Maximizing Resilience under Defender Attacker Model in Heterogeneous Multi-Networks

Our economy, military, and our society as a whole is entirely dependent on our utility infrastructure. This fact makes network security of critical importance to both the public and private sectors. Information about the vulnerability of multi-networks is critical from a defensive point of view, and it may not be immediately obvious which component is the most critical module of an infrastructure system without a sophisticated analysis. Many real-world systems have an inherently hierarchical structure in which the leader and the follower have opposite goals. This makes it of critical importance to develop bi-level models which are representative of reality and also computationally tractable. In this paper we design a nested hierarchical evolutionary model in which the attacker evolves as the defender attempts to maximize flow in their multi-commodity network. This scheme takes advantage of the ability to solve Mixed Integer Linear Programing problems (MILPs) extremely quickly using existing maximum flow techniques, while solving the NP-hard bi-level optimization problem heuristically, as our algorithm evolves towards optimality from the attacker's perspective.