{"id":"https://openalex.org/W2082572992","doi":"https://doi.org/10.1162/evco_a_00129","title":"Order-2 Stability Analysis of Particle Swarm Optimization","display_name":"Order-2 Stability Analysis of Particle Swarm Optimization","publication_year":2014,"publication_date":"2014-04-16","ids":{"openalex":"https://openalex.org/W2082572992","doi":"https://doi.org/10.1162/evco_a_00129","mag":"2082572992","pmid":"https://pubmed.ncbi.nlm.nih.gov/24738856"},"language":"en","primary_location":{"id":"doi:10.1162/evco_a_00129","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00129","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5028303789","display_name":"Qunfeng Liu","orcid":"https://orcid.org/0000-0002-6286-941X"},"institutions":[{"id":"https://openalex.org/I2799850029","display_name":"Dongguan University of Technology","ror":"https://ror.org/01m8p7q42","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799850029"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qunfeng Liu","raw_affiliation_strings":["College of Computing, Dongguan University of Technology, Dongguan, 523808, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computing, Dongguan University of Technology, Dongguan, 523808, China","institution_ids":["https://openalex.org/I2799850029"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028303789"],"corresponding_institution_ids":["https://openalex.org/I2799850029"],"apc_list":null,"apc_paid":null,"fwci":11.1829,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.98440119,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"23","issue":"2","first_page":"187","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.998199999332428,"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":0.998199999332428,"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":0.9818000197410583,"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/T13717","display_name":"Advanced Algorithms and Applications","score":0.9422000050544739,"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/stability","display_name":"Stability (learning theory)","score":0.8261206150054932},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.7514963150024414},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6105466485023499},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5268834233283997},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4706135392189026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46837860345840454},{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.4398885667324066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27768123149871826}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.8261206150054932},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.7514963150024414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6105466485023499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5268834233283997},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4706135392189026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46837860345840454},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.4398885667324066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27768123149871826},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/evco_a_00129","is_oa":false,"landing_page_url":"https://doi.org/10.1162/evco_a_00129","pdf_url":null,"source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},{"id":"pmid:24738856","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24738856","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321026","display_name":"Ministry of Earth Sciences","ror":"https://ror.org/013cf5k59"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W748368181","https://openalex.org/W972907206","https://openalex.org/W1628481780","https://openalex.org/W1875348914","https://openalex.org/W1926832021","https://openalex.org/W1969497412","https://openalex.org/W1986647846","https://openalex.org/W1994445384","https://openalex.org/W1996732238","https://openalex.org/W2012939405","https://openalex.org/W2016695533","https://openalex.org/W2057830724","https://openalex.org/W2067483921","https://openalex.org/W2081749411","https://openalex.org/W2109364787","https://openalex.org/W2110576630","https://openalex.org/W2111393363","https://openalex.org/W2125213524","https://openalex.org/W2127931254","https://openalex.org/W2162012556","https://openalex.org/W2165299997","https://openalex.org/W2169245194","https://openalex.org/W2169291847","https://openalex.org/W2187150571","https://openalex.org/W2543580944","https://openalex.org/W4285719527","https://openalex.org/W4299736415"],"related_works":["https://openalex.org/W2736680465","https://openalex.org/W4288714711","https://openalex.org/W3200708550","https://openalex.org/W2771637876","https://openalex.org/W4240853094","https://openalex.org/W4294093918","https://openalex.org/W2810496283","https://openalex.org/W3089879900","https://openalex.org/W2170656329","https://openalex.org/W2894847811"],"abstract_inverted_index":{"Several":[0,59],"stability":[1,23,34,49,72],"analyses":[2,62],"and":[3,19,52,73,89,109],"stable":[4,55,61,76,125],"regions":[5],"of":[6,17,22,35,48,71,97,133],"particle":[7],"swarm":[8],"optimization":[9],"(PSO)":[10],"have":[11],"been":[12],"proposed":[13,51],"before.":[14],"The":[15],"assumption":[16,85],"stagnation":[18,43,84],"different":[20],"definitions":[21,70,96],"are":[24,66,118],"adopted":[25],"in":[26],"these":[27,95],"analyses.":[28],"In":[29],"this":[30],"paper,":[31],"the":[32,74,82,106,123],"order-2":[33,54],"PSO":[36,65,134],"is":[37,50,57,79,86,100,127,135],"analyzed":[38],"based":[39],"on":[40],"a":[41],"weak":[42],"assumption.":[44],"A":[45,129],"new":[46,130],"definition":[47,104],"an":[53],"region":[56,126],"obtained.":[58],"existing":[60],"for":[63],"canonical":[64],"compared,":[67],"especially":[68],"their":[69],"corresponding":[75],"regions.":[77],"It":[78],"shown":[80,101,137],"that":[81,102,122],"classical":[83],"too":[87],"strict":[88],"not":[90],"necessary.":[91],"Moreover,":[92],"among":[93],"all":[94],"stability,":[98],"it":[99],"our":[103],"requires":[105],"weakest":[107],"conditions,":[108],"additional":[110],"conditions":[111],"bring":[112],"no":[113],"benefit.":[114],"Finally,":[115],"numerical":[116],"experiments":[117],"reported":[119],"to":[120,138],"show":[121],"obtained":[124],"meaningful.":[128],"parameter":[131,147],"combination":[132],"also":[136],"be":[139],"good,":[140],"even":[141],"better":[142],"than":[143],"some":[144],"known":[145],"best":[146],"combinations.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
