{"id":"https://openalex.org/W4405511307","doi":"https://doi.org/10.1007/s44196-024-00702-6","title":"Hyperplane-Assisted Multi-objective Particle Swarm Optimization with Twofold Proportional Assignment Strategy","display_name":"Hyperplane-Assisted Multi-objective Particle Swarm Optimization with Twofold Proportional Assignment Strategy","publication_year":2024,"publication_date":"2024-12-18","ids":{"openalex":"https://openalex.org/W4405511307","doi":"https://doi.org/10.1007/s44196-024-00702-6"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-024-00702-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-024-00702-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-024-00702-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s44196-024-00702-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100748966","display_name":"Qian Song","orcid":"https://orcid.org/0000-0001-9897-0491"},"institutions":[{"id":"https://openalex.org/I4210095439","display_name":"Guizhou Minzu University","ror":"https://ror.org/00qm4t918","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210095439"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Song","raw_affiliation_strings":["School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China","institution_ids":["https://openalex.org/I4210095439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084905540","display_name":"Yanmin Liu","orcid":"https://orcid.org/0000-0002-1571-5370"},"institutions":[{"id":"https://openalex.org/I4210091787","display_name":"Zunyi Normal College","ror":"https://ror.org/00g2pnp92","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210091787"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanmin Liu","raw_affiliation_strings":["Zunyi Normal College, Zunyi, 563002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zunyi Normal College, Zunyi, 563002, China","institution_ids":["https://openalex.org/I4210091787"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039440724","display_name":"Xiaoyan Zhang","orcid":"https://orcid.org/0000-0001-9707-6965"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyan Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100644855","display_name":"Yansong Zhang","orcid":"https://orcid.org/0000-0003-2198-0987"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yansong Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China","institution_ids":["https://openalex.org/I178232147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084905540"],"corresponding_institution_ids":["https://openalex.org/I4210091787"],"apc_list":{"value":2090,"currency":"USD","value_usd":2090},"apc_paid":{"value":2090,"currency":"USD","value_usd":2090},"fwci":0.2564,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60729955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"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":0.9994999766349792,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9587000012397766,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.826578676700592},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7887421250343323},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6111215949058533},{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.5381510853767395},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.5235497355461121},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5031494498252869},{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.4679378867149353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42748379707336426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14745229482650757}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.826578676700592},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7887421250343323},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6111215949058533},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.5381510853767395},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.5235497355461121},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5031494498252869},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.4679378867149353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42748379707336426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14745229482650757}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s44196-024-00702-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-024-00702-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-024-00702-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3da2a19389704ef0b501f849d8cbe823","is_oa":false,"landing_page_url":"https://doaj.org/article/3da2a19389704ef0b501f849d8cbe823","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Computational Intelligence Systems, Vol 17, Iss 1, Pp 1-27 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s44196-024-00702-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-024-00702-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-024-00702-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1885046401","display_name":null,"funder_award_id":"62062071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2487583347","display_name":null,"funder_award_id":"(NSFC 62062071)","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6443769554","display_name":null,"funder_award_id":"NSFC 62062071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405511307.pdf","grobid_xml":"https://content.openalex.org/works/W4405511307.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W890304461","https://openalex.org/W939691211","https://openalex.org/W1585939719","https://openalex.org/W1588375755","https://openalex.org/W2039007401","https://openalex.org/W2072661909","https://openalex.org/W2079934979","https://openalex.org/W2102365077","https://openalex.org/W2104017154","https://openalex.org/W2106334424","https://openalex.org/W2112912151","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2128357515","https://openalex.org/W2143381319","https://openalex.org/W2152195021","https://openalex.org/W2165171393","https://openalex.org/W2432516117","https://openalex.org/W2517908245","https://openalex.org/W2520973147","https://openalex.org/W2563621803","https://openalex.org/W2567327143","https://openalex.org/W2570235502","https://openalex.org/W2606294877","https://openalex.org/W2764251381","https://openalex.org/W2766133347","https://openalex.org/W2896834367","https://openalex.org/W2963185242","https://openalex.org/W2965044785","https://openalex.org/W2981792919","https://openalex.org/W2987257425","https://openalex.org/W3033720139","https://openalex.org/W3041654307","https://openalex.org/W3136073437","https://openalex.org/W3197491224","https://openalex.org/W3202010957","https://openalex.org/W3202855064","https://openalex.org/W3215736639","https://openalex.org/W4211154164","https://openalex.org/W4280533698","https://openalex.org/W4285398841","https://openalex.org/W4290702949","https://openalex.org/W4295762987","https://openalex.org/W4296312233","https://openalex.org/W4312709072","https://openalex.org/W4313368078","https://openalex.org/W4313593820","https://openalex.org/W4386216109","https://openalex.org/W4386470328","https://openalex.org/W4390119962","https://openalex.org/W4390122313","https://openalex.org/W4390887352","https://openalex.org/W4391406755","https://openalex.org/W4391744015","https://openalex.org/W4401933526","https://openalex.org/W4403180927"],"related_works":["https://openalex.org/W2006324351","https://openalex.org/W2965421953","https://openalex.org/W2133833450","https://openalex.org/W2349895019","https://openalex.org/W2116074880","https://openalex.org/W2950423922","https://openalex.org/W2070977815","https://openalex.org/W2121780490","https://openalex.org/W2137136732","https://openalex.org/W2161494499"],"abstract_inverted_index":{"In":[0,25],"the":[1,16,45,51,81,97,115,121,148,152,166,175,191],"simultaneous":[2],"optimization":[3,33,46,132],"of":[4,48,84,117,190],"multiple":[5],"objectives,":[6],"how":[7],"to":[8,43,66,79,90,105],"balance":[9],"convergence":[10,60,92,101],"promotion":[11],"and":[12,22,62,93,100,113,129,162,174,187],"diversity":[13],"preservation":[14],"in":[15,56,155],"evolutionary":[17],"process":[18],"is":[19,41,54,77],"a":[20,28,35,72,107],"key":[21],"challenging":[23],"problem.":[24],"this":[26],"research,":[27],"hyperplane-assisted":[29],"multi-objective":[30,131],"particle":[31,118],"swarm":[32],"with":[34,58,87,126,140],"twofold":[36,73],"proportional":[37,74],"assignment":[38,75],"strategy":[39],"(tpahaMOPSO)":[40],"suggested":[42],"ameliorate":[44],"performance":[47,186],"MOPSO.":[49],"First,":[50],"external":[52],"archive":[53],"maintained":[55],"combination":[57],"hyperplane-based":[59],"evaluation":[61],"shift-based":[63],"density":[64],"estimation":[65],"retain":[67],"high-quality":[68],"candidate":[69,85],"solutions.":[70],"Second,":[71],"scheme":[76],"designed":[78],"search":[80],"surrounding":[82],"region":[83],"solutions":[86],"better":[88],"potential":[89],"emphasize":[91],"diversity,":[94],"respectively.":[95],"Third,":[96],"domination":[98],"relationship":[99],"difference":[102],"are":[103],"combined":[104],"select":[106],"more":[108],"reasonable":[109],"individual":[110],"historical":[111],"best":[112,153],"reduce":[114],"risk":[116],"aggregation.":[119],"Finally,":[120],"proposed":[122,176,192],"tpahaMOPSO":[123,150,193],"was":[124,169],"compared":[125],"ten":[127],"representative":[128],"advanced":[130],"algorithms":[133],"on":[134],"22":[135],"widely":[136],"used":[137],"test":[138,168],"functions":[139,158],"different":[141,198],"characteristics.":[142],"The":[143,184],"simulation":[144],"results":[145],"present":[146],"that":[147],"developed":[149],"got":[151],"result":[154],"11":[156],"benchmark":[157],"for":[159,171],"both":[160],"IGD":[161],"HV":[163],"criteria.":[164],"Concurrently,":[165],"Friedman":[167],"applied":[170],"ranking":[172],"analysis":[173,182],"algorithm":[177],"also":[178],"obtained":[179],"excellent":[180],"statistical":[181],"results.":[183],"promising":[185],"strong":[188],"competitiveness":[189],"have":[194],"been":[195],"verified":[196],"by":[197],"experimental":[199],"studies.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}