Wasserstein Distributionally Robust Shortest Path Problem
Abstract
This paper proposes a datadriven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we aim to find an optimal path to minimize the worstcase $\alpha$reliable meanexcess travel time (METT) over a Wasserstein ball, which is centered at the empirical distribution of the sample dataset and the ball radius quantifies the level of its confidence. In sharp contrast to the existing DRSP models, our model is equivalently reformulated as a tractable mixed 01 convex problem, e.g., 01 linear program or 01 secondorder cone program. Moreover, we also explicitly derive the distribution achieving the worstcase METT by simply perturbing each sample. Experiments demonstrate the advantages of our DRSP model in terms of the outofsample performance and computational complexity. Finally, our DRSP model is easily extended to solve the DR bicriteria shortest path problem and the minimum cost flow problem.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.09128
 Bibcode:
 2019arXiv190209128W
 Keywords:

 Mathematics  Optimization and Control