{"id":"https://openalex.org/W7135191271","doi":"https://doi.org/10.3389/frai.2026.1759688","title":"An improved adaptive large neighborhood search algorithm for the flexible two-tier vehicle routing problem with drone stations","display_name":"An improved adaptive large neighborhood search algorithm for the flexible two-tier vehicle routing problem with drone stations","publication_year":2026,"publication_date":"2026-03-13","ids":{"openalex":"https://openalex.org/W7135191271","doi":"https://doi.org/10.3389/frai.2026.1759688","pmid":"https://pubmed.ncbi.nlm.nih.gov/41908141"},"language":"en","primary_location":{"id":"doi:10.3389/frai.2026.1759688","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frai.2026.1759688","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2026.1759688/pdf","source":{"id":"https://openalex.org/S4210197006","display_name":"Frontiers in Artificial Intelligence","issn_l":"2624-8212","issn":["2624-8212"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://public-pages-files-2025.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2026.1759688/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123791048","display_name":"Qi Li","orcid":null},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Qi Li","raw_affiliation_strings":["Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University","institution_ids":["https://openalex.org/I42999171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123759976","display_name":"Wenhao Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Wenhao Yan","raw_affiliation_strings":["Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University","institution_ids":["https://openalex.org/I42999171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5128978846","display_name":"Tad Gonsalves","orcid":null},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tad Gonsalves","raw_affiliation_strings":["Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University"],"affiliations":[{"raw_affiliation_string":"Department of Information and Communication Sciences, Faculty of Science and Technology, Sophia University","institution_ids":["https://openalex.org/I42999171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5123791048"],"corresponding_institution_ids":["https://openalex.org/I42999171"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.55300607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":null,"first_page":"1759688","last_page":"1759688"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9869999885559082,"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":0.9869999885559082,"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/T11133","display_name":"UAV Applications and Optimization","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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":0.0013000000035390258,"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/simulated-annealing","display_name":"Simulated annealing","score":0.5978000164031982},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.5575000047683716},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5234000086784363},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5188999772071838},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.5012000203132629},{"id":"https://openalex.org/keywords/drone","display_name":"Drone","score":0.4668000042438507},{"id":"https://openalex.org/keywords/variable-neighborhood-search","display_name":"Variable neighborhood search","score":0.40700000524520874},{"id":"https://openalex.org/keywords/traffic-congestion","display_name":"Traffic congestion","score":0.3880999982357025}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6237999796867371},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.5575000047683716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5252000093460083},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5234000086784363},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5188999772071838},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5012000203132629},{"id":"https://openalex.org/C59519942","wikidata":"https://www.wikidata.org/wiki/Q650665","display_name":"Drone","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C2776435737","wikidata":"https://www.wikidata.org/wiki/Q7915703","display_name":"Variable neighborhood search","level":3,"score":0.40700000524520874},{"id":"https://openalex.org/C2779888511","wikidata":"https://www.wikidata.org/wiki/Q244156","display_name":"Traffic congestion","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C62469222","wikidata":"https://www.wikidata.org/wiki/Q17092103","display_name":"Hybrid algorithm (constraint satisfaction)","level":5,"score":0.3824000060558319},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C52121051","wikidata":"https://www.wikidata.org/wiki/Q43193","display_name":"Truck","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C79403827","wikidata":"https://www.wikidata.org/wiki/Q3988","display_name":"Real-time computing","level":1,"score":0.3043000102043152},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C2987704428","wikidata":"https://www.wikidata.org/wiki/Q7900121","display_name":"City logistics","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.25209999084472656},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3389/frai.2026.1759688","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frai.2026.1759688","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2026.1759688/pdf","source":{"id":"https://openalex.org/S4210197006","display_name":"Frontiers in Artificial Intelligence","issn_l":"2624-8212","issn":["2624-8212"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence","raw_type":"journal-article"},{"id":"pmid:41908141","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41908141","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in artificial intelligence","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:13021654","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13021654/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Front Artif Intell","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3389/frai.2026.1759688","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frai.2026.1759688","pdf_url":"https://public-pages-files-2025.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2026.1759688/pdf","source":{"id":"https://openalex.org/S4210197006","display_name":"Frontiers in Artificial Intelligence","issn_l":"2624-8212","issn":["2624-8212"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7191309928894043,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7135191271.pdf","grobid_xml":"https://content.openalex.org/works/W7135191271.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1966842536","https://openalex.org/W1977319619","https://openalex.org/W2096658257","https://openalex.org/W2105002757","https://openalex.org/W2136284166","https://openalex.org/W2557406701","https://openalex.org/W2890722280","https://openalex.org/W2903944199","https://openalex.org/W2915338839","https://openalex.org/W2921047495","https://openalex.org/W2927378423","https://openalex.org/W2963421154","https://openalex.org/W2972055356","https://openalex.org/W3008289549","https://openalex.org/W3010476620","https://openalex.org/W3037622630","https://openalex.org/W3038093615","https://openalex.org/W3130612522","https://openalex.org/W3174853550","https://openalex.org/W3215148040","https://openalex.org/W3216846761","https://openalex.org/W4210344377","https://openalex.org/W4213318779","https://openalex.org/W4220894234","https://openalex.org/W4306632378","https://openalex.org/W4312746739","https://openalex.org/W4313291150","https://openalex.org/W4380785684","https://openalex.org/W4381487038","https://openalex.org/W4386365073","https://openalex.org/W4386997203","https://openalex.org/W4387534531","https://openalex.org/W4390492561","https://openalex.org/W4391605334","https://openalex.org/W4404730118","https://openalex.org/W4407959019","https://openalex.org/W4409710710","https://openalex.org/W4410478333","https://openalex.org/W4414444959","https://openalex.org/W4414808908"],"related_works":[],"abstract_inverted_index":{"The":[0,138,163],"two-tier":[1,45,100],"vehicle":[2,101],"routing":[3,102],"problem":[4,103,112],"(2T-VRP)":[5],"represents":[6],"a":[7,43,114,153],"novel":[8],"variant":[9,93],"differing":[10],"from":[11,37],"the":[12,51,59,68,73,98,111,122,149,160,178,207,210,216,223],"traditional":[13,38],"VRPs.":[14],"It":[15],"can":[16,170],"be":[17],"applied":[18],"to":[19,78,83,89,96,198],"urban":[20],"logistics":[21],"operations":[22],"system,":[23],"offering":[24,189],"significant":[25],"potential":[26],"for":[27],"mitigating":[28],"last-mile":[29],"traffic":[30],"congestion":[31],"and":[32,54,144,152,193],"reducing":[33],"delivering":[34],"costs.":[35],"Distinct":[36],"VRPs,":[39],"this":[40,63,125],"scenario":[41],"contains":[42],"hierarchical":[44,74],"structure,":[46],"with":[47,104,177],"trucks":[48,77],"operating":[49],"on":[50,58,186,206],"first":[52,66],"tier":[53],"drones":[55],"at":[56],"stations":[57,85,106],"second":[60],"tier.":[61],"In":[62,174,203],"study,":[64],"we":[65,109,213],"extend":[67],"2T-VRP":[69],"framework":[70],"by":[71],"relaxing":[72],"constraints,":[75],"enabling":[76],"transport":[79],"goods":[80],"not":[81],"only":[82],"robot":[84],"but":[86],"also":[87],"directly":[88],"customers.":[90],"This":[91],"new":[92],"is":[94,136,157],"referred":[95],"as":[97,113,148,159],"flexible":[99],"drone":[105],"(F2T-VRP-DS).":[107],"Then":[108],"formulate":[110],"mixed-integer":[115],"linear":[116],"programming":[117],"(MILP)":[118],"model.":[119],"Finally,":[120],"given":[121],"complexity":[123],"of":[124,209,218],"problem,":[126],"an":[127,141],"improved":[128],"adaptive":[129],"large":[130],"neighborhood":[131],"search":[132],"heuristic":[133],"algorithm":[134,139,147,169,182],"(IALNS)":[135],"proposed.":[137],"incorporates":[140],"adapted":[142],"Clark":[143],"Wright":[145],"saving":[146],"initial":[150],"solution,":[151],"simulated":[154],"annealing":[155],"scheme":[156],"employed":[158],"acceptance":[161],"criterion.":[162],"experimental":[164],"results":[165,208],"show":[166],"that":[167],"our":[168,181],"provide":[171],"high-quality":[172],"solutions.":[173],"particular,":[175],"compared":[176,197],"MILP":[179],"method,":[180],"demonstrates":[183],"strong":[184],"competitiveness":[185],"large-scale":[187],"instances,":[188],"smaller":[190],"time":[191],"consumption":[192],"better":[194],"solution":[195],"quality":[196],"commercial":[199],"solver":[200],"like":[201],"Gurobi.":[202],"addition,":[204],"based":[205],"sensitivity":[211],"analysis,":[212],"further":[214],"assessed":[215],"influence":[217],"several":[219],"key":[220],"parameters":[221],"within":[222],"F2T-VRP-DS":[224],"framework.":[225]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2026-03-14T00:00:00"}