{"id":"https://openalex.org/W4411551561","doi":"https://doi.org/10.1109/cscwd64889.2025.11033472","title":"Symmetry-Regularized Transformer for Solving Traveling Salesman Problems","display_name":"Symmetry-Regularized Transformer for Solving Traveling Salesman Problems","publication_year":2025,"publication_date":"2025-05-05","ids":{"openalex":"https://openalex.org/W4411551561","doi":"https://doi.org/10.1109/cscwd64889.2025.11033472"},"language":"en","primary_location":{"id":"doi:10.1109/cscwd64889.2025.11033472","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cscwd64889.2025.11033472","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 28th International Conference on Computer Supported Cooperative Work in Design (CSCWD)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047400719","display_name":"Shuyun Li","orcid":"https://orcid.org/0000-0002-6172-784X"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuyun Li","raw_affiliation_strings":["Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031904848","display_name":"Maoli Wang","orcid":"https://orcid.org/0000-0001-5420-1463"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maoli Wang","raw_affiliation_strings":["Qufu Normal University,College of Cyber Security,Jining,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qufu Normal University,College of Cyber Security,Jining,China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043618047","display_name":"Zixin Liu","orcid":"https://orcid.org/0000-0003-3550-9547"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zixin Liu","raw_affiliation_strings":["Qufu Normal University,College of Cyber Security,Jining,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qufu Normal University,College of Cyber Security,Jining,China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019447624","display_name":"Huan Ma","orcid":"https://orcid.org/0000-0002-3206-2324"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huan Ma","raw_affiliation_strings":["Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068577757","display_name":"Zhihui Wang","orcid":"https://orcid.org/0000-0002-2571-702X"},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihui Wang","raw_affiliation_strings":["Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xubing Dou","orcid":null},"institutions":[{"id":"https://openalex.org/I152269853","display_name":"Qilu University of Technology","ror":"https://ror.org/04hyzq608","country_code":"CN","type":"education","lineage":["https://openalex.org/I152269853"]},{"id":"https://openalex.org/I4210142748","display_name":"Shandong Academy of Sciences","ror":"https://ror.org/04y8d6y55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xubing Dou","raw_affiliation_strings":["Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences),Key Laboratory of Computing Power Network and Information Security,Jinan,China","institution_ids":["https://openalex.org/I152269853","https://openalex.org/I4210142748"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101866870","display_name":"Xinchang Zhang","orcid":"https://orcid.org/0000-0001-6113-2099"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinchang Zhang","raw_affiliation_strings":["Shandong Normal University,Jinan,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong Normal University,Jinan,China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"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":"872","last_page":"878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9143999814987183,"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/T10320","display_name":"Neural Networks and Applications","score":0.9143999814987183,"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":0.8363124132156372},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5211668014526367},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.512292742729187},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4949759840965271},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.45025646686553955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.352704793214798},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3381943106651306},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14047756791114807},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.14034605026245117},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11623716354370117},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.06443753838539124}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8363124132156372},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5211668014526367},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.512292742729187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4949759840965271},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.45025646686553955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.352704793214798},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3381943106651306},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14047756791114807},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.14034605026245117},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11623716354370117},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.06443753838539124}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cscwd64889.2025.11033472","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cscwd64889.2025.11033472","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 28th International Conference on Computer Supported Cooperative Work in Design (CSCWD)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2171060218","https://openalex.org/W3014847873","https://openalex.org/W4285814490","https://openalex.org/W4321113880","https://openalex.org/W4382203174","https://openalex.org/W4382237551","https://openalex.org/W4387503929","https://openalex.org/W4399813745","https://openalex.org/W6758687306","https://openalex.org/W6783944145","https://openalex.org/W6802180043","https://openalex.org/W6838910480","https://openalex.org/W6849565481","https://openalex.org/W6941249815"],"related_works":["https://openalex.org/W1525389557","https://openalex.org/W2361554335","https://openalex.org/W2164188042","https://openalex.org/W2359992618","https://openalex.org/W4306878646","https://openalex.org/W2054495636","https://openalex.org/W3005108979","https://openalex.org/W2913191894","https://openalex.org/W4389782626","https://openalex.org/W2495211334"],"abstract_inverted_index":{"The":[0],"Traveling":[1],"Salesman":[2],"Problem":[3],"(TSP),":[4],"a":[5,35,79,96,120,143],"well-known":[6],"NP-hard":[7],"problem,":[8],"is":[9,140],"widely":[10],"applied":[11],"across":[12],"manufacturing,":[13],"biology,":[14],"transportation,":[15],"and":[16,45,101,110,116,129,165],"other":[17],"fields.":[18],"In":[19,73],"recent":[20],"years,":[21],"deep":[22],"reinforcement":[23],"learning":[24],"(DRL),":[25],"particularly":[26],"DRL":[27,64,157],"based":[28,66],"on":[29,67,159],"Transformer":[30,49],"architectures,":[31],"has":[32],"emerged":[33],"as":[34],"popular":[36],"approach":[37],"to":[38,106,171],"solving":[39],"TSP.":[40],"However,":[41],"the":[42,71,76,93,103,127,135,138],"quadratic":[43],"computational":[44],"space":[46],"complexities":[47],"of":[48],"models":[50],"pose":[51],"challenges":[52],"for":[53],"handling":[54],"larger-scale":[55,172],"TSP":[56,173],"instances.":[57,174],"This":[58],"paper":[59],"introduces":[60,130],"Sym-Favformer,":[61],"an":[62],"end-to-end":[63,156],"method":[65],"symmetry":[68],"regularization":[69],"in":[70,134],"Transformer.":[72],"this":[74],"approach,":[75],"encoder":[77,128],"incorporates":[78],"Fast":[80],"Attention":[81],"Via":[82],"positive":[83],"Orthogonal":[84],"Random":[85],"features":[86],"(FAVOR+)":[87],"mechanism":[88],"with":[89],"linear":[90],"complexity,":[91],"while":[92],"decoder":[94],"adopts":[95],"distance-based":[97],"dynamic":[98],"selection":[99],"mechanism,":[100],"employs":[102],"Lion":[104],"optimizer":[105],"reduce":[107],"training":[108],"time":[109],"memory":[111],"consumption.":[112],"To":[113],"enhance":[114],"performance":[115],"generalization,":[117],"Sym-Favformer":[118],"applies":[119],"random":[121],"transformation":[122],"data":[123],"augmentation":[124],"technique":[125],"within":[126],"enhanced":[131],"context":[132],"embedding":[133],"decoder.":[136],"Subsequently,":[137],"model":[139],"trained":[141],"using":[142],"symmetry-regularized":[144],"REINFORCE":[145],"method.":[146],"Experimental":[147],"results":[148],"show":[149],"that":[150],"Sym-":[151],"Favformer":[152],"significantly":[153],"outperforms":[154],"existing":[155],"methods":[158],"both":[160],"randomly":[161],"generated":[162],"benchmark":[163],"instances":[164],"TSPLIB":[166],"datasets,":[167],"demonstrating":[168],"strong":[169],"generalization":[170]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}