{"id":"https://openalex.org/W2797770583","doi":"https://doi.org/10.1155/2018/5036791","title":"Legendre Cooperative PSO Strategies for Trajectory Optimization","display_name":"Legendre Cooperative PSO Strategies for Trajectory Optimization","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2797770583","doi":"https://doi.org/10.1155/2018/5036791","mag":"2797770583"},"language":"en","primary_location":{"id":"doi:10.1155/2018/5036791","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/5036791","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/5036791.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2018/5036791.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100630376","display_name":"Lei Liu","orcid":"https://orcid.org/0000-0003-3606-122X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Liu","raw_affiliation_strings":["National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064567218","display_name":"Yongji Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongji Wang","raw_affiliation_strings":["National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079472841","display_name":"Fuqiang Xie","orcid":"https://orcid.org/0000-0002-3697-9447"},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuqiang Xie","raw_affiliation_strings":["School of Electric Engineering, University of South China, Hengyang, Hunan, China","School of Electric Engineering, University of South China, Hengyang, Hunan"],"affiliations":[{"raw_affiliation_string":"School of Electric Engineering, University of South China, Hengyang, Hunan, China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"School of Electric Engineering, University of South China, Hengyang, Hunan","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016887525","display_name":"Jiashi Gao","orcid":"https://orcid.org/0000-0003-3224-2402"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiashi Gao","raw_affiliation_strings":["National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan 430074","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064567218"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":2.0308,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89739247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9973000288009644,"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":0.9973000288009644,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9546999931335449,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.6293321847915649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6048133969306946},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5892040133476257},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.5381385684013367},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5350488424301147},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5033628344535828},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48559731245040894},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4775888919830322},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.4684925973415375},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.45441779494285583},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3931345045566559},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3530037999153137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33686771988868713},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3303292393684387},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0701768696308136}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6293321847915649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6048133969306946},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5892040133476257},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.5381385684013367},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5350488424301147},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5033628344535828},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48559731245040894},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4775888919830322},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.4684925973415375},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.45441779494285583},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3931345045566559},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3530037999153137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33686771988868713},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3303292393684387},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0701768696308136},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2018/5036791","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/5036791","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/5036791.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:5036791","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2018/5036791.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:d65b9d4fc717491eab01b459265c0811","is_oa":true,"landing_page_url":"https://doaj.org/article/d65b9d4fc717491eab01b459265c0811","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":"Complexity, Vol 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/5036791","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/5036791","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/5036791.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","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/G4318803108","display_name":null,"funder_award_id":"61473124","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/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8208342437","display_name":null,"funder_award_id":"1 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8479992263","display_name":null,"funder_award_id":"61573161","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2797770583.pdf","grobid_xml":"https://content.openalex.org/works/W2797770583.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1970493066","https://openalex.org/W1993626705","https://openalex.org/W1994925753","https://openalex.org/W2057741810","https://openalex.org/W2107128843","https://openalex.org/W2107886654","https://openalex.org/W2122107228","https://openalex.org/W2170307083","https://openalex.org/W2187015862","https://openalex.org/W2213788783","https://openalex.org/W2272748290","https://openalex.org/W2339398450","https://openalex.org/W2396774882","https://openalex.org/W2400328397","https://openalex.org/W2567327143","https://openalex.org/W2767504573","https://openalex.org/W2775562345","https://openalex.org/W3098955026"],"related_works":["https://openalex.org/W2736737644","https://openalex.org/W2385225694","https://openalex.org/W1607269076","https://openalex.org/W2393022482","https://openalex.org/W2377346130","https://openalex.org/W2374325362","https://openalex.org/W2024044475","https://openalex.org/W2053137424","https://openalex.org/W2003479292","https://openalex.org/W3135469233"],"abstract_inverted_index":{"Particle":[0],"swarm":[1],"optimization":[2,8,21,144],"(PSO)":[3],"is":[4,42,54,70,94,126],"a":[5,11,17,48,87,113],"population\u2010based":[6],"stochastic":[7],"technique":[9],"in":[10,16,131],"smooth":[12],"search":[13,92],"space.":[14],"However,":[15],"category":[18],"of":[19,33,62,110,121,124,154,159],"trajectory":[20],"problem":[22,77],"with":[23,78,136],"arbitrary":[24,79],"final":[25,80],"time":[26,81],"and":[27,107,128,140,147,161],"multiple":[28],"control":[29,68,100,167],"variables,":[30],"the":[31,39,46,63,74,83,98,105,111,119,122,132,137,149],"smoothness":[32],"variables":[34],"cannot":[35],"be":[36],"satisfied":[37],"since":[38],"linear":[40,64],"interpolation":[41],"widely":[43],"used.":[44],"In":[45],"paper,":[47],"novel":[49],"Legendre":[50,58],"cooperative":[51],"PSO":[52,139],"(LCPSO)":[53],"proposed":[55,150],"by":[56],"introducing":[57],"orthogonal":[59],"polynomials":[60,125],"instead":[61],"interpolation.":[65],"An":[66],"additional":[67,99],"variable":[69],"introduced":[71],"to":[72,82,96,103,117],"transcribe":[73],"original":[75],"optimal":[76],"fixed":[84],"one.":[85],"Then,":[86],"practical":[88],"fast":[89],"one\u2010dimensional":[90],"interval":[91],"algorithm":[93],"designed":[95],"optimize":[97],"variable.":[101],"Furthermore,":[102],"improve":[104],"convergence":[106],"prevent":[108],"explosion":[109],"LCPSO,":[112],"theorem":[114],"on":[115],"how":[116],"determine":[118],"boundaries":[120],"coefficient":[123],"given":[127],"proven.":[129],"Finally,":[130],"numeral":[133],"simulations,":[134],"compared":[135],"ordinary":[138],"other":[141],"typical":[142],"intelligent":[143],"algorithms":[145],"GA":[146],"DE,":[148],"LCPSO":[151],"has":[152],"traits":[153],"lower":[155],"dimension,":[156],"faster":[157],"speed":[158],"convergence,":[160],"higher":[162],"accuracy,":[163],"while":[164],"providing":[165],"smoother":[166],"variables.":[168]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}