{"id":"https://openalex.org/W4390467729","doi":"https://doi.org/10.3390/axioms13010031","title":"Optimization of Location-Routing for Multi-Vehicle Combinations with Capacity Constraints Based on Binary Equilibrium Optimizers","display_name":"Optimization of Location-Routing for Multi-Vehicle Combinations with Capacity Constraints Based on Binary Equilibrium Optimizers","publication_year":2023,"publication_date":"2023-12-31","ids":{"openalex":"https://openalex.org/W4390467729","doi":"https://doi.org/10.3390/axioms13010031"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13010031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010031","pdf_url":"https://www.mdpi.com/2075-1680/13/1/31/pdf?version=1704010400","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/1/31/pdf?version=1704010400","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101843329","display_name":"Rui Xi","orcid":"https://orcid.org/0009-0008-1764-2006"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Xi","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":"https://orcid.org/0009-0008-1764-2006","affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057836644","display_name":"Danju Lv","orcid":"https://orcid.org/0000-0002-8412-6406"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Danju Lv","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037959263","display_name":"Yueyun Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yueyun Yu","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005663125","display_name":"Huang Xin","orcid":"https://orcid.org/0000-0002-7535-8803"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Huang","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":"https://orcid.org/0000-0002-7535-8803","affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100332224","display_name":"Ziqian Wang","orcid":"https://orcid.org/0000-0002-0282-5941"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziqian Wang","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027054602","display_name":"Lianglian Gu","orcid":null},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lianglian Gu","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016257287","display_name":"Zhicheng Zhu","orcid":"https://orcid.org/0000-0001-5297-2651"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhicheng Zhu","raw_affiliation_strings":["College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Big Data and Intelligent Engineering, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100456255","display_name":"Yan Zhang","orcid":"https://orcid.org/0000-0002-4915-2836"},"institutions":[{"id":"https://openalex.org/I25399270","display_name":"Southwest Forestry University","ror":"https://ror.org/03dfa9f06","country_code":"CN","type":"education","lineage":["https://openalex.org/I25399270"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Zhang","raw_affiliation_strings":["College of Mathematics and Physics, Southwest Forestry University, Kunming 650224, China","College of Mathematics and Physics, Southwest Forestry University, Kunming 650224, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Southwest Forestry University, Kunming 650224, China","institution_ids":["https://openalex.org/I25399270"]},{"raw_affiliation_string":"College of Mathematics and Physics, Southwest Forestry University, Kunming 650224, China;","institution_ids":["https://openalex.org/I25399270"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057836644"],"corresponding_institution_ids":["https://openalex.org/I25399270"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1765,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5988112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"1","first_page":"31","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9988999962806702,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9972000122070312,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6739144921302795},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5808596611022949},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.5279414057731628},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.525920033454895},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.485286682844162},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.45004093647003174},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4353833496570587},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.4286516606807709},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2545435428619385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22275182604789734}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6739144921302795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5808596611022949},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5279414057731628},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.525920033454895},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.485286682844162},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.45004093647003174},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4353833496570587},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.4286516606807709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2545435428619385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22275182604789734},{"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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13010031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010031","pdf_url":"https://www.mdpi.com/2075-1680/13/1/31/pdf?version=1704010400","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8f58e314e0674b5f94d01a7650b89f1c","is_oa":true,"landing_page_url":"https://doaj.org/article/8f58e314e0674b5f94d01a7650b89f1c","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":"Axioms, Vol 13, Iss 1, p 31 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13010031","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010031","pdf_url":"https://www.mdpi.com/2075-1680/13/1/31/pdf?version=1704010400","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2225851447","display_name":"\u519c\u4f5c\u7269\u830e\u4f53\u52a8\u6001\u6c34\u5206\u8c03\u8282\u7684\u8d85\u58f0\u5c04\u9891\u68c0\u6d4b\u7814\u7a76","funder_award_id":"31860332","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5437604798","display_name":null,"funder_award_id":"32360388","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390467729.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1602153886","https://openalex.org/W1973551898","https://openalex.org/W2003677825","https://openalex.org/W2010740862","https://openalex.org/W2012259663","https://openalex.org/W2014114374","https://openalex.org/W2015785429","https://openalex.org/W2024938364","https://openalex.org/W2029350737","https://openalex.org/W2034456245","https://openalex.org/W2035491675","https://openalex.org/W2040546552","https://openalex.org/W2040729418","https://openalex.org/W2043496704","https://openalex.org/W2055539533","https://openalex.org/W2094750626","https://openalex.org/W2120930954","https://openalex.org/W2120968967","https://openalex.org/W2234744346","https://openalex.org/W2251342486","https://openalex.org/W2475189112","https://openalex.org/W2765253543","https://openalex.org/W2889564220","https://openalex.org/W2899318436","https://openalex.org/W2904188105","https://openalex.org/W2972372823","https://openalex.org/W2979607460","https://openalex.org/W2985845430","https://openalex.org/W2990702000","https://openalex.org/W3009349467","https://openalex.org/W3080909521","https://openalex.org/W3107052635","https://openalex.org/W3119051508","https://openalex.org/W3124981722","https://openalex.org/W3136908367","https://openalex.org/W3153011140","https://openalex.org/W3210528453","https://openalex.org/W4207009494","https://openalex.org/W4386476789","https://openalex.org/W6745605500","https://openalex.org/W6768645567"],"related_works":["https://openalex.org/W2018691209","https://openalex.org/W4312143452","https://openalex.org/W2983685817","https://openalex.org/W4285278887","https://openalex.org/W2995925505","https://openalex.org/W134783735","https://openalex.org/W2365237642","https://openalex.org/W3116484972","https://openalex.org/W2941986668","https://openalex.org/W4232431455"],"abstract_inverted_index":{"The":[0,133],"Location-Routing":[1],"Problem":[2],"(LRP)":[3],"becomes":[4],"a":[5,56,76],"more":[6],"intricate":[7],"subject":[8],"when":[9],"the":[10,27,32,40,45,51,64,82,94,99,117,120,124,129,136,140,156,160,177,180,184,188,191,207],"limits":[11],"of":[12,14,29,39,42,47,84,119,135,187],"capacities":[13],"vehicles":[15,30],"and":[16,44,98,169,190,211],"warehouses":[17],"are":[18],"considered,":[19],"which":[20],"is":[21,36,90,143],"an":[22],"NP-hard":[23],"problem.":[24],"Moreover,":[25],"as":[26,110],"number":[28],"increases,":[31],"solution":[33],"to":[34,91,115,128,198,216],"LRP":[35,121,131,189,218],"exacerbated":[37],"because":[38],"complexity":[41],"transportation":[43],"combination":[46],"routes.":[48],"To":[49],"solve":[50],"problem,":[52],"this":[53,72,85],"paper":[54,73],"proposed":[55],"Discrete":[57],"Assembly":[58],"Combination-Delivery":[59],"(DACA)":[60],"strategy":[61,126,142,182],"based":[62],"on,":[63],"Binary":[65],"Equilibrium":[66],"Optimizer":[67],"(BiEO)":[68],"algorithm,":[69],"in":[70,112,173],"addition,":[71],"also":[74],"proposes":[75],"mixed-integer":[77],"linear":[78],"programming":[79],"model":[80],"for":[81],"problem":[83,97,103,194],"paper.":[86],"Our":[87,105],"primary":[88],"objective":[89],"address":[92],"both":[93,206],"route":[95,212],"optimization":[96,186,213],"assembly":[100,208],"group":[101,209],"sum":[102,210],"concurrently.":[104],"BiEO":[106,137,161],"algorithm":[107,138,162,203],"was":[108],"designed":[109],"discrete":[111],"decision":[113],"space":[114],"meet":[116],"requirements":[118],"represented":[122],"by":[123],"DACA":[125,141,181],"catering":[127],"multi-vehicle":[130],"scenario.":[132],"efficacy":[134],"with":[139],"demonstrated.":[144],"through":[145],"empirical":[146],"analysis":[147],"utilizing":[148],"authentic":[149],"data":[150],"from":[151],"Changchun":[152],"City,":[153],"China,":[154],"Remarkably,":[155],"experiments":[157],"reveal":[158],"that":[159],"outperforms":[163],"conventional":[164],"methods,":[165],"specifically":[166],"GA,":[167],"PSO,":[168],"DE":[170],"algorithms,":[171],"resulting":[172],"reduced":[174],"costs.":[175],"Notably,":[176],"results":[178],"show":[179],"enables":[183],"simultaneous":[185],"vehicle":[192],"routing":[193],"(VRP),":[195],"ultimately":[196],"leading":[197],"cost":[199],"reduction.":[200],"This":[201],"innovative":[202],"proficiently":[204],"tackles":[205],"problems":[214],"intrinsic":[215],"multi-level":[217],"instances.":[219]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
