Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic

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.KeywordsLocal SearchVehicle Route ProblemHeuristic InformationAbsolute PerformanceTour LengthThese 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.