Risk and resilience-based restoration optimization of transportation infrastructures under uncertainty.

Disruptive events cause decreased functionality of transportation infrastructures and enormous financial losses. An effective way to reduce the effects of negative consequences is to establish an optimal restoration plan, which is recognized as a method for resilience enhancement and risk reduction in the transportation system. This study takes the total travel time as the resilience measure to formulate a bilevel optimization model for a given scenario. However, the uncertainties involved in restoration activities cannot be overlooked. In this context, the inherent uncertainty is represented with a set of scenarios generated via the Latin hypercube technique. To assess the risk under uncertainty, a conditional value at risk with regret (CVaR-R) measure is introduced when considering the existence of worst-case scenarios. Then, the bilevel programming model is transformed from the deterministic case to the stochastic case, where the upper-level problem determines the restoration sequence to minimize CVaR-R and the lower-level problem is a traffic assignment problem. An integrated framework based on a novel genetic algorithm and the Frank-Wolfe algorithm is designed to solve the stochastic model. Numerical experiments are conducted to demonstrate the properties of the proposed bilevel programming model and the performance of the solution algorithm. The proposed methodology provides new insights into the restoration optimization problem, which provides a reference for emergency decision-making.