A multi-stage quantitative resilience analysis and optimization framework considering dynamic decisions for urban infrastructure systems

In urban infrastructure systems, resilience is crucial for maintaining functionality, minimizing losses, and expediting recovery during disruptive incidents. Effective allocating resources across various phases of emerging disturbances can generally enhance the system's capacity to cope with disasters. However, it is imperative to recognize that distinct resource allocation strategies may lead to divergent outcomes in terms of resilience performance. Therefore, this study develops a framework for optimizing resource allocation based on multiple resilience objectives by understanding the interplay between resilience performance and dynamic decisionmaking. The resilience processes are first formalized into distinct stages, considering the technical and organizational resilience of the infrastructure system in the event of disruption. Building upon this foundation, five decision scenarios are proposed, contingent on the allocation or non-allocation of resources to each resilience stage. A multi-resilience-objective mixed-integer linear programming (MROMILP) model is formulated to optimize the resource allocation scheme for each resilience stage within the constraints of internal resources. Finally, the model and framework are tested using a power system as a tangible example. The integrated multi-stage quantitative resilience assessment and optimization method proposed in this study can assist decision-makers in making dynamic and continuous trade-offs between resources and resilience targets.