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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. J. Bertsimas. Probabilistic Combinatorial Optimization Problems. PhD thesis, MIT, Cambridge, MA, 1988.
D. J. Bertsimas and L. Howell. Further results on the probabilistic traveling salesman problem. European Journal of Operational Research, 65:68–95, 1993.
D. J. Bertsimas, P. Jaillet, and A. Odoni. A priori optimization. Operations Research, 38:1019–1033, 1990.
M. Dorigo, G. Di Caro, and L. M. Gambardella. Ant algorithms for discrete optimization. Arti.cial Life, 5(2):137–172, 1999.
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.
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.
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.
P. Jaillet. Probabilistic Traveling Salesman Problems. PhD thesis, MIT, Cambridge, MA, 1985.
A. Jézéquel. Probabilistic Vehicle Routing Problems. Master’s thesis, MIT, Cambridge, MA, 1985.
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.
F. A. Rossi and I. Gavioli. Aspects of Heuristic Methods in the Probabilistic Traveling Salesman Problem, pages 214–227. World Scienti.c, Singapore, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bianchi, L., Gambardella, L.M., Dorigo, M. (2002). Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic. In: Dorigo, M., Di Caro, G., Sampels, M. (eds) Ant Algorithms. ANTS 2002. Lecture Notes in Computer Science, vol 2463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45724-0_15
Download citation
DOI: https://doi.org/10.1007/3-540-45724-0_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44146-5
Online ISBN: 978-3-540-45724-4
eBook Packages: Springer Book Archive