Interdiction of a Markovian Evader

TL;DR

This paper extends shortest path network interdiction to stochastic evaders modeled as Markovian random walks, proposing a nonlinear optimization formulation and a betweenness centrality heuristic for effective interdiction.

Contribution

It introduces a Markovian model for evaders in network interdiction and develops a heuristic based on betweenness centrality for efficient solution finding.

Findings

The Markovian model captures incomplete evader knowledge.

The heuristic provides high-quality interdiction solutions rapidly.

The nonlinear formulation addresses stochastic evader behavior.

Abstract

Shortest path network interdiction is a combinatorial optimization problem on an activity network arising in a number of important security-related applications. It is classically formulated as a bilevel maximin problem representing an "interdictor" and an "evader". The evader tries to move from a source node to the target node along a path of the least cost while the interdictor attempts to frustrate this motion by cutting edges or nodes. The interdiction objective is to find the optimal set of edges to cut given that there is a finite interdiction budget and the interdictor must move first. We reformulate the interdiction problem for stochastic evaders by introducing a model in which the evader follows a Markovian random walk guided by the least-cost path to the target. This model can represent incomplete knowledge about the evader, and the resulting model is a nonlinear 0-1 optimization problem. We then introduce an optimization heuristic based on betweenness centrality that can rapidly find high-quality interdiction solutions by providing a global view of the network.