{"id":"https://openalex.org/W3176609373","doi":"https://doi.org/10.1109/tits.2021.3086625","title":"Bi-Objective Colored Traveling Salesman Problems","display_name":"Bi-Objective Colored Traveling Salesman Problems","publication_year":2021,"publication_date":"2021-06-16","ids":{"openalex":"https://openalex.org/W3176609373","doi":"https://doi.org/10.1109/tits.2021.3086625","mag":"3176609373"},"language":"en","primary_location":{"id":"doi:10.1109/tits.2021.3086625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2021.3086625","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","raw_type":"journal-article"},"type":"article","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/A5042815921","display_name":"Xiangping Xu","orcid":"https://orcid.org/0000-0002-8676-0195"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangping Xu","raw_affiliation_strings":["Ministry of Education Key Laboratory of Measurement and Control of CSE, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Measurement and Control of CSE, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100696862","display_name":"Jun Li","orcid":"https://orcid.org/0000-0002-5272-9130"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Li","raw_affiliation_strings":["Ministry of Education Key Laboratory of Measurement and Control of CSE, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Measurement and Control of CSE, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081318069","display_name":"MengChu Zhou","orcid":"https://orcid.org/0000-0002-5408-8752"},"institutions":[{"id":"https://openalex.org/I118118575","display_name":"New Jersey Institute of Technology","ror":"https://ror.org/05e74xb87","country_code":"US","type":"education","lineage":["https://openalex.org/I118118575"]},{"id":"https://openalex.org/I111950717","display_name":"Macau University of Science and Technology","ror":"https://ror.org/03jqs2n27","country_code":"MO","type":"education","lineage":["https://openalex.org/I111950717","https://openalex.org/I4391767947"]}],"countries":["MO","US"],"is_corresponding":false,"raw_author_name":"MengChu Zhou","raw_affiliation_strings":["Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, USA","Institute of Systems Engineering and Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology, Macau, China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, USA","institution_ids":["https://openalex.org/I118118575"]},{"raw_affiliation_string":"Institute of Systems Engineering and Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology, Macau, China","institution_ids":["https://openalex.org/I111950717"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042815921"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":3.9383,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.93531431,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"23","issue":"7","first_page":"6326","last_page":"6336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9970999956130981,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.8723940849304199},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.6776198148727417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5369394421577454},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47086301445961},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.4695822596549988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2731815278530121},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.06878325343132019}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8723940849304199},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.6776198148727417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5369394421577454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47086301445961},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.4695822596549988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2731815278530121},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06878325343132019},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tits.2021.3086625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2021.3086625","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6299999952316284,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1536247122","display_name":null,"funder_award_id":"JCYJ20190813152401690","funder_id":"https://openalex.org/F4320329791","funder_display_name":"Shenzhen Fundamental Research Program"},{"id":"https://openalex.org/G2086599979","display_name":null,"funder_award_id":"61773115","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329791","display_name":"Shenzhen Fundamental Research Program","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W189439419","https://openalex.org/W759229525","https://openalex.org/W1972920989","https://openalex.org/W1986840807","https://openalex.org/W1992868085","https://openalex.org/W2002730737","https://openalex.org/W2006236904","https://openalex.org/W2026662237","https://openalex.org/W2032101114","https://openalex.org/W2040263329","https://openalex.org/W2050819731","https://openalex.org/W2054195159","https://openalex.org/W2061594663","https://openalex.org/W2073288620","https://openalex.org/W2074195549","https://openalex.org/W2105060405","https://openalex.org/W2106334424","https://openalex.org/W2106378689","https://openalex.org/W2112912151","https://openalex.org/W2118240569","https://openalex.org/W2126105956","https://openalex.org/W2170766832","https://openalex.org/W2198098822","https://openalex.org/W2497712405","https://openalex.org/W2516530272","https://openalex.org/W2531521796","https://openalex.org/W2626431333","https://openalex.org/W2755052565","https://openalex.org/W2779455732","https://openalex.org/W2904387011","https://openalex.org/W2906108861","https://openalex.org/W2910903121","https://openalex.org/W2915814342","https://openalex.org/W2951307174","https://openalex.org/W2978949425","https://openalex.org/W2991364510","https://openalex.org/W3007423657","https://openalex.org/W3140592728","https://openalex.org/W4252684946","https://openalex.org/W4290734497","https://openalex.org/W4292864963"],"related_works":["https://openalex.org/W4389782626","https://openalex.org/W2359992618","https://openalex.org/W4376138746","https://openalex.org/W2171568915","https://openalex.org/W2361554335","https://openalex.org/W1595757466","https://openalex.org/W2362402143","https://openalex.org/W2073288620","https://openalex.org/W2356976268","https://openalex.org/W2495211334"],"abstract_inverted_index":{"As":[0],"a":[1,10,35,53,62,69,73,92,144],"generalization":[2],"of":[3,22,46,189,205],"the":[4,20,44,101,105,123,203],"well-known":[5],"multiple":[6],"traveling":[7,12],"salesman":[8,13],"problem,":[9],"colored":[11],"problem":[14],"(CTSP)":[15],"utilizes":[16],"colors":[17],"to":[18,25,76,116,125,180],"describe":[19],"accessibility":[21],"individual":[23],"cities":[24],"salesmen.":[26,49,110],"To":[27,50,142],"expand":[28],"its":[29,181],"application":[30],"scope,":[31],"this":[32],"work":[33],"presents":[34],"bi-objective":[36,54],"CTSP":[37],"(BCTSP)":[38],"over":[39],"hypergraphs,":[40],"taking":[41],"into":[42],"account":[43],"balance":[45],"workload":[47],"among":[48,108,133],"solve":[51],"it,":[52],"variable":[55,156],"neighborhood":[56,157],"search":[57,95,158],"(BVNS)":[58],"is":[59,114,178],"proposed":[60],"as":[61],"solution":[63],"framework.":[64],"In":[65,201],"BVNS,":[66],"we":[67],"exploit":[68],"two-stage":[70],"initialization":[71],"and":[72,80,89,154,199,215],"probability-based":[74,211],"insertion":[75],"produce":[77],"feasible":[78],"solutions":[79,102],"generate":[81],"their":[82],"neighborhood.":[83],"Next,":[84],"population-based":[85,213],"multi-insertion,":[86,120,214],"color-preserving":[87,98,216],"exchange":[88,99,217],"2-opt":[90],"constitute":[91],"powerful":[93],"local":[94],"procedure,":[96],"where":[97],"improves":[100],"by":[103,130,162],"modifying":[104],"route":[106,129],"intersections":[107],"distinct":[109],"Besides,":[111],"Delaunay":[112],"triangulation":[113],"utilized":[115],"prepare":[117],"candidates":[118],"for":[119,168],"thereby":[121],"increasing":[122],"possibility":[124],"find":[126],"an":[127,164],"optimal":[128],"shortening":[131],"links":[132],"vertices.":[134],"Extensive":[135],"experiments":[136],"are":[137,160],"conducted":[138],"on":[139],"20":[140],"cases.":[141],"make":[143],"comprehensive":[145],"comparison,":[146],"four":[147,206],"existing":[148],"methods,":[149,159],"i.e.,":[150,194],"two":[151,155],"genetic":[152],"algorithms":[153],"adapted":[161],"exploiting":[163],"elitist":[165],"non-dominated":[166],"sorting":[167],"solving":[169],"BCTSP":[170],"instances.":[171],"The":[172],"experimental":[173],"results":[174],"show":[175],"that":[176,210],"BVNS":[177,207],"superior":[179],"peers":[182],"in":[183,187,221],"achieving":[184],"Pareto":[185],"optima":[186],"terms":[188],"three":[190],"popular":[191],"performance":[192],"metrics,":[193],"hypervolume,":[195],"inverted":[196],"generational":[197],"distance,":[198],"C-metric.":[200],"addition,":[202],"study":[204],"variants":[208],"reveals":[209],"insertion,":[212],"play":[218],"significant":[219],"roles":[220],"BVNS\u2019s":[222],"high":[223],"performance.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}