{"id":"https://openalex.org/W1936306293","doi":"https://doi.org/10.3233/fi-2010-370","title":"A Convergence Proof for the Particle Swarm Optimiser","display_name":"A Convergence Proof for the Particle Swarm Optimiser","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1936306293","doi":"https://doi.org/10.3233/fi-2010-370","mag":"1936306293"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2010-370","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-370","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5047714792","display_name":"F. van den Bergh","orcid":"https://orcid.org/0000-0002-4935-514X"},"institutions":[{"id":"https://openalex.org/I66760702","display_name":"Council of Scientific and Industrial Research","ror":"https://ror.org/021wm7p51","country_code":"IN","type":"government","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I66760702"]},{"id":"https://openalex.org/I21360634","display_name":"Council for Scientific and Industrial Research","ror":"https://ror.org/05j00sr48","country_code":"ZA","type":"funder","lineage":["https://openalex.org/I21360634"]}],"countries":["IN","ZA"],"is_corresponding":true,"raw_author_name":"Frans van den Bergh","raw_affiliation_strings":["CSIR, Meiring Naude Road, Pretoria, South Africa. fvdbergh@csir.co.za","CSIR, Meiring Naude Road, Pretoria, South Africa. fvdbergh@csir.co.za#TAB#"],"affiliations":[{"raw_affiliation_string":"CSIR, Meiring Naude Road, Pretoria, South Africa. fvdbergh@csir.co.za","institution_ids":["https://openalex.org/I21360634"]},{"raw_affiliation_string":"CSIR, Meiring Naude Road, Pretoria, South Africa. fvdbergh@csir.co.za#TAB#","institution_ids":["https://openalex.org/I66760702"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039197997","display_name":"Andries P. Engelbrecht","orcid":"https://orcid.org/0000-0002-0242-3539"},"institutions":[{"id":"https://openalex.org/I69552723","display_name":"University of Pretoria","ror":"https://ror.org/00g0p6g84","country_code":"ZA","type":"education","lineage":["https://openalex.org/I69552723"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Andries Petrus Engelbrecht","raw_affiliation_strings":["Department of Computer Science, University of Pretoria, Pretoria, South Africa. engel@cs.up.ac.za","(Correspd.) Department of Computer Science, University of Pretoria, Pretoria, South Africa. engel@cs.up.ac.za#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Pretoria, Pretoria, South Africa. engel@cs.up.ac.za","institution_ids":["https://openalex.org/I69552723"]},{"raw_affiliation_string":"(Correspd.) Department of Computer Science, University of Pretoria, Pretoria, South Africa. engel@cs.up.ac.za#TAB#","institution_ids":["https://openalex.org/I69552723"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047714792"],"corresponding_institution_ids":["https://openalex.org/I21360634","https://openalex.org/I66760702"],"apc_list":null,"apc_paid":null,"fwci":2.3274,"has_fulltext":false,"cited_by_count":137,"citation_normalized_percentile":{"value":0.89046608,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"105","issue":"4","first_page":"341","last_page":"374"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9993000030517578,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9677000045776367,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12391","display_name":"Artificial Immune Systems Applications","score":0.9538000226020813,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/convergence","display_name":"Convergence (economics)","score":0.5526828169822693},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5067694783210754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4052082896232605},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08184897899627686}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5526828169822693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5067694783210754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4052082896232605},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08184897899627686},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/fi-2010-370","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2010-370","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:repository.up.ac.za:2263/17262","is_oa":false,"landing_page_url":"http://hdl.handle.net/2263/17262","pdf_url":null,"source":{"id":"https://openalex.org/S4306401870","display_name":"UpSpace Institutional Repository (University of Pretoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I69552723","host_organization_name":"University of Pretoria","host_organization_lineage":["https://openalex.org/I69552723"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Postprint Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W129833132","https://openalex.org/W1492990133","https://openalex.org/W1555689267","https://openalex.org/W1577668191","https://openalex.org/W1628481780","https://openalex.org/W1848294875","https://openalex.org/W1875348914","https://openalex.org/W1907706552","https://openalex.org/W2080603568","https://openalex.org/W2081749411","https://openalex.org/W2106625051","https://openalex.org/W2107771236","https://openalex.org/W2109364787","https://openalex.org/W2110576630","https://openalex.org/W2111393363","https://openalex.org/W2117595234","https://openalex.org/W2118840131","https://openalex.org/W2123859926","https://openalex.org/W2135232426","https://openalex.org/W2145113795","https://openalex.org/W2152195021","https://openalex.org/W2165299997","https://openalex.org/W2169245194","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"The":[0],"Particle":[1],"Swarm":[2],"Optimiser":[3],"(PSO)":[4],"is":[5,45],"a":[6,22,36,59,66],"population":[7],"based":[8],"stochastic":[9],"optimisation":[10],"algorithm,":[11],"empirically":[12],"shown":[13],"to":[14,24,35,65,82],"be":[15],"efficient":[16],"and":[17],"robust.":[18],"This":[19],"paper":[20],"provides":[21],"proof":[23],"show":[25],"that":[26],"the":[27,42,51,84,87],"original":[28,43],"PSO":[29,44,60,89,93],"does":[30],"not":[31],"have":[32],"guaranteed":[33,63],"convergence":[34,64,74],"local":[37,67],"optimum.":[38],"A":[39],"flaw":[40,56],"in":[41,58],"identified":[46],"which":[47],"causes":[48],"stagnation":[49],"of":[50,54,86],"swarm.":[52],"Correction":[53],"this":[55],"results":[57,79],"algorithm":[61],"with":[62,71,95],"minimum.":[68],"Further":[69],"extensions":[70],"provable":[72],"global":[73,96],"are":[75,80],"also":[76],"described.":[77],"Experimental":[78],"provided":[81],"elucidate":[83],"behavior":[85],"modified":[88],"as":[90,92],"well":[91],"variations":[94],"convergence.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}