Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience

Resilience is often thought of as the ability to withstand a disruption and recover quickly from it. Thus, improving the resilience of an infrastructure system is often associated with reducing its vulnerability (related to the extent to which a network is disrupted), and increasing its recoverability (related to the speed of restoration). To address these concerns simultaneously, we propose a tri-level protection-interdiction-restoration problem for a system of interdependent networks, to optimally balance vulnerability and recoverability before and after a disruption. In particular, the proposed tri-level model represents decisions made (i) by a defender before a disruption to reduce network vulnerability, (ii) by an attacker to effectively disrupt the network, and (iii) by a defender after the disruption to enhance recoverability. To solve the proposed protection-interdiction-restoration model to optimality, we use a tailored extension of the covering decomposition algorithm. To illustrate the proposed tri-level model and the modified covering decomposition algorithm, we present a case-study of the system of interdependent water, gas, and power utilities in Shelby County, TN. The computational results show the value of simultaneous analysis of both pre-disruption investments (to reinforce critical network components) and post-disruption resource assignment and crew scheduling.