On Some Probabilistic Combinatorial Optimization Problems Defined on Graphs

A probabilistic traveling salesman problem (PTSP) is essentially a traveling salesman problem (TSP) in which the number of nodes to be visited in each problem instance is a random variable. One can define, as well, other probabilistic problems in the context of network optimization. In this paper we give an overview of some results obtained on the PTSP and on a probabilistic version of the shortest-path problem.