Network Interdiction Goes Neural
Lei Zhang, Zhiqian Chen, Chang-Tien Lu, Liang Zhao
TL;DR
This work tackles network interdiction, a bi-level optimization problem where an attacker perturbs a graph to hamper a defender solving a CO problem. It introduces MMILP-GNN, a multipartite graph neural network that operates on MMILP-graphs derived from a single-level MILP reduction of interdiction instances, enabling learning of interdiction decisions with better compatibility to classical solvers. The authors establish theoretical representational guarantees via WL_MMILP and demonstrate algorithmic alignment with exact methods, complemented by empirical results on shortest-path and maximum-flow interdiction showing competitive performance against baselines and practical speedups when combined with a predict-and-search strategy. This approach provides a scalable bridge between neural learning and traditional MILP-based interdiction methods, with potential impact for attackers-defenders problems in networks and logistics.
Abstract
Network interdiction problems are combinatorial optimization problems involving two players: one aims to solve an optimization problem on a network, while the other seeks to modify the network to thwart the first player's objectives. Such problems typically emerge in an attacker-defender context, encompassing areas such as military operations, disease spread analysis, and communication network management. The primary bottleneck in network interdiction arises from the high time complexity of using conventional exact solvers and the challenges associated with devising efficient heuristic solvers. GNNs, recognized as a cutting-edge methodology, have shown significant effectiveness in addressing single-level CO problems on graphs, such as the traveling salesman problem, graph matching, and graph edit distance. Nevertheless, network interdiction presents a bi-level optimization challenge, which current GNNs find difficult to manage. To address this gap, we represent network interdiction problems as Mixed-Integer Linear Programming (MILP) instances, then apply a multipartite GNN with sufficient representational capacity to learn these formulations. This approach ensures that our neural network is more compatible with the mathematical algorithms designed to solve network interdiction problems, resulting in improved generalization. Through two distinct tasks, we demonstrate that our proposed method outperforms theoretical baseline models and provides advantages over traditional exact solvers.