A probabilistic traveling salesman problem: a survey

Abstract

The Probabilistic Traveling Salesman Problem (PTSP) is a variation of the classic Traveling Salesman Problem (TSP) in which only a subset of potential nodes needs to be visited on any given instance of the problem. The number of nodes to be visited each time is a random variable. The objective is to find an a priori tour which minimizes the expected length,with the strategy of visiting the present nodes in a particular instance in the same order as they appear in the a priori tour. In this paper, we survey a number of results obtained for PTSP and we present the different approaches used for solving it.