"different":[33,138],"algorithms,":[34],"set":[36],"uniformly":[38],"distributed":[39],"reference":[40,72,109,130,148,167],"points":[41,73,110,149],"sampled":[42,166],"Pareto":[45,75,87,113,141],"fronts":[46,88],"benchmark":[48],"problems":[49],"are":[50],"needed":[51],"in":[52,135],"calculation":[54],"many":[56,86],"metrics.":[58],"However,":[59],"not":[60,81],"much":[61],"work":[62],"has":[63],"done":[65],"to":[66,118],"investigate":[67],"method":[69],"for":[70,85,137],"sampling":[71,132,154],"fronts,":[76],"even":[77],"though":[78],"it":[79],"is":[80],"an":[82,94],"easy":[83],"task":[84],"with":[89],"irregular":[90],"shapes.":[91],"More":[92],"recently,":[93],"optimization":[97],"platform":[98],"was":[99],"by":[101,151],"us,":[102],"called":[103],"PlatEMO,":[104],"which":[105],"can":[106,156],"automatically":[107],"generate":[108],"each":[112],"front":[114],"use":[116],"them":[117],"calculate":[119],"metric":[122],"values.":[123],"In":[124],"this":[125],"paper,":[126],"we":[127],"report":[128],"point":[131],"methods":[133,155],"used":[134],"PlatEMO":[136],"types":[139],"fronts.":[142],"Experimental":[143],"results":[144],"show":[145],"that":[146],"generated":[150],"evaluate":[157],"more":[162],"accurately":[163],"than":[164],"randomly":[165],"points.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}