{"id":"https://openalex.org/W1992220653","doi":"https://doi.org/10.1007/s11721-011-0059-7","title":"Theoretical analysis of two ACO approaches for the traveling salesman problem","display_name":"Theoretical analysis of two ACO approaches for the traveling salesman problem","publication_year":2011,"publication_date":"2011-10-13","ids":{"openalex":"https://openalex.org/W1992220653","doi":"https://doi.org/10.1007/s11721-011-0059-7","mag":"1992220653"},"language":"en","primary_location":{"id":"doi:10.1007/s11721-011-0059-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11721-011-0059-7","pdf_url":null,"source":{"id":"https://openalex.org/S120411249","display_name":"Swarm Intelligence","issn_l":"1935-3812","issn":["1935-3812","1935-3820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Swarm Intelligence","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/A5004366897","display_name":"Timo K\u00f6tzing","orcid":"https://orcid.org/0000-0002-1028-5228"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Timo K\u00f6tzing","raw_affiliation_strings":["Algorithms and Complexity, Max-Planck-Institut f\u00fcr Informatik, 66123, Saarbr\u00fccken, Germany","Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity, Max-Planck-Institut f\u00fcr Informatik, 66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089531887","display_name":"Frank Neumann","orcid":"https://orcid.org/0000-0002-2721-3618"},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Frank Neumann","raw_affiliation_strings":["School of Computer Science, University of Adelaide, Adelaide, SA, 5005, Australia","*University of Adelaide"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Adelaide, Adelaide, SA, 5005, Australia","institution_ids":["https://openalex.org/I5681781"]},{"raw_affiliation_string":"*University of Adelaide","institution_ids":["https://openalex.org/I5681781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034122679","display_name":"Heiko R\u00f6glin","orcid":"https://orcid.org/0009-0006-8438-3986"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Heiko R\u00f6glin","raw_affiliation_strings":["Department of Computer Science, University of Bonn, Bonn, Germany","University of Bonn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038689623","display_name":"Carsten Witt","orcid":"https://orcid.org/0000-0002-6105-7700"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Carsten Witt","raw_affiliation_strings":["DTU Informatics, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark","#N##TAB##TAB##TAB##TAB# Technical University of Denmark#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DTU Informatics, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# Technical University of Denmark#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004366897"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210109712"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":7.777,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.97020284,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.996399998664856,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9959999918937683,"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":0.8053866624832153},{"id":"https://openalex.org/keywords/extremal-optimization","display_name":"Extremal optimization","score":0.7754515409469604},{"id":"https://openalex.org/keywords/ant-colony-optimization-algorithms","display_name":"Ant colony optimization algorithms","score":0.7209697365760803},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6195470094680786},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.611335277557373},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6056519150733948},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5842772126197815},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5205448865890503},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.4952069818973541},{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.4717836081981659},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4581770598888397},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45366910099983215},{"id":"https://openalex.org/keywords/quadratic-assignment-problem","display_name":"Quadratic assignment problem","score":0.4231763482093811},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.4115600287914276},{"id":"https://openalex.org/keywords/cross-entropy-method","display_name":"Cross-entropy method","score":0.41017428040504456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3143273591995239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3110390603542328},{"id":"https://openalex.org/keywords/meta-optimization","display_name":"Meta-optimization","score":0.20314887166023254}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.8053866624832153},{"id":"https://openalex.org/C188919014","wikidata":"https://www.wikidata.org/wiki/Q5422296","display_name":"Extremal optimization","level":4,"score":0.7754515409469604},{"id":"https://openalex.org/C40128228","wikidata":"https://www.wikidata.org/wiki/Q460851","display_name":"Ant colony optimization algorithms","level":2,"score":0.7209697365760803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6195470094680786},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.611335277557373},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6056519150733948},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5842772126197815},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5205448865890503},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.4952069818973541},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.4717836081981659},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4581770598888397},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45366910099983215},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.4231763482093811},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.4115600287914276},{"id":"https://openalex.org/C75782508","wikidata":"https://www.wikidata.org/wiki/Q3333633","display_name":"Cross-entropy method","level":4,"score":0.41017428040504456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3143273591995239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3110390603542328},{"id":"https://openalex.org/C4935549","wikidata":"https://www.wikidata.org/wiki/Q6822261","display_name":"Meta-optimization","level":3,"score":0.20314887166023254},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s11721-011-0059-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11721-011-0059-7","pdf_url":null,"source":{"id":"https://openalex.org/S120411249","display_name":"Swarm Intelligence","issn_l":"1935-3812","issn":["1935-3812","1935-3820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Swarm Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:digital.library.adelaide.edu.au:2440/70586","is_oa":false,"landing_page_url":"http://hdl.handle.net/2440/70586","pdf_url":null,"source":{"id":"https://openalex.org/S4306401835","display_name":"Adelaide Research & Scholarship (AR&S) (University of Adelaide)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5681781","host_organization_name":"The University of Adelaide","host_organization_lineage":["https://openalex.org/I5681781"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1007/s11721-011-0059-7","raw_type":"Journal article"},{"id":"pmh:oai:pure.atira.dk:publications/4ef44d47-399a-47f2-9553-2aa42188df99","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/4ef44d47-399a-47f2-9553-2aa42188df99","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"K\u00f6tzing , T , Neumann , F , R\u00f6glin , H &amp; Witt , C 2012 , ' Theoretical analysis of two ACO approaches for the traveling salesman problem ' , Swarm Intelligence , vol. 6 , no. 1 , pp. 1-21 . https://doi.org/10.1007/s11721-011-0059-7","raw_type":"article"},{"id":"pmh:oai:pure.mpg.de:item_1858453","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-BE12-E","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Swarm Intelligence","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W187767610","https://openalex.org/W1512383952","https://openalex.org/W1573676079","https://openalex.org/W1632066424","https://openalex.org/W1635549461","https://openalex.org/W1683332710","https://openalex.org/W1801849579","https://openalex.org/W1915653146","https://openalex.org/W1965978641","https://openalex.org/W1993561093","https://openalex.org/W2011904305","https://openalex.org/W2015191101","https://openalex.org/W2034053794","https://openalex.org/W2039865013","https://openalex.org/W2042096932","https://openalex.org/W2079868147","https://openalex.org/W2100137329","https://openalex.org/W2106371135","https://openalex.org/W2144643443","https://openalex.org/W2154929945","https://openalex.org/W2156622046","https://openalex.org/W2293696308","https://openalex.org/W4292408555","https://openalex.org/W4300005723"],"related_works":["https://openalex.org/W4200179302","https://openalex.org/W3001379520","https://openalex.org/W2549218906","https://openalex.org/W3031145066","https://openalex.org/W588755621","https://openalex.org/W2123233098","https://openalex.org/W2146364482","https://openalex.org/W4210470436","https://openalex.org/W4224271060","https://openalex.org/W2072501113"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
