Ant Colony Optimization under Uncertainty

The goal of the thesis is to study the behavior of the ant colony optimization metaheuristic under uncertain conditions. We choose the probabilistic traveling salesman problem (PTSP) as a test-bed amongst stochastic optimization problems, in much the same way as the traveling salesman problem (TSP) has been considered a standard amongst deterministic optimization problems. Given a set of cities and the cost of travel between each pair of them, the goal of the TSP is to find the cheapest way of visiting all of the cities and returning to the starting point. This is a computationally hard problem to solve and called as NP-hard problem. Ant colony optimization metaheuristic is one of the successful techniques to find the nearly optimal solution for this class of problems. The PTSP is a variant of TSP in which each city only needs to be visited with certain probability. To solve this problem, one first decides upon the order in which the cities are to be visited: the ’a priori ’ tour. Subsequently, it is revealed which cities need to be visited, and those which need to be skipped, generating in this way an ’a posteriori tour ’. The objective is to choose an a priori tour which minimizes the expected length of the a posteriori tour. This is again a NP-hard problem. In this thesis, we present a new approach to compute a good solution for PTSP based on sampling and racing techniques. The accuracy of our approach is experimentally evaluated and compared against the standard ant colony optimization metaheuristic.