{"id":"https://openalex.org/W2981880765","doi":"https://doi.org/10.3390/a12110224","title":"A QUBO Model for the Traveling Salesman Problem with Time Windows","display_name":"A QUBO Model for the Traveling Salesman Problem with Time Windows","publication_year":2019,"publication_date":"2019-10-25","ids":{"openalex":"https://openalex.org/W2981880765","doi":"https://doi.org/10.3390/a12110224","mag":"2981880765"},"language":"en","primary_location":{"id":"doi:10.3390/a12110224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12110224","pdf_url":"https://www.mdpi.com/1999-4893/12/11/224/pdf?version=1572340849","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/12/11/224/pdf?version=1572340849","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070153650","display_name":"Christos Papalitsas","orcid":"https://orcid.org/0000-0003-0467-796X"},"institutions":[{"id":"https://openalex.org/I187792471","display_name":"Ionian University","ror":"https://ror.org/01xm4n520","country_code":"GR","type":"education","lineage":["https://openalex.org/I187792471"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Christos Papalitsas","raw_affiliation_strings":["Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece"],"raw_orcid":"https://orcid.org/0000-0003-0467-796X","affiliations":[{"raw_affiliation_string":"Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece","institution_ids":["https://openalex.org/I187792471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110317904","display_name":"Theodore Andronikos","orcid":null},"institutions":[{"id":"https://openalex.org/I187792471","display_name":"Ionian University","ror":"https://ror.org/01xm4n520","country_code":"GR","type":"education","lineage":["https://openalex.org/I187792471"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Theodore Andronikos","raw_affiliation_strings":["Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece","institution_ids":["https://openalex.org/I187792471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001655067","display_name":"Konstantinos Giannakis","orcid":"https://orcid.org/0000-0003-4199-6708"},"institutions":[{"id":"https://openalex.org/I187792471","display_name":"Ionian University","ror":"https://ror.org/01xm4n520","country_code":"GR","type":"education","lineage":["https://openalex.org/I187792471"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Konstantinos Giannakis","raw_affiliation_strings":["Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece"],"raw_orcid":"https://orcid.org/0000-0003-4199-6708","affiliations":[{"raw_affiliation_string":"Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece","institution_ids":["https://openalex.org/I187792471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033962468","display_name":"Georgia Theocharopoulou","orcid":"https://orcid.org/0000-0002-0748-3100"},"institutions":[{"id":"https://openalex.org/I187792471","display_name":"Ionian University","ror":"https://ror.org/01xm4n520","country_code":"GR","type":"education","lineage":["https://openalex.org/I187792471"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Georgia Theocharopoulou","raw_affiliation_strings":["Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece","institution_ids":["https://openalex.org/I187792471"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047011321","display_name":"Sofia Fanarioti","orcid":null},"institutions":[{"id":"https://openalex.org/I187792471","display_name":"Ionian University","ror":"https://ror.org/01xm4n520","country_code":"GR","type":"education","lineage":["https://openalex.org/I187792471"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Sofia Fanarioti","raw_affiliation_strings":["Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Ionian University, Tsirigoti Square 7, 49100 Corfu, Greece","institution_ids":["https://openalex.org/I187792471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001655067","https://openalex.org/A5070153650","https://openalex.org/A5110317904"],"corresponding_institution_ids":["https://openalex.org/I187792471"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":10.2045,"has_fulltext":true,"cited_by_count":83,"citation_normalized_percentile":{"value":0.99066418,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"12","issue":"11","first_page":"224","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9929999709129333,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9850000143051147,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.7765525579452515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.623117983341217},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.540291965007782},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5106695294380188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2549663186073303},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17894914746284485}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.7765525579452515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.623117983341217},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.540291965007782},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5106695294380188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2549663186073303},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17894914746284485},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a12110224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12110224","pdf_url":"https://www.mdpi.com/1999-4893/12/11/224/pdf?version=1572340849","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d9ac6e114a9d4031bf28f1b6174d1d0e","is_oa":true,"landing_page_url":"https://doaj.org/article/d9ac6e114a9d4031bf28f1b6174d1d0e","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":"Algorithms, Vol 12, Iss 11, p 224 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/12/11/224/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/a12110224","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a12110224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12110224","pdf_url":"https://www.mdpi.com/1999-4893/12/11/224/pdf?version=1572340849","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4699999988079071}],"awards":[{"id":"https://openalex.org/G6707449129","display_name":null,"funder_award_id":"2014-2020","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G6870533126","display_name":null,"funder_award_id":"2014-2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2981880765.pdf","grobid_xml":"https://content.openalex.org/works/W2981880765.grobid-xml"},"referenced_works_count":81,"referenced_works":["https://openalex.org/W199424061","https://openalex.org/W817456489","https://openalex.org/W941393951","https://openalex.org/W1501516191","https://openalex.org/W1527520754","https://openalex.org/W1553502100","https://openalex.org/W1568345435","https://openalex.org/W1633549751","https://openalex.org/W1983624953","https://openalex.org/W1990115083","https://openalex.org/W2000449275","https://openalex.org/W2003291739","https://openalex.org/W2011507806","https://openalex.org/W2024060531","https://openalex.org/W2039122980","https://openalex.org/W2040886899","https://openalex.org/W2041432245","https://openalex.org/W2050817363","https://openalex.org/W2050865875","https://openalex.org/W2053275122","https://openalex.org/W2061068130","https://openalex.org/W2065941671","https://openalex.org/W2067002250","https://openalex.org/W2067612530","https://openalex.org/W2077725911","https://openalex.org/W2084652510","https://openalex.org/W2087352629","https://openalex.org/W2092339921","https://openalex.org/W2097279164","https://openalex.org/W2105614108","https://openalex.org/W2109405343","https://openalex.org/W2118518847","https://openalex.org/W2129874988","https://openalex.org/W2131054118","https://openalex.org/W2137147061","https://openalex.org/W2141481566","https://openalex.org/W2153565255","https://openalex.org/W2179731956","https://openalex.org/W2248688291","https://openalex.org/W2297565774","https://openalex.org/W2354302011","https://openalex.org/W2380237055","https://openalex.org/W2534051629","https://openalex.org/W2559394418","https://openalex.org/W2605754424","https://openalex.org/W2619162220","https://openalex.org/W2735281769","https://openalex.org/W2754868542","https://openalex.org/W2757984540","https://openalex.org/W2792255093","https://openalex.org/W2794880473","https://openalex.org/W2897512258","https://openalex.org/W2900962211","https://openalex.org/W2901067438","https://openalex.org/W2903350490","https://openalex.org/W2908699277","https://openalex.org/W2913568030","https://openalex.org/W2915690603","https://openalex.org/W2938689170","https://openalex.org/W2948572415","https://openalex.org/W2963288033","https://openalex.org/W2963546261","https://openalex.org/W2963704146","https://openalex.org/W2963757591","https://openalex.org/W2970621885","https://openalex.org/W2990961515","https://openalex.org/W2999159028","https://openalex.org/W3006807815","https://openalex.org/W3014405689","https://openalex.org/W3098268180","https://openalex.org/W3099380434","https://openalex.org/W3100566623","https://openalex.org/W3101633784","https://openalex.org/W3102870135","https://openalex.org/W3103574448","https://openalex.org/W3104354927","https://openalex.org/W3106015846","https://openalex.org/W3215460652","https://openalex.org/W4234780461","https://openalex.org/W6633207751","https://openalex.org/W6786007649"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2794103424","https://openalex.org/W1996530509","https://openalex.org/W3028317537","https://openalex.org/W2389515972","https://openalex.org/W4245435724","https://openalex.org/W1525389557","https://openalex.org/W2495211334"],"abstract_inverted_index":{"This":[0,53],"work":[1],"focuses":[2],"on":[3,94],"expressing":[4],"the":[5,35,50,57,66,71,86,95],"TSP":[6],"with":[7],"Time":[8],"Windows":[9],"(TSPTW":[10],"for":[11],"short)":[12],"as":[13],"a":[14,28],"quadratic":[15],"unconstrained":[16],"binary":[17],"optimization":[18],"(QUBO)":[19],"problem.":[20],"The":[21],"time":[22,25,59],"windows":[23],"impose":[24],"constraints":[26],"that":[27,80],"feasible":[29],"solution":[30],"must":[31],"satisfy.":[32],"These":[33],"take":[34],"form":[36],"of":[37,89],"inequality":[38],"constraints,":[39],"which":[40],"are":[41],"known":[42],"to":[43,47,78,85],"be":[44],"particularly":[45],"difficult":[46],"articulate":[48],"within":[49],"QUBO":[51,72],"framework.":[52],"is,":[54],"we":[55],"believe,":[56],"first":[58],"this":[60,81],"major":[61],"obstacle":[62],"is":[63,68],"overcome":[64],"and":[65],"TSPTW":[67,92],"cast":[69],"in":[70],"formulation.":[73],"We":[74],"have":[75],"every":[76],"reason":[77],"anticipate":[79],"development":[82],"will":[83],"lead":[84],"actual":[87],"execution":[88],"small":[90],"scale":[91],"instances":[93],"D-Wave":[96],"platform.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}