ANTS 2002: Ant Algorithms pp 176-187 | Cite as

Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic

  • Leonora Bianchi
  • Luca Maria Gambardella
  • Marco Dorigo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2463)

Abstract

The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem in which each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a random subset of customers in the same order as they appear in the a priori tour.

We propose an ant based a priori tour construction heuristic, the probabilistic Ant Colony System (pACS), which is derived from ACS, a similar heuristic previously designed for the TSP problem. We show that pACS finds better solutions than other tour construction heuristics for a wide range of homogeneous customer probabilities. We also show that for high customers probabilities ACS solutions are better than pACS solutions.

Keywords

Local Search Vehicle Route Problem Heuristic Information Absolute Performance Tour Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. J. Bertsimas. Probabilistic Combinatorial Optimization Problems. PhD thesis, MIT, Cambridge, MA, 1988.Google Scholar
  2. 2.
    D. J. Bertsimas and L. Howell. Further results on the probabilistic traveling salesman problem. European Journal of Operational Research, 65:68–95, 1993.MATHCrossRefGoogle Scholar
  3. 3.
    D. J. Bertsimas, P. Jaillet, and A. Odoni. A priori optimization. Operations Research, 38:1019–1033, 1990.MATHMathSciNetGoogle Scholar
  4. 4.
    M. Dorigo, G. Di Caro, and L. M. Gambardella. Ant algorithms for discrete optimization. Arti.cial Life, 5(2):137–172, 1999.CrossRefGoogle Scholar
  5. 5.
    M. Dorigo and L. M. Gambardella. Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1):53–66, 1997.CrossRefGoogle Scholar
  6. 6.
    M. Dorigo, V. Maniezzo, and A. Colorni. The 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
  7. 7.
    L. M. Gambardella and M. Dorigo. Solving symmetric and asymmetric TSPs by ant colonies. In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC’96), pages 622–627. IEEE Press, Piscataway, NJ, 1996.Google Scholar
  8. 8.
    P. Jaillet. Probabilistic Traveling Salesman Problems. PhD thesis, MIT, Cambridge, MA, 1985.Google Scholar
  9. 9.
    A. Jézéquel. Probabilistic Vehicle Routing Problems. Master’s thesis, MIT, Cambridge, MA, 1985.Google Scholar
  10. 10.
    G. Laporte, F. Louveaux, and H. Mercure. An exact solution for the a priori optimization of the probabilistic traveling salesman problem. Operations Research, 42:543–549, 1994.MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    F. A. Rossi and I. Gavioli. Aspects of Heuristic Methods in the Probabilistic Traveling Salesman Problem, pages 214–227. World Scienti.c, Singapore, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Leonora Bianchi
    • 1
  • Luca Maria Gambardella
    • 1
  • Marco Dorigo
    • 2
  1. 1.IDSIAMannoSwitzerland
  2. 2.IRIDIAUniversité Libre de BruxellesBrusselsBelgium

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