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On the Invariance of Ant System

  • Mauro Birattari
  • Paola Pellegrini
  • Marco Dorigo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4150)

Abstract

It is often believed that the performance of ant system, and in general of ant colony optimization algorithms, depends somehow on the scale of the problem instance at hand. The issue has been recently raised explicitly [1] and the hyper-cube framework has been proposed to eliminate this supposed dependency.

In this paper, we show that although the internal state of ant system—that is, the pheromone matrix—depends on the scale of the problem instance under analysis, this does not affect the external behavior of the algorithm. In other words, for an appropriate initialization of the pheromone, the sequence of solutions obtained by ant system does not depend on the scale of the instance.

As a second contribution, the paper introduces a straightforward variant of ant system in which also the pheromone matrix is independent of the scale of the problem instance under analysis.

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References

  1. 1.
    Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE Transactions on Systems, Man, and Cybernetics—Part B 34(2), 1161–1172 (2004)CrossRefGoogle Scholar
  2. 2.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  3. 3.
    Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: An autocatalytic optimizing process. Technical Report 91-016 Revised, Dipartimento di Elettronica, Politecnico di Milano, Milano, Italy (1991)Google Scholar
  4. 4.
    Dorigo, M.: Ottimizzazione, apprendimento automatico, ed algoritmi basati su metafora naturale. PhD thesis, Politecnico di Milano, Milano, Italy (1992) (in Italian)Google Scholar
  5. 5.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics—Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  6. 6.
    Birattari, M., Pellegrini, P., Dorigo, M.: On the invariance of ant colony optimization. Technical Report TR/IRIDIA/2006-004, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium (2006) (Submitted for journal publication)Google Scholar
  7. 7.
    Stützle, T., Hoos, H.H.: The \(\cal MAX\)\(\cal MIN\) Ant System and local search for the traveling salesman problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC 1997), Piscataway, NJ, USA, pp. 309–314. IEEE Press, Los Alamitos (1997)CrossRefGoogle Scholar
  8. 8.
    Stützle, T., Hoos, H.H.: \(\cal MAX\)\(\cal MIN\) ant system. Future Generation Computer Systems 16(8), 889–914 (2000)CrossRefGoogle Scholar
  9. 9.
    Dorigo, M., Gambardella, L.M.: Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mauro Birattari
    • 1
  • Paola Pellegrini
    • 1
    • 2
  • Marco Dorigo
    • 1
  1. 1.IRIDIA, CoDEUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Department of Applied MathematicsUniversità Ca’ FoscariVeniceItaly

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