Network Interdiction Goes Neural

Network interdiction problems, arising in critical applications from military strategy to disease control, involve a complex attacker-defender dynamic: one player optimizes a network-based objective, while the other strategically modifies the network to impede that objective. The inherent bi-level optimization and combinatorial nature of these problems pose a significant computational challenge, often rendering traditional exact solvers impractical and hindering the development of effective heuristics. While Graph Neural Networks (GNNs) have demonstrated promise in solving single-level combinatorial optimization problems on graphs, their direct application to bi-level interdiction problems remains limited. In this paper, we bridge this gap by introducing a novel approach that leverages the power of GNNs to learn Mixed-Integer Linear Programming (MILP) formulations of network interdiction problems. By representing the problem in this structured mathematical form, we empower a multipartite GNN with the representational capacity to effectively capture the complex interplay between the two players. This approach aligns the neural network with the underlying mathematical structure of interdiction problems, leading to improved performance. Through extensive experiments on two network interdiction tasks, we demonstrate the superiority of our proposed method over both baseline GNN models and traditional exact solvers, showcasing its potential for real-world applications.