Risk and resilience-based optimal post-disruption restoration for critical infrastructures under uncertainty

Post-disruption restoration of critical infrastructures (CIs) often faces uncertainties associated with the required repair tasks and the related transportation network. However, such challenges are often overlooked in most studies on the improvement of CI resilience. In this paper, two-stage risk-averse and risk-neutral stochastic optimization models are proposed to schedule repair activities for a disrupted CI network with the objective of maximizing system resilience. Both models are developed based on a scenario-based optimization technique that accounts for the uncertainties of the repair time and the travel time spent on the underlying transportation network. Given the large number of uncertainty realizations associated with post-disruption restoration tasks, an improved fast forward algorithm based on a wait-and-see solution methodology is provided to reduce the number of chosen scenarios, which results in the desired probabilistic performance metrics. To assess the risks associated with post-disruption scheduling plans, a conditional value-at-risk (CVaR) metric is incorporated into the optimization models through a scenario reduction algorithm. The proposed restoration framework is applied to the French RTE electric power network with a DC power flow procedure, and the results demonstrate the added value of using the stochastic optimization models incorporating the travel times related to repair activities. It is essential that risk-averse decision-making under uncertainty largely impacts the optimum schedule and the expected resilience, especially in the worst-case scenarios.