{"id":"https://openalex.org/W4381736198","doi":"https://doi.org/10.3389/fams.2023.1155356","title":"Solving the capacitated vehicle routing problem with time windows via graph convolutional network assisted tree search and quantum-inspired computing","display_name":"Solving the capacitated vehicle routing problem with time windows via graph convolutional network assisted tree search and quantum-inspired computing","publication_year":2023,"publication_date":"2023-06-22","ids":{"openalex":"https://openalex.org/W4381736198","doi":"https://doi.org/10.3389/fams.2023.1155356"},"language":"en","primary_location":{"id":"doi:10.3389/fams.2023.1155356","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1155356","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1155356/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"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 Applied Mathematics and Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1155356/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089602300","display_name":"Jorin Dornemann","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jorin Dornemann","raw_affiliation_strings":["Institute of Mathematics, Hamburg University of Technology, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hamburg University of Technology, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089602300"],"corresponding_institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"],"apc_list":{"value":1285,"currency":"USD","value_usd":1285},"apc_paid":{"value":1285,"currency":"USD","value_usd":1285},"fwci":1.8183,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85289803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"9","issue":null,"first_page":null,"last_page":null},"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9879999756813049,"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/computer-science","display_name":"Computer science","score":0.7343495488166809},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.7187069654464722},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5185861587524414},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.5122193694114685},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4532445967197418},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.449493408203125},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42865705490112305},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.42790094017982483},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4196593463420868},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.40909722447395325},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.38792693614959717},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3322458863258362},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17127564549446106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13859161734580994}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7343495488166809},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.7187069654464722},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5185861587524414},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.5122193694114685},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4532445967197418},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.449493408203125},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42865705490112305},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.42790094017982483},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4196593463420868},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.40909722447395325},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.38792693614959717},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3322458863258362},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17127564549446106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13859161734580994},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fams.2023.1155356","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1155356","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1155356/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"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 Applied Mathematics and Statistics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4691d39cd0b44109a2e9ef846efb3fca","is_oa":true,"landing_page_url":"https://doaj.org/article/4691d39cd0b44109a2e9ef846efb3fca","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":"Frontiers in Applied Mathematics and Statistics, Vol 9 (2023)","raw_type":"article"},{"id":"pmh:oai:null:11420/40886","is_oa":true,"landing_page_url":"https://hdl.handle.net/11420/40886","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"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":"","raw_type":"Journal Article"},{"id":"doi:10.15480/882.5595","is_oa":true,"landing_page_url":"https://doi.org/10.15480/882.5595","pdf_url":null,"source":{"id":"https://openalex.org/S7407052987","display_name":"TUHH Open Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.3389/fams.2023.1155356","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1155356","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1155356/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"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 Applied Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4093464883","display_name":"OpenAccessPublikationskosten / 20222024 / Technische Universit\u00e4t Hamburg (TUHH)","funder_award_id":"491268466","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4381736198.pdf"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W311217234","https://openalex.org/W321964111","https://openalex.org/W1554727768","https://openalex.org/W1965032790","https://openalex.org/W1972974960","https://openalex.org/W1973565128","https://openalex.org/W2018691209","https://openalex.org/W2029341065","https://openalex.org/W2039766013","https://openalex.org/W2054151210","https://openalex.org/W2096305430","https://openalex.org/W2111658959","https://openalex.org/W2116341502","https://openalex.org/W2135680984","https://openalex.org/W2154241802","https://openalex.org/W2156117830","https://openalex.org/W2224737250","https://openalex.org/W2559655401","https://openalex.org/W2603251541","https://openalex.org/W2629084902","https://openalex.org/W2747329762","https://openalex.org/W2768242641","https://openalex.org/W2795112307","https://openalex.org/W2809515324","https://openalex.org/W2906726587","https://openalex.org/W2913954081","https://openalex.org/W2914304175","https://openalex.org/W2917807404","https://openalex.org/W2940740707","https://openalex.org/W2948433391","https://openalex.org/W2952332632","https://openalex.org/W2964121744","https://openalex.org/W2980930344","https://openalex.org/W2981880765","https://openalex.org/W2996246179","https://openalex.org/W3008858828","https://openalex.org/W3025860244","https://openalex.org/W3047863327","https://openalex.org/W3097232108","https://openalex.org/W3097400948","https://openalex.org/W3102895825","https://openalex.org/W3132134635","https://openalex.org/W3168231284","https://openalex.org/W3169220090","https://openalex.org/W3175095632","https://openalex.org/W3207021134","https://openalex.org/W4225406282","https://openalex.org/W4252801674","https://openalex.org/W4285805262","https://openalex.org/W4287756647","https://openalex.org/W4394657357","https://openalex.org/W6634273431","https://openalex.org/W6638667902","https://openalex.org/W6682610290","https://openalex.org/W6725207838","https://openalex.org/W6748487558","https://openalex.org/W6756040250","https://openalex.org/W6762840543","https://openalex.org/W6771561114","https://openalex.org/W6775174418","https://openalex.org/W6784670912","https://openalex.org/W6785065334","https://openalex.org/W6797752405"],"related_works":["https://openalex.org/W2017649536","https://openalex.org/W1990067406","https://openalex.org/W3123878210","https://openalex.org/W3144414831","https://openalex.org/W2337677955","https://openalex.org/W1969514800","https://openalex.org/W2474680198","https://openalex.org/W2597689725","https://openalex.org/W2363855676","https://openalex.org/W1569102320"],"abstract_inverted_index":{"Vehicle":[0],"routing":[1,33,65,113],"problems":[2,10,34,48,66],"are":[3,77],"a":[4,13,54,104,120,126,132,142,150,155,165,183,192,211],"class":[5],"of":[6,15,38,191,229,259],"NP-hard":[7],"combinatorial":[8],"optimization":[9,47,58,196],"which":[11,76,145,174],"attract":[12],"lot":[14],"attention,":[16],"as":[17,90],"they":[18],"have":[19,27],"many":[20],"practical":[21],"applications.":[22],"In":[23],"recent":[24],"years":[25],"there":[26],"been":[28],"new":[29,105,166,184],"developments":[30],"solving":[31,63,109],"vehicle":[32,64,112],"with":[35,85,115,208],"the":[36,50,91,110,187,217,227,240],"help":[37],"machine":[39,68,156],"learning,":[40],"since":[41],"learning":[42,69,157,180],"how":[43],"to":[44,52,79,94,136,148,223,253],"automatically":[45],"solve":[46],"has":[49,70,93],"potential":[51],"provide":[53],"big":[55],"leap":[56],"in":[57,97,125,154,189,206,257],"technology.":[59],"Prior":[60],"work":[61],"on":[62,73,246],"using":[67],"mainly":[71],"focused":[72],"auto-regressive":[74],"models,":[75],"connected":[78],"high":[80],"computational":[81,260],"costs":[82,261],"when":[83],"combined":[84],"classical":[86],"exact":[87],"search":[88,99],"methods":[89,256],"model":[92,130,161],"be":[95],"evaluated":[96],"every":[98],"step.":[100],"This":[101],"paper":[102],"proposes":[103],"method":[106],"for":[107,178,186,232,269],"approximately":[108],"capacitated":[111],"problem":[114,198,213,234],"time":[116],"windows":[117],"(CVRPTW)":[118],"via":[119,203],"supervised":[121],"deep":[122,133,179],"learning-based":[123],"approach":[124],"non-autoregressive":[127],"manner.":[128],"The":[129,160],"uses":[131],"neural":[134,167,219],"network":[135,168,220],"assist":[137],"finding":[138],"solutions":[139],"by":[140],"providing":[141],"probability":[143],"distribution":[144],"is":[146,162,175,199,221],"used":[147],"guide":[149],"tree":[151],"search,":[152],"resulting":[153],"assisted":[158],"heuristic.":[159],"built":[163],"upon":[164,216],"architecture,":[169],"called":[170],"graph":[171],"convolutional":[172],"network,":[173],"particularly":[176],"suited":[177],"tasks.":[181],"Furthermore,":[182],"formulation":[185],"CVRPTW":[188],"form":[190],"quadratic":[193],"unconstrained":[194],"binary":[195],"(QUBO)":[197],"presented":[200],"and":[201,248,262,265],"solved":[202],"quantum-inspired":[204],"computing":[205,231],"cooperation":[207],"Fujitsu,":[209],"where":[210],"learned":[212],"reduction":[214],"based":[215],"proposed":[218,241],"applied":[222],"circumvent":[224],"limitations":[225],"concerning":[226],"usage":[228],"quantum":[230],"large":[233,270],"instances.":[235,271],"Computational":[236],"results":[237],"show":[238],"that":[239],"models":[242],"perform":[243],"very":[244],"well":[245],"small":[247],"medium":[249],"sized":[250],"instances":[251],"compared":[252],"state-of-the-art":[254],"solution":[255,263],"terms":[258],"quality,":[264],"outperform":[266],"commercial":[267],"solvers":[268]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}
