We present a best-first heuristic search approach for determining an optimal policy for a stochastic shortest path problem. A vehicle is to travel from an origin, starting at time t0, to a destination, where once the destination is reached a terminal cost is accrued. The terminal cost depends on the time of arrival. Travel time along each arc in the network is modeled as a random variable with a distribution dependent on the time that travel along the arc is begun. The objective is to determine a routing policy that minimizes expected total cost. A routing policy is a rule that assigns the next arc to traverse, given the current node and time. The heuristic search algorithm that we specialize to this stochastic problem is AO*. We demonstrate the significant computational advantages of AO*, relative to dynamic programming, on the basis of run time and storage, using a 131-intersection network of the major roads in Cleveland, Ohio. Further computational experience is based on grid networks that were randomly generated to have characteristics similar to transportation networks, and on randomly generated unstructured networks.
