Path Determination under Stochastic Travel Times Using Target-Oriented Robust Optimization

This paper addresses an optimal path problem in which the travel time within the travel network is subject to uncertainty. Many relevant works in the literature model the uncertainty using a random variable, however in many cases the underlying distribution of the uncertainty is not accurately determined and a solution obtained under a presumed distribution can perform poorly in practice. In this work, we assume only the lower bound and upper bound of the uncertainty is known, and by only making use of such information we determine a solution using robust optimization techniques. The solution is robust in the sense that a pre-specified travel time target can be guaranteed for an uncertainty set that is as large as possible. Additionally, the robust optimization problem itself is not necessarily to be solved, and its solution can be obtained by solving and updating a deterministic problem using existing algorithms such as Dijkstra repeatedly for several times. This makes the proposed approach applicable to large problem instances. The performance and advantages of the proposed approach is demonstrated by numerical experiments.