{"id":"https://openalex.org/W7133239825","doi":"https://doi.org/10.48550/arxiv.2602.23579","title":"Construct, Merge, Solve & Adapt with Reinforcement Learning for the min-max Multiple Traveling Salesman Problem","display_name":"Construct, Merge, Solve & Adapt with Reinforcement Learning for the min-max Multiple Traveling Salesman Problem","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133239825","doi":"https://doi.org/10.48550/arxiv.2602.23579"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23579","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019374060","display_name":"Guillem Rodr\u00edguez Corominas","orcid":"https://orcid.org/0000-0002-3863-2017"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rodr\u00edguez-Corominas, Guillem","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043499010","display_name":"Maria Jose Blesa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blesa, Maria J.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003063095","display_name":"Christian Blum","orcid":"https://orcid.org/0000-0002-6524-2495"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blum, Christian","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019374060"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"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":0.8772000074386597,"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":0.8772000074386597,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.01640000008046627,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.01600000075995922,"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":0.8356000185012817},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6223000288009644},{"id":"https://openalex.org/keywords/swap","display_name":"Swap (finance)","score":0.5807999968528748},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.527400016784668},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.517300009727478},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.4900999963283539},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4442000091075897},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.3747999966144562}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8356000185012817},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.678600013256073},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6223000288009644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6025000214576721},{"id":"https://openalex.org/C99821215","wikidata":"https://www.wikidata.org/wiki/Q1136583","display_name":"Swap (finance)","level":2,"score":0.5807999968528748},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.4900999963283539},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.33660000562667847},{"id":"https://openalex.org/C75782508","wikidata":"https://www.wikidata.org/wiki/Q3333633","display_name":"Cross-entropy method","level":4,"score":0.3165000081062317},{"id":"https://openalex.org/C188919014","wikidata":"https://www.wikidata.org/wiki/Q5422296","display_name":"Extremal optimization","level":4,"score":0.31470000743865967},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31209999322891235},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31139999628067017},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C40128228","wikidata":"https://www.wikidata.org/wiki/Q460851","display_name":"Ant colony optimization algorithms","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C2778476105","wikidata":"https://www.wikidata.org/wiki/Q628539","display_name":"Workload","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25360000133514404},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23579","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.23579","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23579","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.23579","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7395089268684387,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,64,99],"Multiple":[1],"Traveling":[2,8],"Salesman":[3,9],"Problem":[4,10],"(mTSP)":[5],"extends":[6],"the":[7,30,33,38,59,111,161],"to":[11,36],"m":[12],"tours":[13],"that":[14,139],"start":[15],"and":[16,22,89,96,117,124,129,135,145,160],"end":[17],"at":[18],"a":[19,46,81,85,147],"common":[20],"depot":[21],"jointly":[23],"visit":[24],"all":[25],"customers":[26],"exactly":[27],"once.":[28],"In":[29],"min-max":[31,62],"variant,":[32],"objective":[34],"is":[35,113],"minimize":[37],"longest":[39],"tour,":[40],"reflecting":[41],"workload":[42],"balance.":[43],"We":[44],"propose":[45],"hybrid":[47,149],"approach,":[48],"Construct,":[49],"Merge,":[50],"Solve":[51],"&":[52],"Adapt":[53],"with":[54],"Reinforcement":[55],"Learning":[56],"(RL-CMSA),":[57],"for":[58],"symmetric":[60],"single-depot":[61],"mTSP.":[63],"method":[65],"iteratively":[66],"constructs":[67],"diverse":[68],"solutions":[69,91,144],"using":[70],"probabilistic":[71],"clustering":[72],"guided":[73],"by":[74,103],"learned":[75],"pairwise":[76],"q-values,":[77],"merges":[78],"routes":[79],"into":[80],"compact":[82],"pool,":[83],"solves":[84],"restricted":[86],"set-covering":[87],"MILP,":[88],"refines":[90],"via":[92],"inter-route":[93],"remove,":[94],"shift,":[95],"swap":[97],"moves.":[98],"q-values":[100],"are":[101],"updated":[102],"reinforcing":[104],"city-pair":[105],"co-occurrences":[106],"in":[107],"high-quality":[108],"solutions,":[109],"while":[110],"pool":[112],"adapted":[114],"through":[115],"ageing":[116],"pruning.":[118],"This":[119],"combination":[120],"of":[121,163],"exact":[122],"optimization":[123],"reinforcement-guided":[125],"construction":[126],"balances":[127],"exploration":[128],"exploitation.":[130],"Computational":[131],"results":[132],"on":[133],"random":[134],"TSPLIB":[136],"instances":[137],"show":[138],"RL-CMSA":[140],"consistently":[141],"finds":[142],"(near-)best":[143],"outperforms":[146],"state-of-the-art":[148],"genetic":[150],"algorithm":[151],"under":[152],"comparable":[153],"time":[154],"limits,":[155],"especially":[156],"as":[157],"instance":[158],"size":[159],"number":[162],"salesmen":[164],"increase.":[165]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-03T00:00:00"}