Distributionally robust stochastic shortest path problem

This paper considers a stochastic version of the shortest path problem, the Distributionally Robust Stochastic Shortest Path Problem(DRSSPP) on directed graphs. In this model, the arc costs are deterministic, while each arc has a random delay. The mean vector and the second-moment matrix of the uncertain data are assumed known, but the exact information of the distribution is unknown. A penalty occurs when the given delay constraint is not satisfied. The objective is to minimize the sum of the path cost and the expected path delay penalty. As it is NP-hard, we approximate the DRSSPP with a semidefinite programming (SDP for short) problem, which is solvable in polynomial time and provides tight lower bounds.