TY - JOUR

T1 - New reformulations of distributionally robust shortest path problem

AU - Cheng, Jianqiang

AU - Leung, Janny

AU - Lisser, Abdel

N1 - Funding Information:
This research benefited from the support of the FMJH Program Gaspard Monge in optimization and operation research , and from the support to this program from EDF. PGMO/IROE Grant no. 2012-042H .
Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - This paper considers a stochastic version of the shortest path problem, namely the Distributionally Robust Stochastic Shortest Path Problem (DRSSPP) on directed graphs. In this model, each arc has a deterministic cost and a random delay. The mean vector and the second-moment matrix of the uncertain data are assumed to be 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 this problem is NP-hard, we propose new reformulations and approximations using a sequence of semidefinite programming problems which provide tight lower bounds. Finally, numerical tests are conducted to illustrate the tightness of the bounds and the value of the proposed distributionally robust approach.

AB - This paper considers a stochastic version of the shortest path problem, namely the Distributionally Robust Stochastic Shortest Path Problem (DRSSPP) on directed graphs. In this model, each arc has a deterministic cost and a random delay. The mean vector and the second-moment matrix of the uncertain data are assumed to be 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 this problem is NP-hard, we propose new reformulations and approximations using a sequence of semidefinite programming problems which provide tight lower bounds. Finally, numerical tests are conducted to illustrate the tightness of the bounds and the value of the proposed distributionally robust approach.

KW - Distributionally robust optimization

KW - Semidefinite programming

KW - Shortest path

KW - Stochastic programming

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U2 - 10.1016/j.cor.2016.05.002

DO - 10.1016/j.cor.2016.05.002

M3 - Article

AN - SCOPUS:84969257722

SN - 0305-0548

VL - 74

SP - 196

EP - 204

JO - Computers and Operations Research

JF - Computers and Operations Research

ER -