Optimization under Uncertainty with Bounded Risk Exposure for Community Resilience Planning against Natural Hazards

Abstract

Natural hazards pose a major threat to the safety, functionality, and economic stability of communities. This can cause widespread destruction of buildings and infrastructure, disrupt essential services, and significant loss of life and property. The increasing frequency and severity of such events, due to rapid population growth, urbanization, and the expansion of cities into vulnerable areas, have emphasized the importance of proactive planning and strategic investment in mitigation. Given resource constraints, prioritizing retrofit investments through optimized allocation strategies becomes crucial. This study proposes a chance-constrained optimization framework for determining optimal retrofitting strategies for buildings exposed to natural hazard risks. The model accounts for uncertainty by incorporating multiple scenarios and aims to minimize the maximum expected value loss, subject to budgetary constraints and a probabilistic performance requirement. A case study was conducted in Shelby County, TN, where various earthquake scenarios were simulated to evaluate their potential impacts on the buildings of the community. The chance constraint ensures that the total expected loss stays within an acceptable limit in the required percentage of scenarios, allowing for risk-informed decision-making. The model was tested with different chance-constrained thresholds and budgetary performance levels to evaluate its effectiveness. Results demonstrate the model’s ability to target high-risk buildings and allocate limited resources efficiently. The structure of the mathematical model was also exploited through Benders decomposition approach, where the master problem selects scenarios to consider and the subproblem evaluates strategies based on the selected scenarios. For a large-scale risk-aware infrastructure retrofitting planning framework, the decomposition approach can play a crucial role in finding the optimal strategy. This work highlights the value of integrating risk analysis and optimization in resilience planning and offers a practical tool for policymakers aiming to enhance community resilience. By helping communities prioritize retrofitting actions based on potential losses and scenario probabilities, the framework supports long-term resilience and disaster preparedness in a data-driven manner. Although applied to earthquake hazards in this study, the model can also be adapted to support resilience planning for diverse types of hazards or communities.