{"id":"https://openalex.org/W2782264238","doi":"https://doi.org/10.1142/s0217595918400067","title":"Particle Swarm Optimization for Split Delivery Vehicle Routing Problem","display_name":"Particle Swarm Optimization for Split Delivery Vehicle Routing Problem","publication_year":2018,"publication_date":"2018-01-08","ids":{"openalex":"https://openalex.org/W2782264238","doi":"https://doi.org/10.1142/s0217595918400067","mag":"2782264238"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595918400067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595918400067","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-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/A5068545072","display_name":"Jianli Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianli Shi","raw_affiliation_strings":["National United Engineering Laboratory, of Integrated and Intelligent Transportation, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China"],"affiliations":[{"raw_affiliation_string":"National United Engineering Laboratory, of Integrated and Intelligent Transportation, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","institution_ids":["https://openalex.org/I4800084"]},{"raw_affiliation_string":"School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100717976","display_name":"Jin Zhang","orcid":"https://orcid.org/0000-0002-4161-7694"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Zhang","raw_affiliation_strings":["National United Engineering Laboratory, of Integrated and Intelligent Transportation, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China"],"affiliations":[{"raw_affiliation_string":"National United Engineering Laboratory, of Integrated and Intelligent Transportation, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","institution_ids":["https://openalex.org/I4800084"]},{"raw_affiliation_string":"School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050253183","display_name":"Kun Wang","orcid":"https://orcid.org/0000-0001-7461-4126"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Wang","raw_affiliation_strings":["School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Transportation and Logistics, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, P. R. China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062618665","display_name":"Xin Fang","orcid":"https://orcid.org/0000-0001-7449-972X"},"institutions":[{"id":"https://openalex.org/I145581781","display_name":"Chongqing Technology and Business University","ror":"https://ror.org/05hqf1284","country_code":"CN","type":"education","lineage":["https://openalex.org/I145581781"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Fang","raw_affiliation_strings":["Chongqing Engineering Research Center for Processing, Storage and Transportation of Characterized, Agro-Products, Chongqing 400067, P. R. China","School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, P. R. China","Chongqing Engineering Research Center for Processing, Storage and Transportation of Characterized, Agro-Products, Chongqing 400067, P. R. China; School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, P. R. China"],"affiliations":[{"raw_affiliation_string":"Chongqing Engineering Research Center for Processing, Storage and Transportation of Characterized, Agro-Products, Chongqing 400067, P. R. China","institution_ids":[]},{"raw_affiliation_string":"School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, P. R. China","institution_ids":["https://openalex.org/I145581781"]},{"raw_affiliation_string":"Chongqing Engineering Research Center for Processing, Storage and Transportation of Characterized, Agro-Products, Chongqing 400067, P. R. China; School of Business Planning, Chongqing Technology and Business University, Chongqing 400067, P. R. China","institution_ids":["https://openalex.org/I145581781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068545072"],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":null,"apc_paid":null,"fwci":3.4488,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.93165722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"35","issue":"02","first_page":"1840006","last_page":"1840006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9926000237464905,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9890999794006348,"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":0.6909351348876953},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.6730395555496216},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6229453086853027},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5926721096038818},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.5542588829994202},{"id":"https://openalex.org/keywords/local-search","display_name":"Local search (optimization)","score":0.54599928855896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4891860783100128},{"id":"https://openalex.org/keywords/multi-swarm-optimization","display_name":"Multi-swarm optimization","score":0.45526957511901855},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4445037841796875},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42235130071640015},{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.4105965495109558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38124343752861023},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.3391258120536804}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6909351348876953},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.6730395555496216},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6229453086853027},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5926721096038818},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.5542588829994202},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.54599928855896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4891860783100128},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.45526957511901855},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4445037841796875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42235130071640015},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.4105965495109558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38124343752861023},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.3391258120536804},{"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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0217595918400067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595918400067","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:35:y:2018:i:02:n:s0217595918400067","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595918400067","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322720","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693"},{"id":"https://openalex.org/F4320323711","display_name":"Southwest University","ror":"https://ror.org/01kj4z117"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W623775400","https://openalex.org/W758506392","https://openalex.org/W1486184140","https://openalex.org/W1786863823","https://openalex.org/W1823723575","https://openalex.org/W1965840388","https://openalex.org/W1973494611","https://openalex.org/W1980661488","https://openalex.org/W1985662483","https://openalex.org/W1988242784","https://openalex.org/W1988345713","https://openalex.org/W1992913497","https://openalex.org/W1995719137","https://openalex.org/W1996764736","https://openalex.org/W2004358347","https://openalex.org/W2005944398","https://openalex.org/W2007423183","https://openalex.org/W2010659373","https://openalex.org/W2010778845","https://openalex.org/W2012877079","https://openalex.org/W2015024633","https://openalex.org/W2019774836","https://openalex.org/W2025294647","https://openalex.org/W2030293819","https://openalex.org/W2032004016","https://openalex.org/W2038172102","https://openalex.org/W2044308184","https://openalex.org/W2050133090","https://openalex.org/W2052172017","https://openalex.org/W2057532434","https://openalex.org/W2058463120","https://openalex.org/W2060264904","https://openalex.org/W2065962145","https://openalex.org/W2072128752","https://openalex.org/W2073292534","https://openalex.org/W2075355110","https://openalex.org/W2078227935","https://openalex.org/W2085984717","https://openalex.org/W2093709925","https://openalex.org/W2096305430","https://openalex.org/W2098090443","https://openalex.org/W2107544139","https://openalex.org/W2119365694","https://openalex.org/W2131338629","https://openalex.org/W2139339670","https://openalex.org/W2146547098","https://openalex.org/W2154418786","https://openalex.org/W2158354221","https://openalex.org/W2165515547","https://openalex.org/W2275381519","https://openalex.org/W2323143314","https://openalex.org/W2560154459","https://openalex.org/W2560684347","https://openalex.org/W2591833818","https://openalex.org/W2596402009"],"related_works":["https://openalex.org/W2965421953","https://openalex.org/W2349895019","https://openalex.org/W2950423922","https://openalex.org/W2116074880","https://openalex.org/W2070977815","https://openalex.org/W2137136732","https://openalex.org/W2132113279","https://openalex.org/W2368795850","https://openalex.org/W2972744589","https://openalex.org/W2031835531"],"abstract_inverted_index":{"The":[0,124,172],"split":[1],"delivery":[2],"vehicle":[3,13],"routing":[4,14],"problem":[5,15],"(SDVRP)":[6],"is":[7],"a":[8,31,38,52,121,202],"variation":[9],"of":[10,73,100,146,155,199,205],"the":[11,43,62,68,71,74,77,80,85,91,109,112,130,136,140,144,147,149,153,156,170],"capacitated":[12],"in":[16,70,169,184,192],"which":[17],"some":[18],"customers":[19],"may":[20],"be":[21],"served":[22],"by":[23],"more":[24],"than":[25],"one":[26],"vehicle.":[27],"We":[28],"have":[29],"proposed":[30],"particle":[32],"swarm":[33],"optimization":[34],"approach":[35],"that":[36],"incorporates":[37],"local":[39,86,101,141],"search":[40,142],"to":[41,66,114,134],"solve":[42],"SDVRP.":[44,63],"An":[45],"integer":[46],"coding":[47],"method":[48,54],"was":[49,59,96,126],"presented,":[50],"and":[51,90,152,187,201],"decoding":[53],"based":[55],"on":[56,120,164],"Bellman\u2019s":[57],"equation":[58,151],"modified":[60,131],"for":[61,103],"A":[64],"way":[65],"address":[67],"differences":[69],"length":[72,154],"velocity":[75,150],"vector,":[76,79,84],"position":[78,83,88,94],"personal":[81],"best":[82,87,93],"vector":[89,95],"global":[92],"designed.":[97],"Two":[98],"groups":[99],"searches":[102],"top":[104],"solutions":[105,181,189],"were":[106,161,175,182,190],"incorporated":[107],"into":[108],"algorithm,":[110],"with":[111,195],"ability":[113],"control":[115],"whether":[116],"they":[117],"are":[118],"executed":[119],"given":[122],"solution.":[123],"algorithm":[125],"initially":[127],"tested":[128],"using":[129],"Solomon\u2019s":[132],"instances":[133,167],"verify":[135],"parameters":[137],"used,":[138],"including":[139],"probability,":[143],"size":[145],"swarm,":[148],"vectors.":[157],"Extensive":[158],"computational":[159],"experiments":[160],"carried":[162],"out":[163],"131":[165],"benchmark":[166],"available":[168],"literature.":[171],"results":[173],"obtained":[174],"competitive.":[176],"More":[177],"precisely,":[178],"equally":[179],"good":[180],"found":[183,191],"32":[185],"instances,":[186,194],"improved":[188],"35":[193],"an":[196],"average":[197],"improvement":[198,204],"0.02%":[200],"maximum":[203],"1.12%.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
