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Regular version of the site

Article

On Greedy and Strategic Evaders in Sequential Interdiction Settings with Incomplete Information

Omega. 2020. Vol. 92. P. 102161.
Sergey S. Ketkov, Oleg A. Prokopyev.

We consider a class of sequential network interdiction problem settings where the interdictor has incomplete initial information about the network while the evader has complete knowledge of the network including its structure and arc costs. In each decision epoch, the interdictor can block (for the duration of the epoch) at most k arcs known to him. By observing the evader's actions, the interdictor learns about the network structure and costs and thus, can adjust his actions in subsequent decision epochs. It is known from the literature that if the evader is greedy (i.e., she uses the shortest available path in each decision epochs), then under some assumptions the greedy interdiction policies that block k-most vital arcs in each epoch are efficient and have a finite regret. In this paper, we consider the evader's perspective and explore strategic evasion policies under the assumption that the interdictor is greedy. We first study the theoretical computational complexity of the evader's problem. Then we derive basic constructive properties of optimal evasion policies for two decision epochs when the interdictor has no initial information about the network structure. These properties are then exploited for the design of a heuristic algorithm for a strategic evader in a general setting with an arbitrary time horizon and any initial information available to the interdictor. Our computational experiments demonstrate that the proposed heuristic consistently outperforms the greedy evasion policy on several classes of synthetic network instances under perfect and noisy information feedbacks. Finally, some interesting insights from our theoretical and computational results conclude the paper.