Ant Colony Optimization

Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 36)


Ant colony optimization (ACO) is a metaheuristic that was originally introduced for solving combinatorial optimization problems. In this chapter we present the general description of ACO, as well as its adaptation for the application to continuous optimization problems. We apply this adaptation of ACO to optimize the weights of feed-forward neural networks for the purpose of pattern classification. As test problems we choose three data sets from the well-known PROBEN1 medical database. The experimental results show that our algorithm is comparable to specialized algorithms for feed-forward neural network training. Furthermore, the results compare favourably to the results of other general-purpose methods such as genetic algorithms.

Key words

Ant colony optimization continuous optimization pattern classification feedforward neural network training 


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  1. Alba, E., and Chicano, J.F, 2004, Training Neural Networks with GA Hybrid Algorithms, in: Proceedings of Genetic and Evolutionary Computation–GECCO 2004, Part 1, Lecture Notes in Computer Science, vol. 3102, K. Deb et al, eds., Springer-Verlag, Berlin, Germany, pp. 852–863.CrossRefGoogle Scholar
  2. Battiti, R., and Tecchiolli, G., 1996, The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization, Annals of Operations Research 63:153–188.zbMATHCrossRefGoogle Scholar
  3. Bilchev, G., and Parmee, I. C, 1995, The ant colony metaphor for searching continuous design spaces, in: Proceedings of the AISB Workshop on Evolutionary Computation, Lecture Notes in Computer Science, vol. 993, T.∼C. Fogarty, ed., Springer-Verlag, Berlin, Germany, pp. 25–39.Google Scholar
  4. Birattari, M., 2004, The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective, Ph.D. thesis, ULB, Brussels, Belgium.Google Scholar
  5. Birattari, M., Stützle, T., Paquete, L., and Varrentrapp, K., 2002, A Racing Algorithm for Configuring Metaheuristics, in: Proceedings of Genetic and Evolutionary Conference, W. B. Langdon et al. eds., Morgan Kaufmann, San Francisco, CA, USA, pp. 11–18.Google Scholar
  6. Blum, C, 2005, Beam-ACO—Hybridizing ant colony optimization with beam search: An application to open shop scheduling, Computers & Operations Research 32(6): 1565–1591.CrossRefGoogle Scholar
  7. Blum, C, and Roli, A., 2003, Metaheuristics in combinatorial optimization: Overview and conceptual comparison, ACM Computing Surveys 35(3):268–308.CrossRefGoogle Scholar
  8. Blum, C, and Sampels, M., 2004, An ant colony optimization algorithm for shop scheduling problems, Journal of Mathematical Modelling and Algorithms 3(3):285–308.zbMATHCrossRefGoogle Scholar
  9. Blum, C, 2005, Beam-ACO—Hybridizing ant colony optimization with beam search: An application to open shop scheduling, Computers & Operations Research 32(6): 1565–1591.CrossRefGoogle Scholar
  10. Bonabeau, E., Dorigo, M., and Theraulaz, G., 1999, Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, New York, NY.Google Scholar
  11. Box, G. E. P., and Muller, M. E, 1958, A note on the generation of random normal deviates. Annals of Mathematical Statistics 29(2):610–611.zbMATHCrossRefGoogle Scholar
  12. Černý, V., 1985, A thermodynamical approach to the travelling salesman problem: An efficient simulation algorithm, Optimization Theory and Applications 45:41–51.MathSciNetCrossRefGoogle Scholar
  13. Chelouah, R., and Siarry, P., 2000, A continuous genetic algorithm designed for the global optimization of mulitmodal functions, Journal of Heuristics 6:191–213.zbMATHCrossRefGoogle Scholar
  14. Chelouah, R., and Siarry, P., 2000, Tabu search applied to global optimization, European Journal of Operational Research 123:256–270.zbMATHMathSciNetCrossRefGoogle Scholar
  15. Chelouah, R., and Siarry, P., 2003, Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions, European Journal of Operational Research 148:335–348.zbMATHMathSciNetCrossRefGoogle Scholar
  16. Costa, D., and Hertz, A., 1997, Ants can color graphs, Journal of the Operational Research Society 48:295–305.zbMATHCrossRefGoogle Scholar
  17. den Besten, M. L., Stützle, T., and Dorigo, M., 2000, Ant colony optimization for the total weighted tardiness problem, in: Proceedings of PPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, vol. 1917, M. ∼Schoenauer et al., eds., Springer Verlag, Berlin, Germany, pp. 611–620.CrossRefGoogle Scholar
  18. Deneubourg, J.-L., Aron, S., Goss, S., and Pasteels, J.-M., 1990, The self-organizing exploratory pattern of the argentine ant, Journal of Insect Behaviour 3:159–168.CrossRefGoogle Scholar
  19. Dorigo, M., 1992, Optimization, Learning and Natural Algorithms (in Italian), PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.Google Scholar
  20. Dorigo, M., and Gambardella, L. M, 1997, Ant Colony System: A cooperative learning approach to the travelling salesman problem, IEEE Transactions on Evolutionary Computation l(l):53–66.CrossRefGoogle Scholar
  21. Dorigo, M., Maniezzo, V., and Colorni, A., 1991, Positive feedback as a search strategy, Technical Report 91–016, Dipartimento di Elettronica, Politecnico di Milano, Italy.Google Scholar
  22. Dorigo, M., Maniezzo, V., and Colorni, A., 1996, Ant System: Optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics — Part B 26(1):29–41.CrossRefGoogle Scholar
  23. Dorigo, M., and Stützle, T., 2004, Ant Colony Optimization, MIT Press, Cambridge, MA.CrossRefGoogle Scholar
  24. Dréo, J., and Siarry, P., 2002, A new ant colony algorithm using the heterarchical concept aimed at optimization of multiminima continuous functions, in: Proceedings of ANTS 2002—From Ant Colonies to Artificial Ants: Third International Workshop on Ant Algorithms, Lecture Notes in Computer Science, vol. 2463 of LNCS, M. Dorigo et al., eds., Springer Verlag, Berlin, Germany, pp. 216–221.Google Scholar
  25. Fogel, L. J., Owens, A. J., and Walsh, M. J., 1966, Artificial Intelligence through Simulated Evolution, Wiley.Google Scholar
  26. Gagné, C, Price, W. L., and Gravel, M., 2002, Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times, Journal of the Operational Research Society 53:895–906.zbMATHCrossRefGoogle Scholar
  27. Gambardella, L. M., and Dorigo, M., 2000, Ant Colony System hybridized with a new local search for the sequential ordering problem, INFORMS Journal on Computing 12(3):237–255.zbMATHMathSciNetCrossRefGoogle Scholar
  28. Gambardella, L. M., Taillard, É. D., and Agazzi, G., 1999, MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows, in: New Ideas in Optimization, D. Corne et al., eds., McGraw Hill, London, UK, pp. 63–76.Google Scholar
  29. Glover, F., 1989, Tabu search—Part I, ORSA Journal on Computing 1(3): 190–206.zbMATHGoogle Scholar
  30. Glover, F., 1990, Tabu search—Part II, ORSA Journal on Computing 2(l):4–32.zbMATHGoogle Scholar
  31. Glover, F., and Kochenberger, G., 2002, Handbook of Metaheuristics, Kluwer Academic Publishers, Norwell, MA.zbMATHGoogle Scholar
  32. Glover, F., and Laguna, M., 1997, Tabu Search, Kluwer Academic Publishers.Google Scholar
  33. Goldberg, D. E., 1989, Genetic algorithms in search, optimization, and machine learning, Addison Wesley, Reading, MA.zbMATHGoogle Scholar
  34. Golub, G. H., and van Loan, C. F., 1989, Matrix Computations, 2nd ed., the John Hopkins University Press, Baltimore, MD, USA.Google Scholar
  35. Guntsch, M., and Middendorf, M., 2002, A population based approach for ACO, in: Applications of Evolutionary Computing, Proceedings of EvoWorks hops 2002: EvoCOP, EvoIASP, EvoSTim, vol. 2279, S. Cagnoni, J. Gottlieb, E. Hart, M. Middendorf, and G. Raidl, eds., Springer-Verlag, Berlin, Germany, pp. 71–80.Google Scholar
  36. Hagan, M. T., and Menhaj, M. B., 1994, Training Feedforward Networks with the Marquardt Algorithm, IEEE Transactions on Neural Networks 5:989–993.CrossRefGoogle Scholar
  37. Hastie, T., Tibshirani, R., and Friedman, J., 2001, The Elements of Statistical Learning, Springer-Verlag, Berlin, Germany.zbMATHGoogle Scholar
  38. Holland, J. H., 1975, Adaption in natural and artificial systems, The University of Michigan Press, Ann Harbor, MI.zbMATHGoogle Scholar
  39. Hoos, H. H., and Stützle, T., 2004, Stochastic Local Search: Foundations and Applications, Elsevier, Amsterdam, The Netherlands.Google Scholar
  40. Kern, S., Müller, S. D., Hansen, N., Büche, D., Očenášek, J., and Koumoutsakos, P., 2004, Learning probability distributions in continuous evolutionary algorithms—A comparative review, Natural Computing 3(1):77–112.zbMATHMathSciNetCrossRefGoogle Scholar
  41. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., 1983, Optimization by simulated annealing, Science 220(4598):671–680.MathSciNetADSCrossRefGoogle Scholar
  42. Maniezzo, V., 1999, Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem, INFORMS Journal on Computing 11(4):358–369.zbMATHMathSciNetCrossRefGoogle Scholar
  43. Maniezzo, V., and Colorni, A., 1999, The Ant System applied to the quadratic assignment problem, IEEE Transactions on Data and Knowledge Engineering 11(5):769–778.CrossRefGoogle Scholar
  44. Mathur, M, Karale, S. B., Priye, S., Jyaraman, V. K., and Kulkarni, B. D., 2000, Ant colony approach to continuous function optimization, Industrial & Engineering Chemistry Research 39:3814–3822.CrossRefGoogle Scholar
  45. McGill, R., Tukey, J. W., and Larsen, W. A., 1978, Variations of box plots, The American Statisticia 32:12–16.CrossRefGoogle Scholar
  46. Merkle, D., Middendorf, M., and Schmeck, H., 2002, Ant Colony Optimization for Resource-Constrained Project Scheduling, IEEE Transactions on Evolutionary Computation 6(4):333–346.CrossRefGoogle Scholar
  47. Monmarché, N., Venturing G., and Slimane M., 2000, On how Pachycondyla apicalis ants suggest a new search algorithm, Future Generation Computer Systems 16:937–946.CrossRefGoogle Scholar
  48. Nelder, J. A., and Mead, R., 1965, A simplex method for function minimization, Computer Journal 7:308–313.zbMATHGoogle Scholar
  49. Papadimitriou, C. H., and Steiglitz, K., 1982, Combinatorial Optimization—Algorithms and Complexity, Dover Publications, Inc., New York.Google Scholar
  50. Papliński, A.P., 2004, Lecture 7—Advanced Learning Algorithms for Multilayer Perceptrons, available online at Google Scholar
  51. Prechelt, L., 1994, Probenl—A Set of Neural Network Benchmark Problems and Benchmarking Rules. Technical Report 21, Fakultät für Informatik, Universität Karlsruhe, Karlsruhe, Germany.Google Scholar
  52. Rechenberg, I., 1973, Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Frommann-Holzboog.Google Scholar
  53. Reimann, M., Doerner, K., and Hartl, R. F., 2004, D-ants: Savings based ants divide and conquer the vehicle routing problems, Computers & Operations Research 31(4):563–591.zbMATHCrossRefGoogle Scholar
  54. Rumelhart, D., Hinton, G., and Williams, R., 1986, Learning Representations by Backpropagation Errors, Nature 323:533–536.CrossRefADSGoogle Scholar
  55. Siarry, P., Berthiau, G., Durbin, F., and Haussy, J., 1997, Enhanced simulated annealing for globally minimizing functions of many-continuous variables, ACM Transactions on Mathematical Software 23(2):209.228.zbMATHMathSciNetCrossRefGoogle Scholar
  56. Socha, K., 2003, The Influence of Run-Time Limits on Choosing Ant System Parameters, in Proceedings of GECCO 2003—Genetic and Evolutionary Computation Conference, Lecture Notes in Computer Science, vol. 2723, E. Cantu-Paz et al., eds., Springer-Verlag, Berlin, Germany, pp. 49–60.Google Scholar
  57. Socha, K., 2004, Extended ACO for continuous and mixed-variable optimization, in: Proceedings of ANTS 2004—Fourth International Workshop on Ant Algorithms and Swarm Intelligence, Lecture Notes in Computer Science, M. Dorigo et al., eds., Springer Verlag, Berlin, Germany, pp. 35–46.Google Scholar
  58. Socha, K., Sampels, M., and Manfrin, M., 2003, Ant algorithms for the university course timetabling problem with regard to the state-of-the-art, in: Applications of Evolutionary Computing, Proceedings of EvoWorkshops 2003, vol. 2611, G. Raidl et al., eds., pp 334–345.Google Scholar
  59. Storn, R., and Price, K., 1997, Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization 11:341–359.zbMATHMathSciNetCrossRefGoogle Scholar
  60. Stützle, T., 1998, An Ant Approach to the Flow Shop Problem, in: Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing, EUFIT’98, pp 1560–1564.Google Scholar
  61. Stützle, T., and Hoos, H. H., 2000, MAX-MIN Ant System, Future Generation Computer Systems 16(8):889–914.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.IRIDIAUniversité Libre de BruxellesBrusselsBelgium
  2. 2.ALBCOM, LSIUniversitat Politécnica de CatalunyaBarcelonaSpain

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