{"id":"https://openalex.org/W3033048642","doi":"https://doi.org/10.3390/sym12060922","title":"A Hybrid Multi-Step Probability Selection Particle Swarm Optimization with Dynamic Chaotic Inertial Weight and Acceleration Coefficients for Numerical Function Optimization","display_name":"A Hybrid Multi-Step Probability Selection Particle Swarm Optimization with Dynamic Chaotic Inertial Weight and Acceleration Coefficients for Numerical Function Optimization","publication_year":2020,"publication_date":"2020-06-02","ids":{"openalex":"https://openalex.org/W3033048642","doi":"https://doi.org/10.3390/sym12060922","mag":"3033048642"},"language":"en","primary_location":{"id":"doi:10.3390/sym12060922","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060922","pdf_url":"https://www.mdpi.com/2073-8994/12/6/922/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/6/922/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015469624","display_name":"Yuji Du","orcid":"https://orcid.org/0000-0002-8016-0615"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuji Du","raw_affiliation_strings":["School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China"],"raw_orcid":"https://orcid.org/0000-0002-8016-0615","affiliations":[{"raw_affiliation_string":"School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100931014","display_name":"Fanfan Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanfan Xu","raw_affiliation_strings":["School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015469624"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.1759,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.90106069,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"6","first_page":"922","last_page":"922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9902999997138977,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9839000105857849,"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":0.666357696056366},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6159892082214355},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5959457159042358},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5372294187545776},{"id":"https://openalex.org/keywords/local-optimum","display_name":"Local optimum","score":0.5300671458244324},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.5142638087272644},{"id":"https://openalex.org/keywords/premature-convergence","display_name":"Premature convergence","score":0.5027680397033691},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.42234060168266296},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.4206920862197876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41209039092063904},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3774676024913788},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3421575427055359},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11035940051078796}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.666357696056366},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6159892082214355},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5959457159042358},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5372294187545776},{"id":"https://openalex.org/C141934464","wikidata":"https://www.wikidata.org/wiki/Q3305386","display_name":"Local optimum","level":2,"score":0.5300671458244324},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.5142638087272644},{"id":"https://openalex.org/C58758708","wikidata":"https://www.wikidata.org/wiki/Q7240233","display_name":"Premature convergence","level":3,"score":0.5027680397033691},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.42234060168266296},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4206920862197876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41209039092063904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3774676024913788},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3421575427055359},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11035940051078796},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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":3,"locations":[{"id":"doi:10.3390/sym12060922","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060922","pdf_url":"https://www.mdpi.com/2073-8994/12/6/922/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7cfef1fb5b624de6972cbc93ae41b496","is_oa":true,"landing_page_url":"https://doaj.org/article/7cfef1fb5b624de6972cbc93ae41b496","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 6, p 922 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/6/922/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12060922","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12060922","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060922","pdf_url":"https://www.mdpi.com/2073-8994/12/6/922/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033048642.pdf","grobid_xml":"https://content.openalex.org/works/W3033048642.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W653600130","https://openalex.org/W883434633","https://openalex.org/W1965969360","https://openalex.org/W1985460844","https://openalex.org/W1988482440","https://openalex.org/W1988698908","https://openalex.org/W1993163461","https://openalex.org/W1997190837","https://openalex.org/W2001979953","https://openalex.org/W2002469548","https://openalex.org/W2003961265","https://openalex.org/W2014760270","https://openalex.org/W2023058330","https://openalex.org/W2030029918","https://openalex.org/W2039148220","https://openalex.org/W2042174016","https://openalex.org/W2061438946","https://openalex.org/W2062355752","https://openalex.org/W2072955302","https://openalex.org/W2082324245","https://openalex.org/W2094859983","https://openalex.org/W2104324382","https://openalex.org/W2108270451","https://openalex.org/W2131613989","https://openalex.org/W2145617041","https://openalex.org/W2146171723","https://openalex.org/W2154808242","https://openalex.org/W2168081761","https://openalex.org/W2183843206","https://openalex.org/W2187150571","https://openalex.org/W2232317135","https://openalex.org/W2282226143","https://openalex.org/W2290883490","https://openalex.org/W2310612427","https://openalex.org/W2366573627","https://openalex.org/W2376578267","https://openalex.org/W2377148279","https://openalex.org/W2464587182","https://openalex.org/W2543580944","https://openalex.org/W2554957650","https://openalex.org/W2562463731","https://openalex.org/W2575779996","https://openalex.org/W2763523016","https://openalex.org/W2763907376","https://openalex.org/W2770261335","https://openalex.org/W2783313081","https://openalex.org/W2888506210","https://openalex.org/W2890810619","https://openalex.org/W2895647709","https://openalex.org/W2913003339","https://openalex.org/W2966421640","https://openalex.org/W2971810584","https://openalex.org/W2972333064","https://openalex.org/W2977797706","https://openalex.org/W6658204478","https://openalex.org/W6674420161","https://openalex.org/W6676554820","https://openalex.org/W6682642761","https://openalex.org/W6684237752","https://openalex.org/W6685625979","https://openalex.org/W7024750964"],"related_works":["https://openalex.org/W42170614","https://openalex.org/W2364947648","https://openalex.org/W1934426788","https://openalex.org/W2568269143","https://openalex.org/W2379567910","https://openalex.org/W1959298326","https://openalex.org/W2391178530","https://openalex.org/W2568341866","https://openalex.org/W2998284541","https://openalex.org/W1991387858"],"abstract_inverted_index":{"As":[0],"a":[1,13,31,47,76,82,93,108,214],"meta-heuristic":[2],"algoriTthm,":[3],"particle":[4,52],"swarm":[5,53,161],"optimization":[6,54,199,210,222],"(PSO)":[7],"has":[8,194],"the":[9,35,70,102,122,125,151,157,160,171,174,191],"advantages":[10],"of":[11,38,73,124,159,173,216],"having":[12],"simple":[14],"principle,":[15],"few":[16],"required":[17],"parameters,":[18],"easy":[19,27],"realization":[20],"and":[21,60,96,115,134,144,201,212,220],"strong":[22],"adaptability.":[23],"However,":[24],"it":[25],"is":[26,205],"to":[28,75,100,106,119,162,165],"fall":[29],"into":[30,150],"local":[32,116],"optimum":[33],"in":[34,207],"early":[36],"stage":[37],"iteration.":[39],"Aiming":[40],"at":[41],"this":[42,44],"shortcoming,":[43],"paper":[45],"presents":[46],"hybrid":[48,83],"multi-step":[49,84,94],"probability":[50,85],"selection":[51,86,99],"with":[55,181],"sine":[56,130],"chaotic":[57,63,131,137],"inertial":[58,132],"weight":[59,133],"symmetric":[61,135],"tangent":[62,136],"acceleration":[64,138],"coefficients":[65,139],"(MPSPSO-ST),":[66],"which":[67,90,147,204],"can":[68],"strengthen":[69],"overall":[71],"performance":[72,123],"PSO":[74,218],"large":[77],"extent.":[78],"Firstly,":[79],"we":[80,127,177],"propose":[81],"update":[87],"mechanism":[88,143],"(MPSPSO),":[89],"skillfully":[91],"uses":[92],"process":[95],"roulette":[97],"wheel":[98],"improve":[101],"performance.":[103],"In":[104],"order":[105],"achieve":[107],"good":[109],"balance":[110],"between":[111],"global":[112],"search":[113,117],"capability":[114,118],"further":[120],"enhance":[121],"method,":[126],"also":[128],"design":[129],"inspired":[140],"by":[141],"chaos":[142],"trigonometric":[145],"functions,":[146],"are":[148],"integrated":[149],"MPSPSO-ST":[152,175,192],"algorithm.":[153],"This":[154],"strategy":[155],"enables":[156],"diversity":[158],"be":[163],"preserved":[164],"discourage":[166],"premature":[167],"convergence.":[168],"To":[169],"evaluate":[170],"effectiveness":[172],"algorithm,":[176],"conducted":[178],"extensive":[179],"experiments":[180],"20":[182],"classic":[183],"benchmark":[184],"functions.":[185],"The":[186],"experimental":[187],"results":[188],"show":[189],"that":[190],"algorithm":[193],"faster":[195],"convergence":[196],"speed,":[197],"higher":[198],"accuracy":[200],"better":[202],"robustness,":[203],"competitive":[206],"solving":[208],"numerical":[209],"problems":[211],"outperforms":[213],"lot":[215],"classical":[217],"variants":[219],"well-known":[221],"algorithms.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
