Optimizing Infrastructure Resilience under Budgetary Constraint

Abstract

Natural and manmade disasters are low-probability, high-impact adverse events that incur extravagant cost and hardship on society. One way to mitigate the impact of these unfavorable events is to enhance the resilience of the system. Resilience is defined as the ability of a system to reduce the impact of an event and return it to its initial state in minimal time. The primary objective of this study is to develop methods for enhancing system resilience. To accomplish this goal, this study addresses: i) a quantification method for measuring resilience; ii) the suitability assessment of the developed resilience metric for various systems; iii) an optimization model for allocating a limited budget to components of a system to maximize improvement of the resilience; and iv) under the budget constraint, an optimal selection of multiple components of a system to minimize the total impact when those components are compromised. The resilience metric (RM) is a quantitative measure that can help evaluate the effectiveness of investments on resilience enhancement. A good RM highlights the characteristics indicated in the associated resilience framework. We propose a new resilience metric and a methodology based on analysis of variance and experimental design to assess the suitability of a resilience metric. The numerical results show that our proposed metric performs better for a general system than the existing metrics found in the literature. In our metric, the three abilities of a resilient system (absorbability, adaptability, and rapid recovery) are statistically significant, whereas other metrics either lack one of these abilities or the importance of one ability is entirely neglected. The proposed RM is used to formulate a mathematical programming model to maximize the resiliency of a system by allocating a limited budget to the system’s components. Utility curves are introduced to build alternative component enhancement options that link between the cost of resilience improvement and the effect on the component functionality. Resilience-based component importance is then utilized to map the functionality of the component onto the functionality of the system. This approach provides insights as to which component needs to be enhanced and how much budget is required to do so. To enhance the resilience of a network system, it is also essential to predict the potential action of the adversarial attacks on the network. This can be solved through the problem of finding a predetermined number of arcs whose failure have the highest impact on system functionality. This problem is computationally intensive; thus, we provide a mixed-integer formulation and a heuristic for initialization strategy to reduce the computational cost.