{"id":"https://openalex.org/W4415455687","doi":"https://doi.org/10.1007/s11590-025-02242-0","title":"Some worst-case results related to the asymmetric traveling salesman problem","display_name":"Some worst-case results related to the asymmetric traveling salesman problem","publication_year":2025,"publication_date":"2025-10-23","ids":{"openalex":"https://openalex.org/W4415455687","doi":"https://doi.org/10.1007/s11590-025-02242-0"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-025-02242-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-025-02242-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-025-02242-0.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11590-025-02242-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015988643","display_name":"Luca Bertazzi","orcid":"https://orcid.org/0000-0002-0227-9135"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Bertazzi","raw_affiliation_strings":["Department of Economics and Management, University of Brescia, Contrada Santa Chiara 50, 25122, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0227-9135","affiliations":[{"raw_affiliation_string":"Department of Economics and Management, University of Brescia, Contrada Santa Chiara 50, 25122, Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022968381","display_name":"Bruce Golden","orcid":"https://orcid.org/0000-0002-5270-6094"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bruce Golden","raw_affiliation_strings":["Robert H. Smith School of Business, University of Maryland, College Park, USA"],"raw_orcid":"https://orcid.org/0000-0002-5270-6094","affiliations":[{"raw_affiliation_string":"Robert H. Smith School of Business, University of Maryland, College Park, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054148553","display_name":"Shuhan Kou","orcid":"https://orcid.org/0000-0003-2146-8318"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuhan Kou","raw_affiliation_strings":["Department of Mathematics, University of Maryland, College Park, MD, USA"],"raw_orcid":"https://orcid.org/0000-0003-2146-8318","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015988643"],"corresponding_institution_ids":["https://openalex.org/I79940851"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38128323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"2","first_page":"411","last_page":"425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9950000047683716,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8192999958992004},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.7224000096321106},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6909000277519226},{"id":"https://openalex.org/keywords/traveling-purchaser-problem","display_name":"Traveling purchaser problem","score":0.5684999823570251},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"Triangle inequality","score":0.5156999826431274},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.49889999628067017}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8192999958992004},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.7224000096321106},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6909000277519226},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5931000113487244},{"id":"https://openalex.org/C4331618","wikidata":"https://www.wikidata.org/wiki/Q7836034","display_name":"Traveling purchaser problem","level":4,"score":0.5684999823570251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.531499981880188},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49889999628067017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46219998598098755},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.3476000130176544},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.32190001010894775}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-025-02242-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-025-02242-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-025-02242-0.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:iris.unibs.it:11379/641507","is_oa":false,"landing_page_url":"https://hdl.handle.net/11379/641507","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11590-025-02242-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-025-02242-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-025-02242-0.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415455687.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1561337940","https://openalex.org/W1970025200","https://openalex.org/W1977056448","https://openalex.org/W1984451472","https://openalex.org/W1985595965","https://openalex.org/W2004882088","https://openalex.org/W2025698306","https://openalex.org/W2035610952","https://openalex.org/W2040865164","https://openalex.org/W2042787170","https://openalex.org/W2049287714","https://openalex.org/W2054177169","https://openalex.org/W2084839533","https://openalex.org/W2092353499","https://openalex.org/W2095430141","https://openalex.org/W2107612355","https://openalex.org/W2111622332","https://openalex.org/W4234387718"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"the":[2,15,19,25,28,33,42,47,50,69,90,93,100,103,105,108,120,123,129,151,154],"Asymmetric":[3],"Traveling":[4],"Salesman":[5],"Problem":[6],"(ATSP),":[7],"an":[8],"interesting":[9],"research":[10],"question":[11],"is":[12,125,137],"to":[13,88,141,158],"evaluate":[14],"maximum":[16,94],"ratio":[17,95,124],"between":[18,49],"cost":[20,26],"of":[21,27,41,71,92,99,122,146,153],"a":[22,38,59,85,147,159],"route":[23,30],"and":[24,107],"same":[29],"traversed":[31],"in":[32,64,68],"opposite":[34],"direction.":[35],"This":[36],"provides":[37],"worst-case":[39,86],"measure":[40],"tour":[43,163],"length":[44],"asymmetry.":[45],"Selecting":[46],"best":[48],"two":[51,155],"routes":[52],"can":[53,156],"be":[54],"advantageous":[55],"not":[56],"only":[57],"from":[58],"theoretical":[60],"standpoint":[61],"but":[62],"also":[63],"practical":[65],"settings:":[66],"particularly":[67],"presence":[70],"factors":[72],"such":[73],"as":[74,149],"elevation":[75],"changes,":[76],"traffic":[77],"patterns,":[78],"or":[79],"operational":[80],"constraints.":[81],"We":[82],"carry":[83],"out":[84],"analysis":[87],"provide":[89],"value":[91,121],"on":[96,115,133],"all":[97],"instances":[98,117],"problem,":[101],"when":[102],"classical,":[104],"sharpened,":[106],"relaxed":[109],"triangle":[110],"inequalities":[111],"hold.":[112],"Computational":[113],"results":[114],"benchmark":[116],"show":[118],"that":[119],"significantly":[126],"smaller":[127],"than":[128],"worst":[130],"case":[131],"bound,":[132],"average.":[134],"Nonetheless,":[135],"it":[136],"still":[138],"large":[139],"enough":[140],"justify":[142],"considering":[143],"both":[144],"directions":[145],"tour,":[148],"selecting":[150],"better":[152],"lead":[157],"substantially":[160],"shorter":[161],"total":[162],"length.":[164]},"counts_by_year":[],"updated_date":"2026-06-17T06:14:20.161405","created_date":"2025-10-23T00:00:00"}