{"id":"https://openalex.org/W2044686528","doi":"https://doi.org/10.1155/2014/895629","title":"An Improved Central Force Optimization Algorithm for Multimodal Optimization","display_name":"An Improved Central Force Optimization Algorithm for Multimodal Optimization","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2044686528","doi":"https://doi.org/10.1155/2014/895629","mag":"2044686528"},"language":"en","primary_location":{"id":"doi:10.1155/2014/895629","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/895629","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/895629.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/895629.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101672754","display_name":"Jie Liu","orcid":"https://orcid.org/0000-0002-2504-7492"},"institutions":[{"id":"https://openalex.org/I110440473","display_name":"Xi'an University of Science and Technology","ror":"https://ror.org/046fkpt18","country_code":"CN","type":"education","lineage":["https://openalex.org/I110440473"]},{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Liu","raw_affiliation_strings":["College of Science, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China","School of Mathematics and Statistics, Xi\u2019dian University, Xi\u2019an 710071, China","School of Mathematics and Statistics, Xi'dian University, Xi'an 710071, China","College of Science, Xi'an University of Science and Technology, Xi'an 710054, China"],"affiliations":[{"raw_affiliation_string":"College of Science, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China","institution_ids":["https://openalex.org/I110440473"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019dian University, Xi\u2019an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'dian University, Xi'an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"College of Science, Xi'an University of Science and Technology, Xi'an 710054, China","institution_ids":["https://openalex.org/I110440473"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100339104","display_name":"Yuping Wang","orcid":"https://orcid.org/0000-0001-6868-0004"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-ping Wang","raw_affiliation_strings":["School of Computer, Xi\u2019dian University, Xi\u2019an 710071, China","School of Computer, Xi'dian University, Xi'an 710071, China"],"affiliations":[{"raw_affiliation_string":"School of Computer, Xi\u2019dian University, Xi\u2019an 710071, China","institution_ids":["https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Computer, Xi'dian University, Xi'an 710071, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101672754"],"corresponding_institution_ids":["https://openalex.org/I110440473","https://openalex.org/I149594827"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":3.3829,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.93068328,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"12"},"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9951000213623047,"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":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/imperialist-competitive-algorithm","display_name":"Imperialist competitive algorithm","score":0.7145755290985107},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6849258542060852},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.649550199508667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6221697330474854},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.6115937829017639},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5892305374145508},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5704579949378967},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5503584146499634},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5239934325218201},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5105262994766235},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.4927518665790558},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.4646007716655731},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.46100208163261414},{"id":"https://openalex.org/keywords/optimization-algorithm","display_name":"Optimization algorithm","score":0.44021520018577576},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4369584918022156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22664454579353333},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14688697457313538},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.12044921517372131}],"concepts":[{"id":"https://openalex.org/C101219045","wikidata":"https://www.wikidata.org/wiki/Q10859646","display_name":"Imperialist competitive algorithm","level":4,"score":0.7145755290985107},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6849258542060852},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.649550199508667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6221697330474854},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6115937829017639},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5892305374145508},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5704579949378967},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5503584146499634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5239934325218201},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5105262994766235},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.4927518665790558},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4646007716655731},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.46100208163261414},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.44021520018577576},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4369584918022156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22664454579353333},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14688697457313538},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.12044921517372131},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/895629","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/895629","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/895629.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425306085","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425306085","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:895629","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/895629.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:581b0e68a69b451cb2c1477dff046dce","is_oa":true,"landing_page_url":"https://doaj.org/article/581b0e68a69b451cb2c1477dff046dce","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/895629","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/895629","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/895629.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2644399335","display_name":null,"funder_award_id":"61272119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2660956991","display_name":null,"funder_award_id":"11226173","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G385937226","display_name":null,"funder_award_id":"11301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6802454936","display_name":null,"funder_award_id":"11301414","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","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/W2044686528.pdf","grobid_xml":"https://content.openalex.org/works/W2044686528.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1573125231","https://openalex.org/W1975162393","https://openalex.org/W1978740922","https://openalex.org/W1981024297","https://openalex.org/W1997600725","https://openalex.org/W2006566825","https://openalex.org/W2024060531","https://openalex.org/W2031014442","https://openalex.org/W2041629655","https://openalex.org/W2042647239","https://openalex.org/W2058709169","https://openalex.org/W2060203686","https://openalex.org/W2072955302","https://openalex.org/W2076422645","https://openalex.org/W2076670249","https://openalex.org/W2109116383","https://openalex.org/W2137514952","https://openalex.org/W2171074980","https://openalex.org/W2355503583","https://openalex.org/W2963042730"],"related_works":["https://openalex.org/W2185826091","https://openalex.org/W2048470382","https://openalex.org/W2477407501","https://openalex.org/W2384679317","https://openalex.org/W2911215968","https://openalex.org/W1570109187","https://openalex.org/W1583787753","https://openalex.org/W2491692165","https://openalex.org/W2366013513","https://openalex.org/W4244786412"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"the":[3,9,33,38,45,71,102],"hybrid":[4],"CSM-CFO":[5,23,72],"algorithm":[6,73,104],"based":[7],"on":[8],"simplex":[10],"method":[11],"(SM),":[12],"clustering":[13,55],"technique,":[14],"and":[15,44,51,57,68,81,94,107],"central":[16],"force":[17],"optimization":[18],"(CFO)":[19],"for":[20],"unconstrained":[21],"optimization.":[22],"is":[24,105],"still":[25],"a":[26],"deterministic":[27],"swarm":[28,90],"intelligent":[29],"algorithm,":[30],"such":[31],"that":[32,101],"complex":[34],"statistical":[35],"analysis":[36],"of":[37,79],"numerical":[39],"results":[40,99],"can":[41],"be":[42],"omitted,":[43],"convergence":[46,82],"intends":[47],"to":[48,85],"produce":[49],"faster":[50],"more":[52],"accurate":[53],"by":[54],"technique":[56],"good":[58],"points":[59],"set.":[60],"When":[61],"tested":[62],"against":[63],"benchmark":[64],"functions,":[65],"in":[66,77],"low":[67],"high":[69],"dimensions,":[70],"has":[74],"competitive":[75],"performance":[76],"terms":[78],"accuracy":[80],"speed":[83],"compared":[84],"other":[86],"evolutionary":[87,92],"algorithms:":[88],"particle":[89],"optimization,":[91],"program,":[93],"simulated":[95],"annealing.":[96],"The":[97],"comparison":[98],"demonstrate":[100],"proposed":[103],"effective":[106],"efficient.":[108]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}