A mathematical framework to optimize resilience of interdependent critical infrastructure systems under spatially localized attacks

This paper defines the hazards that can cause direct localized damage or interruption as Spatially Localized Attacks (SLAs). The SLAs-induced impact on a critical infrastructure system (CIS) is modeled as the failure of system components that exist within some localized area while those outside this area remain operating. Instead of identifying and analyzing each type of the SLAs-related hazards, this paper makes a worst-case analysis and proposes a mathematical framework to support resilience optimization of interdependent CISs under the worst SLA. For illustrative purposes, this paper mainly considers two types of strategies to enhance CIS resilience, including protecting weak components, and building new components to increase redundancy. The problem is mathematically formulated as a tri-level defender-attacker-defender model, which is exactly solved by a proposed decomposition algorithm. The case study on interdependent power and water systems demonstrates how the proposed approach can not only identify the optimum resilience enhancement strategy as well as the worst-case SLA, but also analyze the importance of considering interdependencies from both the attacker's and the defender's perspectives.