A hierarchical Markov decision framework for enhancing critical infrastructure resilience under sequential interdictions

The resilience of critical infrastructure systems (CIS) has drawn great attention in recent years due to the increasing number of man-made threats and natural disasters. Although CIS resilience has been extensively studied in the literature, significant gaps still exist, where stochastic attacks, facility interdependencies, and preventive resource allocations have yet to be thoroughly and holistically investigated, limiting the practicality of state-of-the-art research. In this study, we propose a novel two-stage hierarchical optimization framework to enhance CIS resilience under multi-level dependencies. The framework optimizes planning decisions including CIS network design and resource allocation, together with dynamic defense strategies against sequential attacks, resulting in a complex nonlinear optimization model with integer variables. We further derive mathematical properties and design two decomposition-based solution algorithms. Through comprehensive experiments, we show that our decomposition algorithms significantly outperform modern commercial solvers in terms of solution quality and efficiency. Utilizing analytical results, the proposed nested decomposition improves the objective value by over 102% compared with an existing nonlinear approach. A case study is conducted using real-world data from a mid-sized city in the U.S. to provide practical insights, validating the effectiveness of the dynamic policies from our framework against benchmarks.