An iterative security game for computing robust and adaptive network flows

Abstract We study the robust and adaptive maximum network flow problem in an uncertain environment where the network parameters (e.g., capacities) are known and deterministic, but the network structure (e.g., edges) is vulnerable to adversarial attacks or failures. We propose a robust and sustainable network flow model to effectively and proactively counter plausible attacking behaviors of an adversary operating under a budget constraint. Specifically, we introduce a novel scenario generation approach based on an iterative two-player game between a defender and an adversary. We assume that the adversary always takes a best myopic response (out of some feasible attacks) against the current flow scenario prepared by the defender. On the other hand, we assume that the defender considers all the attacking behaviors revealed by the adversary in previous iterations of the game in order to generate a new conservative flow strategy that is robust (maximin) against all those attacks. This iterative game continues until the objectives of the adversary and the administrator both converge. We show that the robust network flow problem to be solved by the defender is NP-hard and that the complexity of the adversary’s decision problem grows exponentially with the network size and the adversary’s budget value. We propose two principled heuristic approaches for solving the adversary’s problem at the scale of a large urban network. Extensive computational results on multiple synthetic and real-world data sets demonstrate that the solution provided by the defender’s problem significantly increases the amount of flow pushed through the network and reduces the expected amount of lost flow over four state-of-the-art benchmark approaches.