{"id":"https://openalex.org/W3120254694","doi":"https://doi.org/10.3390/a14010021","title":"Dynamic Shortest Paths Methods for the Time-Dependent TSP","display_name":"Dynamic Shortest Paths Methods for the Time-Dependent TSP","publication_year":2021,"publication_date":"2021-01-12","ids":{"openalex":"https://openalex.org/W3120254694","doi":"https://doi.org/10.3390/a14010021","mag":"3120254694"},"language":"en","primary_location":{"id":"doi:10.3390/a14010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14010021","pdf_url":"https://www.mdpi.com/1999-4893/14/1/21/pdf?version=1610499607","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/1999-4893/14/1/21/pdf?version=1610499607","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032282695","display_name":"Christoph Hansknecht","orcid":"https://orcid.org/0000-0003-3948-9344"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christoph Hansknecht","raw_affiliation_strings":["Institute for Mathematical Optimization, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106 Braunschweig, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Optimization, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001342618","display_name":"Imke Joormann","orcid":"https://orcid.org/0000-0002-0189-0557"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Imke Joormann","raw_affiliation_strings":["Cluster of Excellence SE<sup>2</sup>A\u2014Sustainable and Energy-Efficient Aviation, Technische Universit\u00e4t Braunschweig, 38106 Braunschweig, Germany","Institute of Automotive Management and Industrial Production, Technische Universit\u00e4t Braunschweig, M\u00fchlenpfordtstr. 23, 38106 Braunschweig, Germany","Cluster of Excellence SE2A\u2014Sustainable and Energy-Efficient Aviation, Technische Universit\u00e4t Braunschweig, 38106 Braunschweig, Germany"],"affiliations":[{"raw_affiliation_string":"Cluster of Excellence SE<sup>2</sup>A\u2014Sustainable and Energy-Efficient Aviation, Technische Universit\u00e4t Braunschweig, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]},{"raw_affiliation_string":"Institute of Automotive Management and Industrial Production, Technische Universit\u00e4t Braunschweig, M\u00fchlenpfordtstr. 23, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]},{"raw_affiliation_string":"Cluster of Excellence SE2A\u2014Sustainable and Energy-Efficient Aviation, Technische Universit\u00e4t Braunschweig, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052061811","display_name":"Sebastian Stiller","orcid":"https://orcid.org/0000-0002-8792-4390"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Stiller","raw_affiliation_strings":["Institute for Mathematical Optimization, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106 Braunschweig, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Optimization, Technische Universit\u00e4t Braunschweig, Universit\u00e4tsplatz 2, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032282695"],"corresponding_institution_ids":["https://openalex.org/I94509681"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":991,"currency":"EUR","value_usd":1068},"fwci":2.499,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88298928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"1","first_page":"21","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9983999729156494,"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/T11942","display_name":"Transportation and Mobility Innovations","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/column-generation","display_name":"Column generation","score":0.7701382637023926},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.7469345927238464},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.6763520836830139},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6056040525436401},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6021227836608887},{"id":"https://openalex.org/keywords/traveling-purchaser-problem","display_name":"Traveling purchaser problem","score":0.5854178071022034},{"id":"https://openalex.org/keywords/generality","display_name":"Generality","score":0.5617414712905884},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5413354635238647},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.48914316296577454},{"id":"https://openalex.org/keywords/constrained-shortest-path-first","display_name":"Constrained Shortest Path First","score":0.4551829993724823},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.4196811616420746},{"id":"https://openalex.org/keywords/k-shortest-path-routing","display_name":"K shortest path routing","score":0.38637810945510864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36558961868286133},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3432656228542328},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20436236262321472}],"concepts":[{"id":"https://openalex.org/C168956720","wikidata":"https://www.wikidata.org/wiki/Q3123181","display_name":"Column generation","level":2,"score":0.7701382637023926},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.7469345927238464},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.6763520836830139},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6056040525436401},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6021227836608887},{"id":"https://openalex.org/C4331618","wikidata":"https://www.wikidata.org/wiki/Q7836034","display_name":"Traveling purchaser problem","level":4,"score":0.5854178071022034},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.5617414712905884},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5413354635238647},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.48914316296577454},{"id":"https://openalex.org/C178067994","wikidata":"https://www.wikidata.org/wiki/Q1128278","display_name":"Constrained Shortest Path First","level":5,"score":0.4551829993724823},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.4196811616420746},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.38637810945510864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36558961868286133},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3432656228542328},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20436236262321472},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a14010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14010021","pdf_url":"https://www.mdpi.com/1999-4893/14/1/21/pdf?version=1610499607","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:ffe16d0859164ea2ba908c295d055d27","is_oa":true,"landing_page_url":"https://doaj.org/article/ffe16d0859164ea2ba908c295d055d27","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 14, Iss 1, p 21 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/14/1/21/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a14010021","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; Volume 14; Issue 1; Pages: 21","raw_type":"Text"},{"id":"pmh:oai:publikationsserver.tu-braunschweig.de:dbbs_mods_00069257","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:gbv:084-2021011510234","pdf_url":null,"source":{"id":"https://openalex.org/S4306402617","display_name":"Digitale Bibliothek Braunschweig (Verbundzentrale G\u00f6ttingen (VZG))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210149878","host_organization_name":"Verbundzentrale des GBV","host_organization_lineage":["https://openalex.org/I4210149878"],"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, 2021, 14(1), 21; https://doi.org/10.3390/a14010021 -- http://www.mdpi.com/journal/algorithms -- http://www.bibliothek.uni-regensburg.de/ezeit/?2455149 -- 1999-4893","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a14010021","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14010021","pdf_url":"https://www.mdpi.com/1999-4893/14/1/21/pdf?version=1610499607","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":[{"score":0.49000000953674316,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1802626196","display_name":null,"funder_award_id":"Project-ID 390881007","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3120254694.pdf","grobid_xml":"https://content.openalex.org/works/W3120254694.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W166260623","https://openalex.org/W626292722","https://openalex.org/W1557310162","https://openalex.org/W1571087346","https://openalex.org/W1601649239","https://openalex.org/W1968429519","https://openalex.org/W1969186119","https://openalex.org/W1969413967","https://openalex.org/W1970355999","https://openalex.org/W1977129671","https://openalex.org/W1985327268","https://openalex.org/W1998736169","https://openalex.org/W2009803313","https://openalex.org/W2014328192","https://openalex.org/W2017708378","https://openalex.org/W2020898729","https://openalex.org/W2022179164","https://openalex.org/W2041754841","https://openalex.org/W2058937865","https://openalex.org/W2059816321","https://openalex.org/W2064816527","https://openalex.org/W2072136110","https://openalex.org/W2080484716","https://openalex.org/W2088769880","https://openalex.org/W2096796578","https://openalex.org/W2109923933","https://openalex.org/W2122268482","https://openalex.org/W2127988931","https://openalex.org/W2135480108","https://openalex.org/W2155694204","https://openalex.org/W2399100674","https://openalex.org/W2587602778","https://openalex.org/W2809211340","https://openalex.org/W2913564078","https://openalex.org/W2943890712","https://openalex.org/W2956015669","https://openalex.org/W2968741693","https://openalex.org/W4292027170","https://openalex.org/W6712579731"],"related_works":["https://openalex.org/W2362402143","https://openalex.org/W4389782626","https://openalex.org/W2359992618","https://openalex.org/W1984036937","https://openalex.org/W4376138746","https://openalex.org/W4312198704","https://openalex.org/W4220987199","https://openalex.org/W2156431668","https://openalex.org/W2361554335","https://openalex.org/W2022506245"],"abstract_inverted_index":{"The":[0,83],"time-dependent":[1,39,88,167],"traveling":[2,51],"salesman":[3,52],"problem":[4,97,124],"(TDTSP)":[5],"asks":[6],"for":[7,49,78,147,192],"a":[8,13,56,87,111,156,160],"shortest":[9,89,168],"Hamiltonian":[10],"tour":[11],"in":[12,47,74,110,117,182],"directed":[14],"graph":[15,113],"where":[16],"(asymmetric)":[17],"arc-costs":[18],"depend":[19],"on":[20,194,204],"the":[21,23,50,72,95,99,118,132,148,166,180,199,213,229,233],"time":[22],"arc":[24],"is":[25,55,86,103,125],"entered.":[26],"With":[27],"traffic":[28],"data":[29],"abundantly":[30],"available,":[31],"methods":[32,69],"to":[33,38,70,107,178,211,221],"optimize":[34],"routes":[35],"with":[36,165,185],"respect":[37],"travel":[40],"times":[41],"are":[42,115,209],"widely":[43],"desired.":[44],"This":[45],"holds":[46],"particular":[48],"problem,":[53,91],"which":[54,92],"corner":[57],"stone":[58],"of":[59,98,104,134,140,151,198,216,228,232,241],"logistic":[60],"planning.":[61],"In":[62,143,201],"this":[63,123],"paper,":[64],"we":[65,129,145,171,208],"devise":[66],"column-generation-based":[67],"IP":[68],"solve":[71,179,212],"TDTSP":[73,181],"full":[75],"generality,":[76],"both":[77],"arc-":[79],"and":[80,102,159,184,196],"path-based":[81],"formulations.":[82],"algorithmic":[84],"key":[85],"path":[90,169],"arises":[93],"from":[94],"pricing":[96,170],"column":[100],"generation":[101],"independent":[105],"interest\u2014namely,":[106],"find":[108],"paths":[109,135],"time-expanded":[112],"that":[114,136],"acyclic":[116],"underlying":[119],"(non-expanded)":[120],"graph.":[121],"As":[122],"computationally":[126],"too":[127],"costly,":[128],"price":[130],"over":[131],"set":[133],"contain":[137],"no":[138],"cycles":[139],"length":[141],"k.":[142],"addition,":[144],"devise\u2014tailored":[146],"TDTSP\u2014several":[149],"families":[150],"valid":[152],"inequalities,":[153],"primal":[154],"heuristics,":[155],"propagation":[157],"method,":[158],"branching":[161],"rule.":[162],"Combining":[163],"these":[164],"provide\u2014to":[172],"our":[173],"knowledge\u2014the":[174],"first":[175],"elaborate":[176],"method":[177],"general":[183,187],"fully":[186],"time-dependence.":[188],"We":[189],"also":[190],"provide":[191],"results":[193],"complexity":[195],"approximability":[197],"TDTSP.":[200],"computational":[202],"experiments":[203],"randomly":[205],"generated":[206],"instances,":[207],"able":[210],"large":[214,234],"majority":[215],"small":[217],"instances":[218,235],"(20":[219],"nodes)":[220,237],"optimality,":[222],"while":[223],"closing":[224],"about":[225],"two":[226],"thirds":[227],"remaining":[230],"gap":[231],"(40":[236],"after":[238],"one":[239],"hour":[240],"computation.":[242]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
