{"id":"https://openalex.org/W2130482553","doi":"https://doi.org/10.1109/acc.2009.5160341","title":"Stability and l&lt;sup&gt;2&lt;/sup&gt; gain analysis for the particle swarm optimization algorithm","display_name":"Stability and l&lt;sup&gt;2&lt;/sup&gt; gain analysis for the particle swarm optimization algorithm","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2130482553","doi":"https://doi.org/10.1109/acc.2009.5160341","mag":"2130482553"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2009.5160341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-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/A5023926564","display_name":"Yuji Wakasa","orcid":"https://orcid.org/0000-0002-6586-2889"},"institutions":[{"id":"https://openalex.org/I173915773","display_name":"Yamaguchi University","ror":"https://ror.org/03cxys317","country_code":"JP","type":"education","lineage":["https://openalex.org/I173915773"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuji Wakasa","raw_affiliation_strings":["Science and Engineering, Yamaguchi University, Yamaguchi, Japan","Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science and Engineering, Yamaguchi University, Yamaguchi, Japan","institution_ids":["https://openalex.org/I173915773"]},{"raw_affiliation_string":"Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan","institution_ids":["https://openalex.org/I173915773"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103642723","display_name":"Kanya Tanaka","orcid":null},"institutions":[{"id":"https://openalex.org/I173915773","display_name":"Yamaguchi University","ror":"https://ror.org/03cxys317","country_code":"JP","type":"education","lineage":["https://openalex.org/I173915773"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kanya Tanaka","raw_affiliation_strings":["Science and Engineering, Yamaguchi University, Yamaguchi, Japan","Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science and Engineering, Yamaguchi University, Yamaguchi, Japan","institution_ids":["https://openalex.org/I173915773"]},{"raw_affiliation_string":"Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan","institution_ids":["https://openalex.org/I173915773"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045648943","display_name":"Takuya Akashi","orcid":"https://orcid.org/0000-0001-9177-7306"},"institutions":[{"id":"https://openalex.org/I173915773","display_name":"Yamaguchi University","ror":"https://ror.org/03cxys317","country_code":"JP","type":"education","lineage":["https://openalex.org/I173915773"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takuya Akashi","raw_affiliation_strings":["Science and Engineering, Yamaguchi University, Yamaguchi, Japan","Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science and Engineering, Yamaguchi University, Yamaguchi, Japan","institution_ids":["https://openalex.org/I173915773"]},{"raw_affiliation_string":"Graduate School of Science and Engineering Yamaguchi University 2\u201016\u20101 Tokiwadai Ube 755\u20108611 Japan","institution_ids":["https://openalex.org/I173915773"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9059,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81597029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"3","issue":null,"first_page":"1748","last_page":"1753"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9919999837875366,"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":0.9919999837875366,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12676","display_name":"Machine Learning and ELM","score":0.9851999878883362,"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/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.684485912322998},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6428405046463013},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6354824900627136},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5624091029167175},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48354434967041016},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.444691002368927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4405449628829956},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3767523169517517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3714313805103302},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3473520278930664},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07921895384788513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06950092315673828}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.684485912322998},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6428405046463013},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6354824900627136},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5624091029167175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48354434967041016},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.444691002368927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4405449628829956},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3767523169517517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3714313805103302},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3473520278930664},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07921895384788513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06950092315673828},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2009.5160341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2016695533","https://openalex.org/W2048458482","https://openalex.org/W2081749411","https://openalex.org/W2124910095","https://openalex.org/W2141249818","https://openalex.org/W2152195021","https://openalex.org/W2171770308","https://openalex.org/W2402846924","https://openalex.org/W3210839039"],"related_works":["https://openalex.org/W3019402777","https://openalex.org/W2031835531","https://openalex.org/W2388590088","https://openalex.org/W4386596916","https://openalex.org/W1969166468","https://openalex.org/W2097519318","https://openalex.org/W2116377213","https://openalex.org/W2122371747","https://openalex.org/W2069224524","https://openalex.org/W2378894046"],"abstract_inverted_index":{"Stability":[0],"of":[1,23,40,58,68,76,81],"the":[2,15,20,24,26,36,41,52,59,69,77,82,118,127,130],"particle":[3],"swarm":[4],"optimization":[5,109],"algorithm":[6,60],"is":[7,29,44,48,88],"analyzed":[8],"without":[9],"any":[10],"simplifying":[11],"assumptions":[12],"made":[13],"in":[14,129],"previous":[16],"works.":[17],"To":[18],"evaluate":[19],"convergence":[21],"speed":[22],"algorithm,":[25,70],"decay":[27,42],"rate":[28,43],"introduced,":[30],"and":[31,71,100,123],"a":[32,72],"method":[33,73],"for":[34,74],"finding":[35,75],"largest":[37],"lower":[38],"bound":[39,80],"presented.":[45],"Moreover,":[46],"it":[47],"pointed":[49],"out":[50,104],"that":[51,117],"l":[53,83],"<sup":[54,84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[55,85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[56,86],"gain":[57,87],"can":[61],"be":[62],"used":[63],"to":[64,115,125],"measure":[65],"exploration":[66],"ability":[67],"smallest":[78],"upper":[79],"provided.":[89],"The":[90],"above":[91],"methods":[92,120],"are":[93,102,113,121],"based":[94],"on":[95],"linear":[96],"matrix":[97],"inequality":[98],"techniques":[99],"therefore":[101],"carried":[103],"efficiently":[105],"by":[106],"using":[107],"convex":[108],"tools.":[110],"Numerical":[111],"examples":[112],"given":[114],"show":[116],"analysis":[119],"reasonable":[122],"effective":[124],"select":[126],"parameters":[128],"algorithm.":[131]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
