An Iterative Security Game for Computing Robust and Adaptive Network Flows

The recent advancement in cyberphysical systems has led to an exponential growth in the use of automated devices which in turn has created new security challenges. By manipulating cyberphysical components, a potential attacker can modify the capacities of multiple edges so as to disrupt the network of interest. Existing robust network flow models typically assume that the entire flow of an attacked edge gets lost. However, in many practical systems, the flow of an attacked edge could potentially be rerouted through adjacent edges with residual capacity. In order to address this feature, we propose a robust and adaptive network flow model to effectively counter possible 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 response (out of some feasible attacking scenarios) 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 in order to generate a new robust (maximin) flow strategy. This iterative game continues until the objectives of both the players converge. We show that the robust and adaptive network flow problem 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 over four state-of-the-art benchmark approaches.