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The Probabilistic Traveling Salesman Problem, an ant colony approach
Leonora Bianchi
IDSIA
Lugano, Switzerland
leonora@idsia.ch

Abstract

The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem where 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. The PTSP may be seen as a "simple" version of a vehicle routing problem with stochastic demands, where there is one vehicle and where the demand may either zero (the customer does not require a visit) or one (the customer requires a visit). An important question about this problem is whether and in which context an a-priori tour found by a TSP heuristic can also be a good solution for the PTSP. We investigate this issue by experimentally testing the relative performance of two ant colony optimization algorithms, Ant Colony System (ACS) which is a TSP heuristic, and a variant of it (pACS) that aims to minimize the PTSP objective function.

Keywords

traveling salesman problem, stochastic optimization problems, ant colony optimization.

References

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