New Ideas for Applying Ant Colony Optimization to the Probabilistic TSP

  • Jürgen Branke
  • Michael Guntsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2611)


The Probabilistic Traveling Salesperson Problem (PTSP) is a stochastic variant of the Traveling Salesperson Problem (TSP); each customer has to be serviced only with a given probability. The goal is to find an a priori tour with shortest expected tour-length, with the customers being served in the specified order and customers not requiring service being skipped. In this paper, we use the Ant Colony Optimization (ACO) metaheuristic to construct solutions for PTSP. We propose two new heuristic guidance schemes for this problem, and examine the idea of using approximations to calculate the expected tour length. This allows to find better solutions or use less time than the standard ACO approach.


Solution Quality Full Evaluation Approximation Depth Heuristic Information Evaluation Depth 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. J. Berstimas, P. Jaillet, and A. Odoni. A priori optimization. Operations Research, 38:1019–1033, 1990.MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Jezequel. Probabilistic vehicle routing problems. Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA, 1985.Google Scholar
  3. 3.
    F. Rossi and I. Gavioli. Aspects of heuristic methods in the probabilistic traveling salesman problem. Andreatta, G., F. Mason, and P. Serani (eds.), Advanced School on Stochastics in Combinatorial Optimization, World Scientic, Singapore, pp. 214–227, 1987.Google Scholar
  4. 4.
    D. Bertsimas and L. H. Howell. Further results on the probabilistic traveling salesman problem. European Journal of Operational Research, 65:68–95, 1993.zbMATHCrossRefGoogle Scholar
  5. 5.
    G. Laporte, F. V. Louveaux, and H. Mercure. A priori optimization of the probabilistic traveling salesman problem. Operations Research, 42(3):543–549, 1994.zbMATHMathSciNetGoogle Scholar
  6. 6.
    L. Bianchi, L. M. Gambardella, and M. Dorigo. An ant colony optimization approach to the probabilistic traveling salesman problem. In J. J. Merelo Guervos et al., editor, Parallel Problem Solving from Nature, volume 2439 of LNCS, pages 883–892. Springer, 2002.Google Scholar
  7. 7.
    L. Bianchi, L. M. Gambardella, and M. Dorigo. Solving the homogeneous probabilistic traveling salesman problem by the aco metaheuristic. In M. Dorigo, G. Di Caro, and M. Sampels, editors, Ant Algorithms, volume 2463 of LNCS, pages 176–187. Springer, 2002.CrossRefGoogle Scholar
  8. 8.
    M. Dorigo. Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1992. pp. 140.Google Scholar
  9. 9.
    A. Colorni M. Dorigo, V. Maniezzo. The ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, B(26):29–41, 1996.Google Scholar
  10. 10.
    M. Dorigo and G. Di Caro. The ant colony optimization meta-heuristic. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages11–32. McGraw-Hill, 1999.Google Scholar
  11. 11.
    P. Jaillet. Probabilistic traveling salesman problems. PhD thesis, MIT, Cambridge, MA, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jürgen Branke
    • 1
  • Michael Guntsch
    • 1
  1. 1.Institute AIFBUniversity of Karlsruhe (TH)Germany

Personalised recommendations