On greedy and strategic evaders in sequential interdiction settings with incomplete information

Abstract

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/her. By observing the evader's actions, the interdictor learns about the network structure and costs and thus, can adjust his/her actions in subsequent decision epochs. It is known from the literature that if the evader is greedy (i.e., the shortest available path is used in each decision epoch), 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 deterministic "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 outperforms the greedy evasion policy on several classes of synthetic network instances under either perfect or noisy information feedback. Finally, some interesting insights from our theoretical and computational results conclude the paper.

Providing homeland security strategies against interdictions in the city transportation network: A case study in Turkey

“…Ketkov and Prokopyev studied SPNIP with different levels of information for two sides and presented a heuristic algorithm to solve this problem with respect to some assumptions. As a result, greedy interdiction policies that block k-most vital arcs and provided computational complexity of the evader problem [48]. A summary of all reviewed SNIP studies is given in Table 1.…”

Human trafficking interdiction with decision dependent success

“…Another important aspect in a multi-stage model with uncertainties is the timeline of events and decisions. While some multi-stage network interdiction models assume that the interdictor wishes to make an interdiction decision, wait to observe the outcome of the interdiction decisions, and then adapt their strategy for future stages based on the outcome of the present stage (e.g., Ketkov & Prokopyev (2020); Borrero et al (2016); Held & Woodruff (2005)), we do not assume such "sequential" decision making.…”

On the multi-stage shortest path problem under distributional uncertainty

“…In general, the second assumption, A2, is rather standard in the robust and distributionally robust optimization literature. However, we refer to the studies in [8,9,26] for multi-stage shortest path interdiction models, in which the attacker has incomplete knowledge about the structure of the underlying network and observes the existence and precise costs of particular arcs by observing the user's decisions. Finally, Assumption A3 indicates that the distributional constraints in Q and the auxiliary constraints are of the same form.…”