Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances
Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm...
Saved in:
| Published in: | IEEE transactions on evolutionary computation Vol. 13; no. 5; pp. 1083 - 1092 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York, NY
IEEE
01.10.2009
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 1089-778X, 1941-0026 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime. |
|---|---|
| AbstractList | Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime. |
| Author | Yuren Zhou |
| Author_xml | – sequence: 1 givenname: Yuren Zhou surname: Yuren Zhou fullname: Yuren Zhou, Yuren Zhou |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22159711$$DView record in Pascal Francis |
| BookMark | eNp9kU9PGzEQxa0KpAboB6h6WVUqPS14_GdtH1EEhQoJ1KZVbytnbYPRxg62c0g_PQ6JcuDAZTy2fu-NPO8IHYQYLEKfAZ8BYHU-u_w7PSMYq1qg4wJ_QBNQDFqMSXdQeyxVK4T89xEd5fyEMTAOaoJ-_lqF4he2uQh6XGefm-gaHeq1NNM4xrBu7pYV8P918bG-jw8x-fK4aFxMzez3fXMTctFhsPkEHTo9Zvtpdx6jP1eXs-l1e3v342Z6cdsOVPLSQse00oQZ1lFhmANqFDZKGye54nOKHbcSq_l8MHQAJTkjhjFtDe0sMcLRY_R967tM8Xllc-kXPg92HHWwcZV7KTgGySWp5Om7JOWYMklYBb--AZ_iKtWNVDcuGJG0kxX6toN0HvToUv21z_0y-YVO654Q4EoAVA623JBizsm6PQK434TVb8LqN2H1u7CqRrzRDL68brwk7cd3lV-2Sm-t3U_ilaGM0xdVcaHl |
| CODEN | ITEVF5 |
| CitedBy_id | crossref_primary_10_1109_TASE_2021_3087353 crossref_primary_10_1007_s00453_011_9606_2 crossref_primary_10_1016_j_tcs_2017_10_012 crossref_primary_10_1145_3472304 crossref_primary_10_1016_j_eswa_2011_07_062 crossref_primary_10_1007_s00500_014_1279_8 crossref_primary_10_4018_IJAMC_2017070104 crossref_primary_10_1007_s42452_025_06809_5 crossref_primary_10_1109_TEVC_2018_2878221 crossref_primary_10_1109_TCC_2021_3122445 crossref_primary_10_1016_j_swevo_2016_06_006 crossref_primary_10_1016_j_asoc_2021_107991 crossref_primary_10_1007_s11042_017_5466_3 crossref_primary_10_1109_JSEN_2022_3203127 crossref_primary_10_3390_s151024996 crossref_primary_10_1109_TFUZZ_2013_2276863 crossref_primary_10_1109_TCYB_2025_3587025 crossref_primary_10_4028_www_scientific_net_AMR_605_607_2149 crossref_primary_10_1016_j_engappai_2018_03_015 crossref_primary_10_1109_JSYST_2018_2795255 crossref_primary_10_1109_ACCESS_2022_3233786 crossref_primary_10_1016_j_swevo_2021_100875 crossref_primary_10_1007_s40747_020_00138_3 crossref_primary_10_1007_s11721_011_0059_7 crossref_primary_10_3390_s20164480 crossref_primary_10_1109_TEVC_2017_2667713 crossref_primary_10_1155_2016_6051046 crossref_primary_10_1109_TIE_2019_2896235 crossref_primary_10_1007_s11424_019_8176_2 crossref_primary_10_1080_00207543_2010_507608 crossref_primary_10_1080_00207160_2015_1071359 crossref_primary_10_1117_1_JMI_9_5_055001 crossref_primary_10_1109_TIE_2019_2901644 crossref_primary_10_1016_j_ins_2017_12_047 crossref_primary_10_1016_j_plrev_2024_09_014 crossref_primary_10_1109_ACCESS_2019_2928012 crossref_primary_10_1016_j_eswa_2015_11_026 crossref_primary_10_3390_s18041020 crossref_primary_10_1007_s10489_021_02424_0 crossref_primary_10_1016_j_eswa_2012_10_011 crossref_primary_10_1016_j_jda_2011_06_002 crossref_primary_10_1155_2015_713043 crossref_primary_10_1109_ACCESS_2019_2934889 crossref_primary_10_3390_a14100295 crossref_primary_10_1109_JSEN_2022_3150065 crossref_primary_10_1039_c2ib00133k crossref_primary_10_1007_s11704_013_2302_4 crossref_primary_10_1080_00207721_2023_2293687 crossref_primary_10_1049_iet_wss_2011_0128 crossref_primary_10_1016_j_eswa_2018_09_045 crossref_primary_10_4018_ijncr_2014070102 crossref_primary_10_4018_IJSIR_2017100101 crossref_primary_10_1016_j_tcs_2014_06_035 crossref_primary_10_1145_2492248_2492271 crossref_primary_10_1016_j_apm_2020_05_009 |
| Cites_doi | 10.1109/TSMCC.2004.841903 10.1016/j.cor.2006.12.017 10.1016/j.tcs.2005.05.020 10.1007/s11009-007-9047-1 10.1287/opre.21.2.498 10.1016/S0167-739X(00)00044-3 10.1145/1276958.1276964 10.1016/j.ipl.2007.06.016 10.1016/S0377-2217(99)00284-2 10.1007/s11721-007-0001-1 10.1007/978-3-540-74446-7_5 10.1109/CEC.2007.4424512 10.1109/3477.484436 10.1109/TEVC.2002.802444 10.1145/1068009.1068202 10.1109/MCI.2006.329691 10.1016/j.ipl.2007.08.013 10.1007/s11009-006-7291-4 10.1007/978-3-540-92695-5_12 10.1145/1276958.1277118 10.1016/j.jda.2004.02.001 10.1016/S0304-3975(01)00182-7 10.1016/S0304-3975(02)00137-8 10.1007/s11721-008-0023-3 10.1109/CEC.2007.4424800 10.1016/S0167-739X(00)00043-1 10.1023/B:ANOR.0000039526.52305.af |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2009 |
| Copyright_xml | – notice: 2015 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2009 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1109/TEVC.2009.2016570 |
| DatabaseName | Accès UTTOP - IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Applied Sciences |
| EISSN | 1941-0026 |
| EndPage | 1092 |
| ExternalDocumentID | 2294849681 22159711 10_1109_TEVC_2009_2016570 5200345 |
| Genre | orig-research |
| GroupedDBID | -~X .DC 0R~ 29I 4.4 5GY 5VS 6IF 6IK 6IL 6IN 97E AAJGR AARMG AASAJ AAWTH ABAZT ABJNI ABQJQ ABVLG ACGFO ACGFS ACIWK ADZIZ AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CHZPO CS3 EBS EJD HZ~ H~9 IEGSK IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P PQQKQ RIA RIE RIL RNS TN5 VH1 AAYXX CITATION IQODW RIG 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| ID | FETCH-LOGICAL-c385t-164a9a24d4637d4f13d90d9adf8595b30f5e809bbcd3c198542d44aed36e2d7f3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 79 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000270144100009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1089-778X |
| IngestDate | Sun Nov 09 12:02:58 EST 2025 Thu Oct 02 09:48:17 EDT 2025 Sun Jun 29 12:25:00 EDT 2025 Mon Jul 21 09:13:57 EDT 2025 Sat Nov 29 03:13:45 EST 2025 Tue Nov 18 21:29:49 EST 2025 Tue Aug 26 16:47:42 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Insecta Evolutionary algorithm Travelling salesman problem Combinatorial optimization Formicoidea heuristic algorithm Swarm intelligence Ant colony optimization (ACO) Aculeata Mathematical programming Probabilistic approach Complete graph Pheromone Social insect Particle swarm optimization Arthropoda Heuristic method Minimax method Problem solving runtime analysis Visibility Hymenoptera Invertebrata Algorithm analysis traveling salesman problem (TSP) |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c385t-164a9a24d4637d4f13d90d9adf8595b30f5e809bbcd3c198542d44aed36e2d7f3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23 |
| PQID | 857428368 |
| PQPubID | 23500 |
| PageCount | 10 |
| ParticipantIDs | proquest_miscellaneous_875018582 crossref_primary_10_1109_TEVC_2009_2016570 proquest_journals_857428368 pascalfrancis_primary_22159711 ieee_primary_5200345 proquest_miscellaneous_35034824 crossref_citationtrail_10_1109_TEVC_2009_2016570 |
| PublicationCentury | 2000 |
| PublicationDate | 2009-10-01 |
| PublicationDateYYYYMMDD | 2009-10-01 |
| PublicationDate_xml | – month: 10 year: 2009 text: 2009-10-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: New York |
| PublicationTitle | IEEE transactions on evolutionary computation |
| PublicationTitleAbbrev | TEVC |
| PublicationYear | 2009 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref12 ref15 ref14 ref31 ref30 ref33 ref11 ref10 ref2 zlochin (ref9) 2004; 131 ref16 ref19 wegener (ref32) 2005; 3580 neumann (ref18) 2006; 4288 ref24 ref23 ref25 ref20 lawler (ref26) 1985 dorigo (ref3) 2004 dorigo (ref1) 1991 ref22 ref21 ref28 ref27 witt (ref13) 2005; 3404 ref29 ref8 ref7 friedrich (ref17) 2007 ref4 ref6 ref5 |
| References_xml | – volume: 3580 start-page: 589 year: 2005 ident: ref32 article-title: simulated annealing beats metropolis in combinatorial optimization publication-title: Proc ICALP – start-page: 1 year: 1985 ident: ref26 publication-title: The Traveling Salesman Problem A Guided Tour of Combinatorial Optimization – ident: ref15 doi: 10.1109/TSMCC.2004.841903 – ident: ref19 doi: 10.1016/j.cor.2006.12.017 – ident: ref5 doi: 10.1016/j.tcs.2005.05.020 – year: 1991 ident: ref1 publication-title: The Ant System An Autocatalytic Optimizing Process – ident: ref22 doi: 10.1007/s11009-007-9047-1 – ident: ref30 doi: 10.1287/opre.21.2.498 – ident: ref6 doi: 10.1016/S0167-739X(00)00044-3 – ident: ref21 doi: 10.1145/1276958.1276964 – ident: ref33 doi: 10.1016/j.ipl.2007.06.016 – ident: ref31 doi: 10.1016/S0377-2217(99)00284-2 – ident: ref29 doi: 10.1007/s11721-007-0001-1 – ident: ref27 doi: 10.1007/978-3-540-74446-7_5 – ident: ref20 doi: 10.1109/CEC.2007.4424512 – volume: 4288 start-page: 618 year: 2006 ident: ref18 article-title: runtime analysis of a simple ant colony optimization algorithm publication-title: Proc 15th Int l Symp Algorithms and Computation (ISAAC) – ident: ref2 doi: 10.1109/3477.484436 – ident: ref7 doi: 10.1109/TEVC.2002.802444 – ident: ref14 doi: 10.1145/1068009.1068202 – ident: ref4 doi: 10.1109/MCI.2006.329691 – ident: ref25 doi: 10.1016/j.ipl.2007.08.013 – ident: ref8 doi: 10.1007/s11009-006-7291-4 – ident: ref24 doi: 10.1007/978-3-540-92695-5_12 – start-page: 797 year: 2007 ident: ref17 article-title: approximating covering problems by randomized search heuristics using multiobjective models publication-title: Proc Genetic Evol Comput Conf (GECCO) doi: 10.1145/1276958.1277118 – ident: ref11 doi: 10.1016/j.jda.2004.02.001 – ident: ref10 doi: 10.1016/S0304-3975(01)00182-7 – ident: ref12 doi: 10.1016/S0304-3975(02)00137-8 – volume: 3404 start-page: 44 year: 2005 ident: ref13 article-title: worst-case and average-case approximations by simple randomized search heuristic publication-title: Proc 10th Ann Symp Theoretical Aspects Comput Sci – start-page: 153 year: 2004 ident: ref3 publication-title: Ant Colony Optimization – ident: ref23 doi: 10.1007/s11721-008-0023-3 – ident: ref16 doi: 10.1109/CEC.2007.4424800 – ident: ref28 doi: 10.1016/S0167-739X(00)00043-1 – volume: 131 start-page: 373 year: 2004 ident: ref9 article-title: model-based search for combinatorial optimization: a critical survey publication-title: Ann Oper Res doi: 10.1023/B:ANOR.0000039526.52305.af |
| SSID | ssj0014519 |
| Score | 2.2782192 |
| Snippet | Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1083 |
| SubjectTerms | Algorithm design and analysis Algorithmics. Computability. Computer arithmetics Algorithms Ant colony optimization Ant colony optimization (ACO) Applied sciences Artificial intelligence Benchmarking Biological system modeling Colonies Combinatorial analysis Computer science; control theory; systems Evolution (biology) Evolutionary algorithms Evolutionary computation Exact sciences and technology Flows in networks. Combinatorial problems Graphs heuristic algorithm Heuristic algorithms Learning and adaptive systems Logistics Operational research and scientific management Operational research. Management science Optimization Particle swarm optimization Partitioning algorithms Runtime runtime analysis Theoretical computing Traveling salesman problem traveling salesman problem (TSP) Traveling salesman problems |
| Title | Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances |
| URI | https://ieeexplore.ieee.org/document/5200345 https://www.proquest.com/docview/857428368 https://www.proquest.com/docview/35034824 https://www.proquest.com/docview/875018582 |
| Volume | 13 |
| WOSCitedRecordID | wos000270144100009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0026 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014519 issn: 1089-778X databaseCode: RIE dateStart: 19970101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB61FQc4UGhBhELxgRMi1K_E9rFatQIOpYIF7S2yY7tU6iZoN4vEv8d2vFERD4lbIk8ky2OPZzIz3wfwkoVbigmjS0E8L7kLAYqucFtaRVvPuGVa6UQ2IS4u5GKhLnfg9dQL45xLxWfuTXxMuXzbt5v4q-wkQgQxXu3CrhD12Ks1ZQwiTMpYTK-CxygXOYNJsDqZn32ZjciUNDbvRF7iW3dQIlWJJZF6HVbFj3QWv1nmdN2c7__fRB_A_exWotNxHzyEHdcdwP6WsgHlE3wA927hDx7C-4-RKGLp0BaaBPUe6S68DmgWrGL3A30IJmWZezXR6c1Vv7oevi5RcHXR_NMlepe8y2BrHsHn87P57G2ZyRXKlslqKEOYFNRAueU1E5Z7wqzCVmnrI-KZYdhXTmJlTGtZS5SsOLWca2dZ7agVnj2Gva7v3BNARGBrPDPEUMapU4aSWlpTU-eN1sYXgLfL3bQZeTwSYNw0KQLBqokaioSYqskaKuDV9Mm3EXbjX8KHUQWTYF79Ao5_0ek0ToObowQhBRxtldzkk7tuZCUiBl0tC3gxjYYjF_MounP9Zt2wCkdIIF4A-otECAJxcIQkffrnqR3B3ZSVSkWBz2BvWG3cc7jTfh-u16vjtLF_AgIL9as |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Nb9QwEB2VggQ9UGiLGlpaHzghQv2VxD5Wq1YtlKWCBe0tsmMbKnWTajdbiX-P7WSjogISt0SeSJbHHs9kZt4DeM38LcUKrdKCOJ5y6wMUleEqNZJWjnHDlFSRbKIYj8V0Ki_X4O3QC2OtjcVn9l14jLl801TL8KvsKEAEMZ49gIcZ5xR33VpDziAApXTl9NL7jGLa5zAJlkeTk2-jDpuShvadwEx85xaKtCqhKFIt_Lq4jtDinm2OF87p5v9N9Rk87R1LdNzthOewZust2FyRNqD-DG_Bxh0Ewm14_zlQRcwsWoGToMYhVfvXFo28Xax_ok_eqMz6bk10fP29mV-1P2bIO7to8uUSnUf_0lubHfh6ejIZnaU9vUJaMZG1qQ-UvCIoNzxnheGOMCOxkcq4gHmmGXaZFVhqXRlWESkyTg3nyhqWW2oKx17Aet3UdhcQKbDRjmmiKePUSk1JLozOqXVaKe0SwKvlLqseezxQYFyXMQbBsgwaCpSYsuw1lMCb4ZObDnjjX8LbQQWDYL_6CRz8ptNhnHpHRxaEJLC3UnLZn91FKbIioNDlIoHDYdQfupBJUbVtlouSZTiAAvEE0F8kfBiIvSsk6Ms_T-0QHp9NPl6UF-fjD3vwJOaoYongPqy386V9BY-q2_ZqMT-Im_wX6aL48g |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Runtime+Analysis+of+an+Ant+Colony+Optimization+Algorithm+for+TSP+Instances&rft.jtitle=IEEE+transactions+on+evolutionary+computation&rft.au=Zhou%2C+Yuren&rft.date=2009-10-01&rft.issn=1089-778X&rft.volume=13&rft.issue=5&rft_id=info:doi/10.1109%2FTEVC.2009.2016570&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-778X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-778X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-778X&client=summon |