Shortest path network interdiction with asymmetric uncertainty
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- Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York USA, Sandia National Laboratories Livermore California USA, Operations Research The MITRE Corporation McLean Virginia USA
- Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York USA
- Operations Research The MITRE Corporation McLean Virginia USA, Operations Research and Computational Analysis Department Sandia National Laboratories Livermore California USA
- Operations Research The MITRE Corporation McLean Virginia USA, Discrete Math and Optimization Department Sandia National Laboratories Livermore California USA
- Operations Research The MITRE Corporation McLean Virginia USA, Advanced Science &, Technology Division Sandia National Laboratories Livermore California USA
Abstract This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed‐integer semi‐infinite bilevel program and show that it can be converted into a mixed‐integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst‐case possibilities.
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- DE‐NA000352
- OSTI ID:
- 2282219
- Journal Information:
- Networks, Journal Name: Networks; ISSN 0028-3045
- Publisher:
- Wiley Blackwell (John Wiley & Sons)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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