{"id":"https://openalex.org/W4414223321","doi":"https://doi.org/10.1609/icaps.v35i1.36134","title":"New Exact Methods for Solving Quadratic Traveling Salesman Problem","display_name":"New Exact Methods for Solving Quadratic Traveling Salesman Problem","publication_year":2025,"publication_date":"2025-09-16","ids":{"openalex":"https://openalex.org/W4414223321","doi":"https://doi.org/10.1609/icaps.v35i1.36134"},"language":"en","primary_location":{"id":"doi:10.1609/icaps.v35i1.36134","is_oa":true,"landing_page_url":"https://doi.org/10.1609/icaps.v35i1.36134","pdf_url":"https://ojs.aaai.org/index.php/ICAPS/article/download/36134/38288","source":{"id":"https://openalex.org/S4387283601","display_name":"Proceedings of the International Conference on Automated Planning and Scheduling","issn_l":"2334-0835","issn":["2334-0835","2334-0843"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Conference on Automated Planning and Scheduling","raw_type":"journal-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/ICAPS/article/download/36134/38288","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100366786","display_name":"Yuxiao Chen","orcid":"https://orcid.org/0000-0001-5276-7156"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yuxiao Chen","raw_affiliation_strings":["University of Toronto"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100676679","display_name":"Anubhav Pratap Singh","orcid":"https://orcid.org/0000-0001-9006-9578"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anubhav Singh","raw_affiliation_strings":["University of Toronto"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037848536","display_name":"Ryo Kuroiwa","orcid":"https://orcid.org/0000-0002-3753-1644"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryo Kuroiwa","raw_affiliation_strings":["National Institute of Informatics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Informatics","institution_ids":["https://openalex.org/I184597095"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082373681","display_name":"J. Christopher Beck","orcid":"https://orcid.org/0000-0002-4656-8908"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"J. Christopher Beck","raw_affiliation_strings":["University of Toronto"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.673,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85100746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"35","issue":"1","first_page":"325","last_page":"333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9248999953269958,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9248999953269958,"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":0.7010999917984009},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5404000282287598},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.527899980545044},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.48669999837875366},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4440000057220459},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.3977999985218048},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.39079999923706055},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.38370001316070557},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.36890000104904175}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.7010999917984009},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6804999709129333},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5404000282287598},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5062999725341797},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4440000057220459},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42899999022483826},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.351500004529953},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32249999046325684},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C168956720","wikidata":"https://www.wikidata.org/wiki/Q3123181","display_name":"Column generation","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.26350000500679016},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.25850000977516174},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1609/icaps.v35i1.36134","is_oa":true,"landing_page_url":"https://doi.org/10.1609/icaps.v35i1.36134","pdf_url":"https://ojs.aaai.org/index.php/ICAPS/article/download/36134/38288","source":{"id":"https://openalex.org/S4387283601","display_name":"Proceedings of the International Conference on Automated Planning and Scheduling","issn_l":"2334-0835","issn":["2334-0835","2334-0843"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Conference on Automated Planning and Scheduling","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1609/icaps.v35i1.36134","is_oa":true,"landing_page_url":"https://doi.org/10.1609/icaps.v35i1.36134","pdf_url":"https://ojs.aaai.org/index.php/ICAPS/article/download/36134/38288","source":{"id":"https://openalex.org/S4387283601","display_name":"Proceedings of the International Conference on Automated Planning and Scheduling","issn_l":"2334-0835","issn":["2334-0835","2334-0843"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Conference on Automated Planning and Scheduling","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320322015","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087"},{"id":"https://openalex.org/F4320331257","display_name":"Alliance de recherche num\u00e9rique du Canada","ror":"https://ror.org/010r6td27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414223321.pdf","grobid_xml":"https://content.openalex.org/works/W4414223321.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,22],"Quadratic":[1],"Traveling":[2,11],"Salesman":[3,12],"Problem":[4,13],"(QTSP)":[5],"is":[6,37,229],"a":[7,134,144],"generalization":[8],"of":[9,29,81,88,105,189],"the":[10,33,86,130,141,154,162,173,178,190,203,213],"(TSP)":[14],"with":[15,129,185,202],"important":[16],"applications":[17],"in":[18,32,107,219,233],"robotics":[19],"and":[20,39,56,73,120,126,136,140,160],"bioinformatics.":[21],"QTSP":[23,106],"objective":[24],"value":[25],"depends":[26],"on":[27,53,60,166,193],"pairs":[28],"consecutive":[30],"edges":[31],"tour;":[34],"hence,":[35],"it":[36,218],"quadratic":[38,117],"generally":[40,207],"hard":[41],"to":[42,58],"optimize.":[43],"While":[44],"various":[45],"exact-solving":[46],"approaches":[47],"have":[48,68],"been":[49],"explored,":[50],"many":[51],"rely":[52],"specialized":[54],"procedures":[55],"struggle":[57],"scale":[59],"large":[61],"instances.":[62,196],"More":[63],"recently,":[64],"carefully":[65],"crafted":[66],"metaheuristics":[67],"demonstrated":[69],"better":[70,158,209],"primal":[71],"bounds":[72],"scalability,":[74],"but":[75],"they":[76],"cannot":[77],"provide":[78],"any":[79,89],"guarantees":[80],"solution":[82,181],"quality":[83],"nor":[84],"prove":[85],"optimality":[87],"solution.":[90],"In":[91],"this":[92],"work,":[93],"we":[94],"propose":[95],"new":[96],"exact":[97,132,170],"models":[98],"for":[99],"QTSP.":[100,234],"We":[101],"define":[102],"direct":[103],"encodings":[104],"domain-independent":[108],"dynamic":[109],"programming":[110,113,118,124],"(DIDP),":[111],"constraint":[112],"(CP),":[114],"mixed":[115,121],"integer":[116,122],"(MIQP),":[119],"linear":[123],"(MILP),":[125],"compare":[127],"them":[128],"best-known":[131],"method,":[133],"branch":[135],"cut":[137],"(B&amp;C)":[138],"algorithm,":[139],"state-of-the-art":[142],"metaheuristic,":[143],"hybrid":[145],"genetic":[146],"algorithm":[147,215],"(HGA).":[148],"Our":[149],"experimental":[150],"results":[151],"demonstrate":[152],"that":[153,223],"DIDP":[155,186],"model":[156,201],"shows":[157],"scalability":[159],"finds":[161,177,208],"best":[163,179],"feasible":[164,180,210],"solutions":[165,211],"average":[167],"among":[168,182],"all":[169,183,194],"solvers,":[171],"including":[172],"B&amp;C":[174,214],"algorithm.":[175],"HGA":[176,191],"approaches,":[184],"within":[187],"15%":[188],"cost":[192],"experimented":[195],"Also,":[197],"interestingly,":[198],"our":[199],"MILP":[200],"subtour":[204],"elimination":[205,227],"constraints":[206],"than":[212],"while":[216],"matching":[217],"proving":[220],"optimality,":[221],"suggesting":[222],"lazily":[224],"adding":[225],"sub-tour":[226],"cuts":[228],"not":[230],"particularly":[231],"helpful":[232]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
