Distributionally robust stochastic shortest path problem |
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| Institution: | 1. LIA, Université d''Avignon et des Pays des Vaucluse, Avignon, France;2. UMR CNRS 5506 LIRMM, Université de Montpellier, Montpellier, France;3. PESC, UFRJ, Rio de Janeiro, Brazil;1. State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. Department of Energy Technology, Aalborg University, Aalborg DK9220, Denmark;1. School of Mathematics and Statistics, Xi''an Jiaotong University, Xi''an, Shaanxi, 710049, P. R. China;2. Laboratoire de Recherche en Informatique, Université Paris Sud, Bat 650 Ada Lovelace, Orsay, 91405, France;1. LUNAM Université, École Centrale de Nantes, IRCCyN UMR CNRS 6597 (Institut de Recherche en Communications et Cybernétique de Nantes), 1 rue de la Noë, B.P. 92101, 44321 Nantes Cedex 3, France;2. National Institute of Informatics, 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan;3. CNRS, Laboratoire de Recherche en Informatique, UMR CNRS 8623, Université Paris-Sud, 91405 Orsay Cedex, France |
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| Abstract: | 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. |
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| Keywords: | Stochastic programming Shortest path Distributionally robust Semidefinite programming |
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