{"id":"https://openalex.org/W2295128024","doi":"https://doi.org/10.1080/00207160.2015.1071359","title":"Approximation performance of ant colony optimization for the TSP(1,2) problem","display_name":"Approximation performance of ant colony optimization for the TSP(1,2) problem","publication_year":2015,"publication_date":"2015-07-10","ids":{"openalex":"https://openalex.org/W2295128024","doi":"https://doi.org/10.1080/00207160.2015.1071359","mag":"2295128024"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1071359","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1071359","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5045295754","display_name":"Xue Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xue Peng","raw_affiliation_strings":["School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108402799","display_name":"Yuren Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]},{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuren Zhou","raw_affiliation_strings":["School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China; School of Advanced Computing, Sun Yat-sen University, Guangzhou 510275, China","School of Advanced Computing, Sun Yat-sen University, Guangzhou 510275, China","School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China; School of Advanced Computing, Sun Yat-sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Advanced Computing, Sun Yat-sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080289760","display_name":"Gang Xu","orcid":"https://orcid.org/0000-0003-2329-9458"},"institutions":[{"id":"https://openalex.org/I141649914","display_name":"Nanchang University","ror":"https://ror.org/042v6xz23","country_code":"CN","type":"education","lineage":["https://openalex.org/I141649914"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Xu","raw_affiliation_strings":["Department of Mathematics, Nanchang University, Nanchang 330031, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanchang University, Nanchang 330031, China","institution_ids":["https://openalex.org/I141649914"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108402799"],"corresponding_institution_ids":["https://openalex.org/I157773358","https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":0.8881,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83753571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"93","issue":"10","first_page":"1683","last_page":"1694"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998000264167786,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.8325619697570801},{"id":"https://openalex.org/keywords/ant-colony-optimization-algorithms","display_name":"Ant colony optimization algorithms","score":0.796045184135437},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6398639678955078},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6396439671516418},{"id":"https://openalex.org/keywords/extremal-optimization","display_name":"Extremal optimization","score":0.5648859739303589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5561794638633728},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5070531368255615},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.4755299389362335},{"id":"https://openalex.org/keywords/local-search","display_name":"Local search (optimization)","score":0.4316522777080536},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41725990176200867},{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.41218122839927673},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38902801275253296},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33864039182662964},{"id":"https://openalex.org/keywords/meta-optimization","display_name":"Meta-optimization","score":0.13589659333229065}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8325619697570801},{"id":"https://openalex.org/C40128228","wikidata":"https://www.wikidata.org/wiki/Q460851","display_name":"Ant colony optimization algorithms","level":2,"score":0.796045184135437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6398639678955078},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6396439671516418},{"id":"https://openalex.org/C188919014","wikidata":"https://www.wikidata.org/wiki/Q5422296","display_name":"Extremal optimization","level":4,"score":0.5648859739303589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5561794638633728},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5070531368255615},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.4755299389362335},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.4316522777080536},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41725990176200867},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.41218122839927673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38902801275253296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33864039182662964},{"id":"https://openalex.org/C4935549","wikidata":"https://www.wikidata.org/wiki/Q6822261","display_name":"Meta-optimization","level":3,"score":0.13589659333229065}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1071359","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1071359","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4750680818","display_name":null,"funder_award_id":"61170081,61472143","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1494455882","https://openalex.org/W1532063097","https://openalex.org/W1543480758","https://openalex.org/W1635549461","https://openalex.org/W1979409761","https://openalex.org/W1992220653","https://openalex.org/W1993561093","https://openalex.org/W2039865013","https://openalex.org/W2042986967","https://openalex.org/W2052176278","https://openalex.org/W2057398816","https://openalex.org/W2086917808","https://openalex.org/W2100308637","https://openalex.org/W2105039734","https://openalex.org/W2131004531","https://openalex.org/W2141355868","https://openalex.org/W2144643443","https://openalex.org/W2401610261","https://openalex.org/W2614370452"],"related_works":["https://openalex.org/W4385871958","https://openalex.org/W3007033359","https://openalex.org/W1611875833","https://openalex.org/W4200602616","https://openalex.org/W2144575552","https://openalex.org/W2559478821","https://openalex.org/W2625683255","https://openalex.org/W2187257958","https://openalex.org/W2624176670","https://openalex.org/W2062103774"],"abstract_inverted_index":{"Ant":[0],"colony":[1],"optimization":[2,17],"(ACO)":[3],"is":[4,44,49],"a":[5],"kind":[6],"of":[7,24,59,76],"powerful":[8],"and":[9,30,40,79,91],"popular":[10],"randomized":[11],"search":[12,98],"heuristic":[13,80],"for":[14],"solving":[15],"combinatorial":[16],"problems.":[18],"This":[19],"paper":[20],"investigates":[21],"the":[22,33,64,74,83,96],"performance":[23],"two":[25,41,52],"ACO":[26,53,94],"algorithms,":[27],"called":[28],"MMASOrd\u2217":[29],"MMASArb\u2217,":[31],"on":[32,82,100],"travelling":[34],"salesman":[35],"problem":[36],"with":[37,61],"distance":[38],"one":[39],"(TSP(1,2))":[42],"which":[43],"an":[45,56,89],"NP-complete":[46],"problem.":[47],"It":[48],"shown":[50],"that":[51,93],"algorithms":[54,99],"obtain":[55],"approximation":[57,84],"ratio":[58],"3/2":[60],"regard":[62],"to":[63],"optimal":[65],"solutions":[66],"in":[67],"expected":[68],"polynomial":[69],"runtimes.":[70],"We":[71],"also":[72],"study":[73],"influence":[75],"pheromone":[77],"information":[78,81],"performance.":[85],"Finally,":[86],"we":[87],"construct":[88],"instance":[90],"demonstrate":[92],"outperforms":[95],"local":[97],"this":[101],"instance.":[102]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
