The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Ant colony optimization theory: A survey
Open accessAbstract
Research on a new metaheuristic for optimization is often initially focused on proof-of-concept applications. It is only after experimental work has shown the practical interest of the method that researchers try to deepen their understanding of the method's functioning not only through more and more sophisticated experiments but also by means of an effort to build a theory. Tackling questions such as "how and why the method works" is important, because finding an answer may help in improving its applicability. Ant colony optimization, which was introduced in the early 1990s as a novel technique for solving hard combinatorial optimization problems, finds itself currently at this point of its life cycle. With this article we provide a survey on theoretical results on ant colony optimization. First, we review some convergence results. Then we discuss relations between ant colony optimization algorithms and other approximate methods for optimization. Finally, we focus on some research efforts directed at gaining a deeper understanding of the behavior of ant colony optimization algorithms. Throughout the paper we identify some open questions with a certain interest of being solved in the near future.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
Ant colony system: a cooperative learning approach to the traveling salesman problem
Dorigo, M., & Gambardella, L. M. (1997) · IEEE Transactions on Evolutionary Computation · doi:10.1109/4235.585892 · Cited by 8,081
Self-citationGlover, F., & Laguna, M. (1997) · doi:10.1007/978-1-4615-6089-0 · Cited by 3,001
AntNet: Distributed Stigmergetic Control for Communications Networks
Di Caro, G., & Dorigo, M. (1998) · Journal of Artificial Intelligence Research · doi:10.1613/jair.530 · Cited by 1,579
Self-citation
Research works printed but not linked: 48
- Baum, 1968, Growth transformations for functions on manifolds, Pacific J. Math., 27, 211, 10.2140/pjm.1968.27.211 · DOI · Paper page
- M. Birattari, G. Di Caro, M. Dorigo, Toward the formal foundation of ant programming, in: M. Dorigo, G. Di Caro, M. Sampels (Eds.), Ant Algorithms, Proc. ANTS 2002, Third Internat. Workshop, Lecture Notes in Computer Science, Vol. 2463, Springer, Berlin, Germany, 2002, pp. 188–201. · DOI
- C. Blum, Theoretical and Practical Aspects of Ant Colony Optimization, Dissertations in Artificial Intelligence, Vol. 282, Akademische Verlagsgesellschaft Aka GmbH, Berlin, Germany, 2004. · doi:10.1007/978-3-540-28646-2_11
- Blum, 2005, Beam-ACO—Hybridizing ant colony optimization with beam search: an application to open shop scheduling, Comput. Oper. Res., 32, 1565, 10.1016/j.cor.2003.11.018 · DOI · Paper page
- C. Blum, M. Dorigo, Deception in ant colony optimization, in: M. Dorigo, M. Birattari, C. Blum, L.M. Gambardella, F. Mondada, T. Stützle (Eds.), Proc. ANTS 2004, Fourth Internat. Workshop on Ant Colony Optimization and Swarm Intelligence, Lecture Notes in Computer Science, Vol. 3172, Springer, Berlin, Germany, 2004, pp. 119–130. · doi:10.1007/978-3-540-28646-2_11
- Blum, 2004, The hyper-cube framework for ant colony optimization, IEEE Trans. Systems, Man, Cybernet.-Part B, 34, 1161, 10.1109/TSMCB.2003.821450 · DOI · Paper page
- Blum, 2005, Search bias in ant colony optimization: on the role of competition-balanced systems, IEEE Trans. Evol. Comput., 9, 159, 10.1109/TEVC.2004.841688 · doi:10.1109/tevc.2004.841688
- Blum, 2003, Metaheuristics in combinatorial optimization: overview and conceptual comparison, ACM Comput. Surveys, 35, 268, 10.1145/937503.937505 · DOI · Paper page
- Blum, 2002, Ant Colony Optimization for FOP shop scheduling: a case study on different pheromone representations, Vol. 2, 1558
- C. Blum, M. Sampels, When model bias is stronger than selection pressure, in: J.J. Merelo Guervós et al. (Eds.), Proc. PPSN-VII, Seventh Internat. Conf. on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, Vol. 2439, Springer, Berlin, Germany, 2002, pp. 893–902. · doi:10.1007/3-540-45712-7_86
- Blum, 2004, An ant colony optimization algorithm for shop scheduling problems, J. Math. Model. Algorithms, 3, 285, 10.1023/B:JMMA.0000038614.39977.6f · doi:10.1023/b:jmma.0000038614.39977.6f
- Černý, 1985, A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm, J. Optim. Theory Appl., 45, 41, 10.1007/BF00940812 · DOI · Paper page
- Costa, 1997, Ants can color graphs, J. Oper. Res. Soc., 48, 295, 10.1057/palgrave.jors.2600357 · DOI · Paper page
- J.S. de Bonet, C.L. Isbell Jr., P. Viola, MIMIC: finding optima by estimating probability densities, in: M.C. Mozer, M.I. Jordan, T. Petsche (Eds.), Adv. Neural Inform. Process. Systems, Vol. 7 (NIPS7), MIT Press, Cambridge, MA, 1997, pp. 424–431.
- Deb, 1993, Analyzing deception in trap functions, Vol. 2, 93
- M.L. den Besten, T. Stützle, M. Dorigo, Ant colony optimization for the total weighted tardiness problem, in: M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J.J. Merelo, H.-P. Schwefel (Eds.), Proc. PPSN-VI, Sixth Internat. Conf. on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, Vol. 1917, Springer, Berlin, Germany, 2000, pp. 611–620. · DOI
- Deneubourg, 1990, The self-organizing exploratory pattern of the argentine ant, J. Insect Behav., 3, 159, 10.1007/BF01417909 · DOI · Paper page
- M. Dorigo, Optimization, learning and natural algorithms (in Italian), Ph.D. Thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1992.
- Dorigo, 1996, Ant system: optimization by a colony of cooperating agents, IEEE Trans. Systems, Man, Cybernet.-Part B, 26, 29, 10.1109/3477.484436 · DOI · Paper page
- M. Dorigo, M. Zlochin, N. Meuleau, M. Birattari, Updating ACO pheromones using stochastic gradient ascent and cross-entropy methods, in: S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, G.R. Raidl (Eds.), Applications of Evolutionary Computing, Proc. EvoWorkshops 2002, Lecture Notes in Computer Science, Vol. 2279, Springer, Berlin, Germany, 2002, pp. 21–30. · DOI
- Gagné, 2002, Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times, J. Oper. Res. Soc., 53, 895, 10.1057/palgrave.jors.2601390 · doi:10.1057/palgrave.jors.2601390
- Gambardella, 2000, Ant colony system hybridized with a new local search for the sequential ordering problem, INFORMS J. Comput., 12, 237, 10.1287/ijoc.12.3.237.12636 · DOI · Paper page
- Glover, 1989, Tabu search—Part I, ORSA J. Comput., 1, 190, 10.1287/ijoc.1.3.190 · DOI · Paper page
- Glover, 1990, Tabu search—Part II, ORSA J. Comput., 2, 4, 10.1287/ijoc.2.1.4 · DOI · Paper page
- F. Glover, G. Kochenberger (Eds.), Handbook of Metaheuristics, Kluwer Academic Publishers, Norwell, MA, 2002. · DOI · Paper page
- M. Guntsch, M. Middendorf, Pheromone modification strategies for ant algorithms applied to dynamic TSP, in: E.J.W. Boers, J. Gottlieb, P.L. Lanzi, R.E. Smith, S. Cagnoni, E. Hart, G.R. Raidl, H. Tijink (Eds.), Applications of Evolutionary Computing: Proc. EvoWorkshops 2001, Lecture Notes in Computer Science, Vol. 2037, Springer, Berlin, Germany, 2001, pp. 213–222. · DOI
- Gutjahr, 2000, A graph-based ant system and its convergence, Future Gen. Comput. Systems, 16, 873, 10.1016/S0167-739X(00)00044-3 · DOI · Paper page
- Gutjahr, 2002, ACO algorithms with guaranteed convergence to the optimal solution, Inform. Process. Lett., 82, 145, 10.1016/S0020-0190(01)00258-7 · doi:10.1016/s0020-0190(01)00258-7
- M.I. Jordan (Ed.), Learning in Graphical Models, MIT Press, Cambridge, MA, 1998. · DOI · Paper page
- L. Kallel, B. Naudts, A. Rogers (Eds.), Theoretical Aspects of Evolutionary Computing, Natural Computing Series, Springer, Berlin, Germany, 2001. · DOI
- Kirkpatrick, 1983, Optimization by simulated annealing, Science, 220, 671, 10.1126/science.220.4598.671 · DOI · Paper page
- Maniezzo, 1999, Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem, INFORMS J. Comput., 11, 358, 10.1287/ijoc.11.4.358 · DOI
- Maniezzo, 1999, The ant system applied to the quadratic assignment problem, IEEE Trans. Data Knowledge Eng., 11, 769, 10.1109/69.806935 · DOI · Paper page
- D. Merkle, M. Middendorf, Modelling ACO: composed permutation problems, in: M. Dorigo, G. Di Caro, M. Sampels (Eds.), Ant Algorithms, Proc. ANTS 2002, Third Internat. Workshop, Lecture Notes in Computer Science, Vol. 2463, Springer, Berlin, Germany, 2002, pp. 149–162.
- Merkle, 2002, Modelling the dynamics of ant colony optimization algorithms, Evol. Comput., 10, 235, 10.1162/106365602760234090 · doi:10.1162/106365602760234090
- D. Merkle, M. Middendorf, Competition controlled pheromone update for ant colony optimization, in: M. Dorigo, M. Birattari, C. Blum, L.M. Gambardella, F. Mondada, T. Stützle (Eds.), Proc. ANTS 2004, Fourth Internat. Workshop on Ant Colony Optimization and Swarm Intelligence, Lecture Notes in Computer Science, Vol. 3172, Springer, Berlin, Germany, 2004, pp. 95–105. · doi:10.1007/978-3-540-28646-2_9
- Merkle, 2002, Ant colony optimization for resource-constrained project scheduling, IEEE Trans. Evol. Comput., 6, 333, 10.1109/TEVC.2002.802450 · DOI · Paper page
- Meuleau, 2002, Ant colony optimization and stochastic gradient descent, Artif. Life, 8, 103, 10.1162/106454602320184202 · DOI
- J. Montgomery, M. Randall, T. Hendtlass, Search bias in constructive metaheuristics and implications for ant colony optimization, in: M. Dorigo, M. Birattari, C. Blum, L.M. Gambardella, F. Mondada, T. Stützle (Eds.), Proc. ANTS 2004, Fourth Internat. Workshop on Ant Colony Optimization and Swarm Intelligence, Lecture Notes in Computer Science, Vol. 3172, Springer, Berlin, Germany, 2004, pp. 391–398. · DOI
- H. Mühlenbein, G. Paaß. From recombination of genes to the estimation of distributions, in: H.-M. Voigt, W. Ebeling, I. Rechenberg, H.-P. Schwefel (Eds.), Proc. 4th Conf. on Parallel Problem Solving from Nature, PPSN IV, Lecture Notes in Computer Science, Vol. 1411, Springer, Berlin, 1996, pp. 178–187.
- Prügel-Bennett, 2001, Modelling genetic algorithm dynamics, 59, 10.1007/978-3-662-04448-3_4 · doi:10.1007/978-3-662-04448-3_4
- Reimann, 2004, D-ants: savings based ants divide and conquer the vehicle routing problems, Comput. Oper. Res., 31, 563, 10.1016/S0305-0548(03)00014-5 · DOI · Paper page
- K. Socha, ACO for continuous and mixed-variable optimization, in: M. Dorigo, M. Birattari, C. Blum, L.M. Gambardella, F. Mondada, T. Stützle (Eds.), Proc. ANTS 2004, Fourth Internat. Workshop on Ant Colony Optimization and Swarm Intelligence, Lecture Notes in Computer Science, Vol. 3172, Springer, Berlin, Germany, 2004, pp. 25–36. · DOI
- K. Socha, M. Sampels, M. Manfrin, Ant algorithms for the university course timetabling problem with regard to the state-of-the-art, in: G. Raidl et al. (Ed.), Applications of Evolutionary Computing, Proc. EvoWorkshops 2003, Vol. 2611, 2003, pp. 334–345. · DOI
- T. Stützle, An ant approach to the flow shop problem, in: Fifth European Congr. on Intelligent Techniques and Soft Computing, EUFIT’98, 1998, pp. 1560–1564.
- Stützle, 2002, A short convergence proof for a class of ACO algorithms, IEEE Trans. Evol. Comput., 6, 358, 10.1109/TEVC.2002.802444 · DOI · Paper page
- Stützle, 2000, MAX-MIN ant system, Future Gen. Comput. Systems, 16, 889, 10.1016/S0167-739X(00)00043-1 · DOI
- Zlochin, 2004, Model-based search for combinatorial optimization: a critical survey, Ann. Oper. Res., 131, 373, 10.1023/B:ANOR.0000039526.52305.af · DOI · Paper page
Cited by
A Competitive Swarm Optimizer for Large Scale Optimization
Cheng, R., & Jin, Y. (2015) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2014.2322602 · Cited by 1,052
A social learning particle swarm optimization algorithm for scalable optimization
Cheng, R., & Jin, Y. (2015) · Information Sciences · doi:10.1016/j.ins.2014.08.039 · Cited by 747
Ant Colony Optimization: Overview and Recent Advances
Dorigo, M., & Stützle, T. (2019) · International Series in Operations Research & Management Science · doi:10.1007/978-3-319-91086-4_10 · Cited by 722
Self-citationAnt Colony Optimization: Overview and Recent Advances
Dorigo, M., & Stützle, T. (2010) · International Series in Operations Research & Management Science · doi:10.1007/978-1-4419-1665-5_8 · Cited by 579
Self-citationBio inspired computing – A review of algorithms and scope of applications
Kar, A. K. (2016) · Expert Systems with Applications · doi:10.1016/j.eswa.2016.04.018 · Cited by 578
Metadata
- Authors
- Dorigo, M., & Blum, C.
- Venue
- Theoretical Computer Science
- Publisher
- Elsevier BV
- Published
- 2005-11
- Volume
- 344
- Issue
- 2-3
- Pages
- 243-278
- ISSN
- 0304-3975 (ISSN-L)
- OpenAlex
- W2118573797
- Cited by
- 2,295
- References
- 4
- FWCI
- 51.87
- Type
- journal article
- Language
- en
- Open access
- bronze
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 2851 d)
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Ant colony optimization theory: A survey. https://app.cochat.ai/papers/10.1016/j.tcs.2005.05.020
- The paper
- Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical Computer Science. https://doi.org/10.1016/j.tcs.2005.05.020
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.