Skip to main content
SpringerLink
Log in

The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances

  • Chapter
Handbook of Metaheuristics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 57))

Conclusions

The field of ACO algorithms is very lively, as testified, for example, by the successful biannual workshop (ANTS—From Ant Colonies to Artificial Ants: A Series of International Workshops on Ant Algorithms; http://iridia.ulb.ac.be/~ants/) where researchers meet to discuss the properties of ACO and other ant algorithms, both theoretically and experimentally.

From the theory side, the most interesting ongoing work concern the study of the relationship between ACO algorithms and other well-known stochastic optimization techniques. For example, it has been shown [68] that, when interpreting ACO algorithms as methods for searching in the space of pheromones (i.e., artificial ants are seen as procedures to update pheromone trails so to increase the probability of generating very good solutions to the combinatorial optimization problem), then AS can be interpreted as an approximate form of stochastic gradient descent [92] (a well- known algorithm which has been extensively used in machine learning) in the space of pheromones. Similarly, it has been shown [41,94] that there are strong connections between ACO algorithms and the Cross-Entropy method [77].

From the experimental side, most of the current research is in the direction of increasing the number of problems that are successfully solved by ACO algorithms, including real-word, industrial applications [39].

Currently, the great majority of problems attacked by ACO are static and well- defined combinatorial optimization problems, that is, problems for which all the necessary information is available and does not change during problem solution. For this kind of problems ACO algorithms must compete with very well established algorithms, often specialized for the given problem. Also, very often the role played by local search is extremely important to obtain good results (see for example [46]). Although rather successful on these problems, we believe that ACO algorithms will really show their greatest advantage when they are systematically applied to “ill-structured” problems for which it is not clear how to apply local search, or to highly dynamic domains with only local information available. A first step in this direction has already been made with the application to telecommunications networks routing, but much further research will be necessary. The reader interested in learning more about ACO is referred to the book “Ant Colony Optimization” by the same authors [40].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.A. Alexandrov and Y.A. Kochetov (2000) The behavior of the ant colony algorithm for the set covering problem. In: K. Inderfurth, G. Schwödiauer, W. Domschke, F. Juhnke, P. Kleinschmidt, and G. Wäscher (eds.), Operations Research Proceedings 1999. Springer-Verlag, Berlin, Germany, pp. 255–260.

    Google Scholar 

  2. A. Bauer, B. Bullnheimer, R.F. Hartl and C. Strauss (1999) An ant colony optimization approach for the single machine total tardiness problem. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99), IEEE Press, Piscataway, NJ, pp. 1445–1450.

    Google Scholar 

  3. R. Beckers, J.-L. Deneubourg and S. Goss (1993) Modulation of trail laying in the ant Lasius niger (hymenoptera: Formicidae) and its role in the collective selection of a food source. Journal of Insect Behavior, 6(6), 751–759.

    Article  Google Scholar 

  4. R. Bellman, A.O. Esogbue and I. Nabeshima (1982) Mathematical Aspects of Scheduling and Applications. Pergamon Press, New York, NJ.

    Google Scholar 

  5. D. Bertsekas (1998) Network Optimization: Continuous and Discrete Models. Athena Scientific, Belmont, MA.

    Google Scholar 

  6. K.D. Boese, A.B. Kahng and S. Muddu (1994) A new adaptive multi-start technique for combinatorial global optimization. Operations Research Letters, 16, 101–113.

    Article  MathSciNet  Google Scholar 

  7. M. Bolondi and M. Bondanza (1993) Parallelizzazione di un algoritmo per la risoluzione del problema del commesso viaggiatore. Master’s thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.

    Google Scholar 

  8. E. Bonabeau, M. Dorigo and G. Theraulaz (1999) Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, New York, NJ.

    Google Scholar 

  9. E. Bonabeau, M. Dorigo and G. Theraulaz (2000) Inspiration for optimization from social insect behavior. Nature, 406, 39–42.

    Article  Google Scholar 

  10. E. Bonabeau, F. Henaux, S. Guérin, D. Snyers, P. Kuntz and G. Theraulaz (1998) Routing in telecommunication networks with “Smart” ant-like agents. In: Proceedings of IATA’98, Second International Workshop on Intelligent Agents for Telecommunication Applications, volume 1437 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, Germany, pp. 60–72.

    Google Scholar 

  11. E. Bonabeau and G. Theraulaz (2000) Swarm smarts. Scientific American, 282(3), 54–61.

    Google Scholar 

  12. B. Bullnheimer, R.F. Hartl and C. Strauss (1999) Applying the Ant System to the vehicle routing problem. In: S. Voß, S. Martello, I.H. Osman and C. Roucairol (eds.), Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 285–296.

    Google Scholar 

  13. B. Bullnheimer, R.F. Hartl and C. Strauss (1999) An improved Ant System algorithm for the vehicle routing problem. Annals of Operations Research, 89, 319–328.

    Article  MathSciNet  Google Scholar 

  14. B. Bullnheimer, R.F. Hartl and C. Strauss (1999) A new rank-based version of the Ant System: A computational study. Central European Journal for Operations Research and Economics, 7(1), 25–38.

    MathSciNet  Google Scholar 

  15. B. Bullnheimer, G. Kotsis and C. Strauss (1998) Parallelization strategies for the Ant System. In: R. De Leone, A. Murli, P. Pardalos and G. Toraldo (eds.), High Performance Algorithms and Software in Nonlinear Optimization, volume 24 of Applied Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 87–100.

    Google Scholar 

  16. E. Cantú-Paz (2000) Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic Publishers, Boston, MA.

    Google Scholar 

  17. A. Colorni, M. Dorigo and V. Maniezzo (1992) Distributed optimization by ant colonies. In: F.J. Varela and P. Bourgine (eds.), Proceedings of the First European Conference on Artificial Life, MIT Press, Cambridge, MA, pp. 134–142.

    Google Scholar 

  18. A. Colorni, M. Dorigo, V. Maniezzo and M. Trubian (1994) Ant System for job-shop scheduling. JORBEL—Belgian Journal of Operations Research, Statistics and Computer Science, 34(1), 39–53.

    Google Scholar 

  19. O. Cordón, I. Fernández de Viana, F. Herrera and L. Moreno (2000) A new ACO model integrating evolutionary computation concepts: The best-worst Ant System. In: M. Dorigo, M. Middendorf and T. Stützle (eds.), Abstract proceedings of ANTS2000—From Ant Colonies to Artificial Ants: A Series of International Workshops on Ant Algorithms. IRIDIA, Université Libre de Bruxelles, Belgium, pp. 22–29.

    Google Scholar 

  20. D. Costa and A. Hertz (1997) Ants can colour graphs. Journal of the Operational Research Society, 48, 295–305.

    Article  Google Scholar 

  21. M. den Besten (2000) Ants for the single machine total weighted tardiness problem. Master’s thesis, University of Amsterdam, The Netherlands.

    Google Scholar 

  22. M.L. den Besten, T. Stützle and M. Dorigo (2000) Ant colony optimization for the total weighted tardiness problem. In: M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J.J. Merelo and H.-P. Schwefel (eds.), Proceedings ofPPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature, volume 1917 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, pp. 611–620.

    Google Scholar 

  23. J.-L. Deneubourg, S. Aron, S. Goss and J.-M. Pasteels (1990) The self-organizing exploratory pattern of the Argentine ant. Journal of Insect Behavior, 3, 159–168.

    Google Scholar 

  24. G. Di Caro and M. Dorigo (1997) AntNet: A mobile agents approach to adaptive routing. Technical Report IRIDIA/97-12, IRIDIA, Université Libre de Bruxelles, Belgium.

    Google Scholar 

  25. G. Di Caro and M. Dorigo (1998) Ant colonies for adaptive routing in packet-switched communications networks. In: A.E. Eiben, T. Bäck, M. Schoenauer and H.-P. Schwefel (eds.), Proceedings ofPPSN-V, Fifth International Conference on Parallel Problem Solving from Nature, volume 1498 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, pp. 673–682.

    Google Scholar 

  26. G. Di Caro and M. Dorigo (1998) AntNet: Distributed stigmergetic control for communications networks. Journal of Artificial Intelligence Research, 9, 317–365.

    Google Scholar 

  27. G. Di Caro and M. Dorigo (1998) Extending AntNet for best-effort Quality-of-Service routing. Unpublished presentation at ANTS’98—From Ant Colonies to Artificial Ants: First International Workshop on Ant Colony Optimization, http://iridia.ulb.ac.be/ants98/ants98.html, October 15–16.

  28. G. Di Caro and M. Dorigo (1998) Mobile agents for adaptive routing. In: H. El-Rewini (ed.), Proceedings of the 31st International Conference on System Sciences (HICSS-31). IEEE Computer Society Press, Los Alamitos, CA, pp. 74–83.

    Google Scholar 

  29. G. Di Caro and M. Dorigo (1998) Two antcolony algorithms forbest-effortrouting in datagram networks. In: Y. Pan, S.G. Akl and K. Li (eds.), Proceedings of the Tenth IASTED International Conference on Parallel and Distributed Computing and Systems (PDCS’98), IASTED/ACTA Press, Anaheim, CA, pp. 541–546.

    Google Scholar 

  30. M. Dorigo (1992) Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 140 pp.

    Google Scholar 

  31. M. Dorigo, E. Bonabeau and G. Theraulaz (2000) Ant algorithms and stigmergy. Future Generation Computer Systems, 16(8), 851–871.

    Google Scholar 

  32. M. Dorigo and G. Di Caro (1999) The Ant Colony Optimization meta-heuristic. In: D. Corne, M. Dorigo and F. Glover (eds.), New Ideas in Optimization. McGraw Hill, London, UK, pp. 11–32.

    Google Scholar 

  33. M. Dorigo, G. Di Caro and L.M. Gambardella (1999) Ant algorithms for discrete optimization. Artificial Life, 5(2), 137–172.

    Article  Google Scholar 

  34. M. Dorigo and L.M. Gambardella (1997) Ant colonies for the traveling salesman problem. BioSystems, 43, 73–81.

    Article  Google Scholar 

  35. M. Dorigo and L.M. Gambardella (1997) Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1), 53–66.

    Article  Google Scholar 

  36. M. Dorigo, V. Maniezzo and A. Colorni (1991) The Ant System: An autocatalytic optimizing process. Technical Report 91-016 Revised, Dipartimento di Elettronica, Politecnico di Milano, Italy.

    Google Scholar 

  37. M. Dorigo, V. Maniezzo and A. Colorni (1991) Positive feedback as a search strategy. Technical Report 91-016, Dipartimento di Elettronica, Politecnico di Milano, Italy.

    Google Scholar 

  38. M. Dorigo, V. Maniezzo, and A. Colorni (1996) The Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics—PartB, 26(1), 29–41.

    Google Scholar 

  39. M. Dorigo, M. Middendorf and T. Stützle (2000) (eds.) Abstract proceedings of ANTS2000—From Ant Colonies to Artificial Ants: A Series of International Workshops on Ant Algorithms. IRIDIA, Université Libre de Bruxelles, Belgium, 7–9 September.

    Google Scholar 

  40. M. Dorigo and T. Stützle Ant Colony Optimization. MIT Press, Cambridge, MA (forthcoming).

    Google Scholar 

  41. M. Dorigo, M. Zlochin, N. Meuleau and M. Birattari (2001) Updating ACO pheromones using stochastic gradient ascent and cross-entropy methods. Technical Report IRIDIA/2001-19, IRIDIA, Université Libre de Bruxelles, Belgium. Proceedings of the 2nd European Workshop on Evolutionary Computation in Combinatorial Optimization (EvoCOP-2002), (to appear).

    Google Scholar 

  42. T.A. Feo and M.G.C. Resende (1995) Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133.

    Article  MathSciNet  Google Scholar 

  43. L.M. Gambardella and M. Dorigo (1995) Ant-Q: A reinforcement learning approach to the traveling salesman problem. In: A. Prieditis and S. Russell (eds.), Proceedings of the Twelfth International Conference on Machine Learning (ML-95), Morgan Kaufmann Publishers, Palo Alto, CA, pp. 252–260.

    Google Scholar 

  44. L.M. Gambardella and M. Dorigo (1996) Solving symmetric and asymmetric TSPs by ant colonies. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC96), IEEE Press, Piscataway, NJ, pp. 622–627.

    Google Scholar 

  45. L.M. Gambardella and M. Dorigo (1997) HAS-SOP: An hybrid Ant System for the sequential ordering problem. Technical Report IDSIA-11-97, IDSIA, Lugano, Switzerland.

    Google Scholar 

  46. L.M. Gambardella and M. Dorigo (2000) Ant Colony System hybridized with a new local search for the sequential ordering problem. INFORMS Journal on Computing, 12(3), 237–255.

    Article  MathSciNet  Google Scholar 

  47. L.M. Gambardella, È D. Taillard and G. Agazzi (1999) MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In: D. Corne, M. Dorigo and F. Glover (eds.), New Ideas in Optimization. McGraw Hill, London, UK, pp. 63–76.

    Google Scholar 

  48. L.M. Gambardella, È.D. Taillard and M. Dorigo (1999) Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society, 50(2), 167–176.

    Google Scholar 

  49. M.R. Garey and D.S. Johnson (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA.

    Google Scholar 

  50. F. Glover (1990) Tabu search—part II. ORSA Journal on Computing, 2(1), 4–32.

    MATH  Google Scholar 

  51. F. Glover and M. Laguna (1997) Tabu Search. Kluwer Academic Publishers, Boston, MA.

    Google Scholar 

  52. S. Goss, S. Aron, J.L. Deneubourg and J.M. Pasteels (1989) Self-organized shortcuts in the Argentine ant. Naturwissenschaften, 76, 579–581.

    Article  Google Scholar 

  53. W.J. Gutjahr (2000) A Graph-based Ant System and its convergence. Future Generation Computer Systems, 16(8), 873–888.

    Article  Google Scholar 

  54. W.J. Gutjahr (2002) ACO algorithms with guaranteed convergence to the optimal solution. Information Processing Letters, (in press).

    Google Scholar 

  55. R. Hadji, M. Rahoual, E. Talbi and V. Bachelet (2000) Ant colonies for the set covering problem. In: M. Dorigo, M. Middendorf and T. Stützle (eds.), Abstract proceedings ofANTS2000—From Ant Colonies to Artificial Ants: A Series of International Workshops on Ant Algorithms. IRIDIA, Université Libre de Bruxelles, Belgium, pp. 63–66.

    Google Scholar 

  56. M. Heusse, S. Guérin, D. Snyers and P. Kuntz (1998) Adaptive agent-driven routing and load balancing in communication networks. Advances in Complex Systems, 1(2), 237–254.

    Google Scholar 

  57. D.S. Johnson and L.A. McGeoch (1997) The travelling salesman problem: A case study in local optimization. In: E.H.L. Aarts and J.K. Lenstra (eds.), Local Search in Combinatorial Optimization. John Wiley & Sons, Chichester, UK, pp. 215–310.

    Google Scholar 

  58. M. Jünger, G. Reinelt and S. Thienel (1994) Provably good solutions for the traveling salesman problem. Zeitschrift für Operations Research, 40, 183–217.

    Google Scholar 

  59. F. Krüger, D. Merkle and M. Middendorf Studies on a parallel Ant System for the BSP model. Unpublished manuscript.

    Google Scholar 

  60. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (1985) The Travelling Salesman Problem. John Wiley & Sons, Chichester, UK.

    Google Scholar 

  61. G. Leguizamón and Z. Michalewicz (1999) A new version of Ant System for subset problems. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99). IEEE Press, Piscataway, NJ, pp. 1459–1464.

    Google Scholar 

  62. Y.-C. Liang and A.E. Smith (1999) An Ant System approach to redundancy allocation. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99). IEEE Press, Piscataway, NJ, pp. 1478–1484.

    Google Scholar 

  63. V. Maniezzo (1999) Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS Journal on Computing, 11(4), 358–369.

    MATH  MathSciNet  Google Scholar 

  64. V. Maniezzo and A. Carbonaro (2000) An ANTS heuristic for the frequency assignment problem. Future Generation Computer Systems, 16(8), 927–935.

    Article  Google Scholar 

  65. V. Maniezzo and A. Colorni (1999) The Ant System applied to the quadratic assignment problem. IEEE Transactions on Data and Knowledge Engineering, 11(5), 769–778.

    Google Scholar 

  66. V. Maniezzo, A. Colorni and M. Dorigo (1994) The Ant System applied to the quadratic assignment problem. Technical Report IRIDIA/94-28, IRIDIA, Université Libre de Bruxelles, Belgium.

    Google Scholar 

  67. D. Merkle, M. Middendorf and H. Schmeck (2000) Ant colony optimization for resource-constrained project scheduling. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000), Morgan Kaufmann Publishers, San Francisco, CA, pp. 893–900.

    Google Scholar 

  68. N. Meuleau and M. Dorigo (2002) Ant colony optimization and stochastic gradient descent. Artificial Life, (in press).

    Google Scholar 

  69. R. Michel and M. Middendorf (1998) An island model based Ant System with lookahead for the shortest supersequence problem. In: A.E. Eiben, T. Bäck, M. Schoenauer and H.-P. Schwefel (eds.), Proceedings of PPSN-V, Fifth International Conference on Parallel Problem Solving from Nature, volume 1498 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, pp. 692–701.

    Google Scholar 

  70. R. Michel and M. Middendorf (1999) An ACO algorithm for the shortest super-sequence problem. In: D. Corne, M. Dorigo and F. Glover (eds.), New Ideas in Optimization. McGraw Hill, London, UK, pp. 51–61.

    Google Scholar 

  71. M. Middendorf, F. Reischle and H. Schmeck (2002) Multi colony ant algorithms. Journal of Heuristics, (in press).

    Google Scholar 

  72. T.E. Morton, R.M. Rachamadugu and A. Vepsalainen (1984) Accurate myopic heuristics for tardiness scheduling. GSIA Working Paper 36-83-84, Carnegie-Mellon University, PA.

    Google Scholar 

  73. G. Navarro Varela and M.C. Sinclair (1999) Ant colony optimisation for virtual-wavelength-path routing and wavelength allocation. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99). IEEE Press, Piscataway, NJ, pp. 1809–1816.

    Google Scholar 

  74. C.H. Papadimitriou (1994) Computational Complexity. Addison-Wesley, Reading, MA.

    Google Scholar 

  75. H. Ramalhinho Lourenço and D. Serra (1998) Adaptive approach heuristics for the generalized assignment problem. Technical Report Economic Working Papers Series No. 304, Universitat Pompeu Fabra, Department of Economics and Management, Barcelona, Spain.

    Google Scholar 

  76. G. Reinelt (1994) The Traveling Salesman: Computational Solutions for TSP Applications, volume 840 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany.

    Google Scholar 

  77. R.Y. Rubinstein (2001) Combinatorial optimization via the simulated cross-entropy method. In: Encyclopedia of Operations Research and Management Science. Kluwer Academic Publishers, Boston, MA.

    Google Scholar 

  78. R. Schoonderwoerd, O. Holland and J. Bruten (1997) Ant-like agents for load balancing in telecommunications networks. In: Proceedings of the First International Conference on Autonomous Agents. ACM Press, New York, NY, pp. 209–216.

    Google Scholar 

  79. R. Schoonderwoerd, O. Holland, J. Bruten and L. Rothkrantz (1996) Ant-based load balancing in telecommunications networks. Adaptive Behavior, 5(2), 169–207.

    Google Scholar 

  80. C. Solnon (2000) Solving permutation constraint satisfaction problems with artificial ants. In: W. Horn (ed.), Proceedings of the 14th European Conference on Artificial Intelligence. IOS Press, Amsterdam, The Netherlands, pp. 118–122.

    Google Scholar 

  81. T. Stützle (1997) MAX-MIN Ant System for the quadratic assignment problem. Technical Report AIDA-97-4, FG Intellektik, FB Informatik, TU Darmstadt, Germany.

    Google Scholar 

  82. T. Stützle (1998) An ant approach to the flow shop problem. In: Proceedings of the 6th European Congress on Intelligent Techniques & Soft Computing (EUFIT’98), volume 3, Verlag Mainz, Wissenschaftsverlag, Aachen, Germany, pp. 1560–1564.

    Google Scholar 

  83. T. Stützle (1998) Parallelization strategies for ant colony optimization. In: A.E. Eiben, T. Bäck, M. Schoenauer and H.-P. Schwefel (eds.), Proceedings ofPPSN-V, Fifth International Conference on Parallel Problem Solving from Nature, volume 1498 of Lecture Notes in Computer Science. Springer Verlag, Berlin, Germany, pp. 722–731.

    Google Scholar 

  84. T. Stützle (1999) Local Search Algorithms for Combinatorial Problems: Analysis, Improvements and New Applications. Infix, Sankt Augustin, Germany.

    Google Scholar 

  85. T. Stützle and M. Dorigo (1999) ACO algorithms for the quadratic assignment problem. In: D. Corne, M. Dorigo and F. Glover (eds.), New Ideas in Optimization. McGraw Hill, London, UK, pp. 33–50.

    Google Scholar 

  86. T. Stützle and M. Dorigo (2002) A short convergence proof for a class of ACO algorithms. IEEE Transactions on Evolutionary Computation (in press).

    Google Scholar 

  87. T. Stützle and H.H. Hoos (1997) The MAX-MIM Ant System and local search for the traveling salesman problem. In: T. Bäck, Z. Michalewicz and X. Yao (eds.), Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC’97), IEEE Press, Piscataway, NJ, pp. 309–314.

    Google Scholar 

  88. T. Stützle and H.H. Hoos (2000) MAX-MIM Ant System. Future Generation Computer Systems, 16(8):889–914.

    Google Scholar 

  89. R.S. Sutton and A.G. Barto (1998) Reinforcement Learning: An Introduction. MIT Press, Cambridge, MA.

    Google Scholar 

  90. R. van der Put (1998) Routing in the faxfactory using mobile agents. Technical Report R&D-SV-98-276, KPN Research, The Netherlands.

    Google Scholar 

  91. T. White, B. Pagurek and F. Oppacher (1998) Connection management using adaptive mobile agents. In: H.R. Arabnia (ed.), Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA’98). CSREA Press, pp. 802–809.

    Google Scholar 

  92. R.J. Williams (1992) Simple statistical gradient-following algorithms forconnectionist reinforcement learning. Machine Learning, 8(3), 229–256.

    MATH  Google Scholar 

  93. M. Yannakakis (1997) Computational complexity. In: E.H.L. Aarts and J.K. Lenstra (eds.), Local Search in Combinatorial Optimization. John Wiley & Sons, Chichester, UK, pp. 19–55.

    Google Scholar 

  94. M. Zlochin, M. Birattari, N. Meuleau and M. Dorigo (2001) Combinatorial optimization using model-based search. Technical Report IRIDIA/2001-15, IRIDIA, Université Libre de Bruxelles, Belgium, (submitted to Annals of Operations Research).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRIDIA, Université Libre de Bruxelles, Belgium

    Marco Dorigo

  2. Intellectics Group, TU Darmstadt, Germany

    Thomas Stützle

Authors
  1. Marco Dorigo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Stützle
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Leeds School of Business, University of Colorado at Boulder, USA

    Fred Glover

  2. College of Business, University of Colorado at Denver, USA

    Gary A. Kochenberger

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Dorigo, M., Stützle, T. (2003). The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances. In: Glover, F., Kochenberger, G.A. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 57. Springer, Boston, MA. https://doi.org/10.1007/0-306-48056-5_9

Download citation

  • DOI: https://doi.org/10.1007/0-306-48056-5_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7263-5

  • Online ISBN: 978-0-306-48056-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation