Ant Colony Optimization and Local Search based on Exact and Estimated Objective Values for the Probabilistic Traveling Salesman Problem

This paper deals with a general choice that one faces when developing an algorithm for a stochastic optimization problem: either design problem-specific algorithms that exploit the exact objective function, or to consider algorithms that only use estimated values of the objective function, which are very general and for which simple non-sophisticated versions can be quite easily designed. The Probabilistic Traveling Salesman Problem and the Ant Colony Optimization metaheuristic are used as a case study for this general issue. We consider four Ant Colony Optimization algorithms with different characteristics. Two algorithms exploit the exact objective function of the problem, and the other two use only estimated values of the objective function by Monte Carlo sampling. For each of these two groups, we consider both hybrid and non-hybrid versions (that is, with and without the application of a local search procedure). Computational experiments show that the hybrid version based on exact objective values outperforms the other variants and other state-of-the-art metaheuristics from the literature. Experimental analysis on a benchmark of instances designed on purpose let us identify in which conditions the performance of estimationbased variants can be competitive with the others.