An Approximate Dynamic Programming Approach to Community Recovery Management (Extended Abstract)

The functioning of interdependent civil infrastructure systems in the aftermath of a disruptive event is critical to the performance and vitality of any modern urban community. Post-event stressors and chaotic circumstances, time limitations, and complexities in the community recovery process highlight the necessity for a comprehensive decision-making framework at the community-level for post-event recovery management. Such a framework must be able to handle large-scale scheduling and decision processes, which involve difficult control problems with large combinatorial decision spaces. This study utilizes approximate dynamic programming algorithms along with heuristics for the identification of optimal community recovery actions following the occurrence of an extreme earthquake event. The proposed approach addresses the curse of dimensionality in its analysis and management of multi-state, large-scale infrastructure systems. Furthermore, the proposed approach can consider the cur-rent recovery policies of responsible public and private entities within the community and shows how their performance might be improved. A testbed community coarsely modeled after Gilroy, California, is utilized as an illustrative example. While the illustration provides optimal policies for the Electrical Power Network serving Gilroy following a severe earthquake, preliminary work shows that the methodology is computationally well suited to other infrastructure systems and hazards.

💡 Research Summary

The paper addresses the challenging problem of post‑disaster community‑level infrastructure recovery, focusing on the electrical power network (EPN) of Gilroy, California, after a severe earthquake. Traditional dynamic programming (DP) can theoretically yield optimal recovery schedules, but its state‑and‑action spaces explode for realistic, large‑scale systems, making DP computationally infeasible. To overcome this “curse of dimensionality,” the authors adopt an Approximate Dynamic Programming (ADP) technique known as the rollout algorithm.

In the rollout framework a base heuristic (the “policy”) is used to approximate the cost‑to‑go function Jα that appears in the Bellman recursion. The authors deliberately choose a random heuristic, demonstrating that the method works with any admissible policy, including existing municipal recovery plans or risk‑based heuristics. At each decision epoch t, the algorithm evaluates the expected benefit of assigning the limited number of repair units (RUs) to any subset of the currently damaged components (|Dt| ≫ N) and selects the subset that maximizes the approximated value function. This yields a near‑optimal sequence of repair actions X = {x1,…,xt end}.

Two objective functions are defined. Objective 1 seeks to minimize the time required to restore electricity to a target fraction γ of the total population p (e.g., γ = 0.8). Objective 2 adds a second societal goal: restoring power to the six major food retailers that are critical for food distribution. Both objectives are expressed as minimization of a cost‑to‑go function that aggregates the number of people or facilities benefiting from restored service over time.

The case study models Gilroy as a 36‑cell grid covering 41.9 km², with each cell containing power lines, substations, and residential demand. Earthquake ground motion is generated using the Abrahamson et al. (2013) GMPE, and component fragility is taken from HAZUS and Xie et al. (2012). Restoration times are assigned according to damage severity based on HAZUS and Nozhati et al. (2018b). The limited resource pool N is assumed to consist of identical repair units, each capable of fixing one component at a time.

Simulation results compare the random‑policy baseline (denoted H) with the rollout‑enhanced policy. For Objective 1, the rollout reduces the expected time to achieve γ = 0.8 population coverage from roughly 30 days (baseline) to about 8 days. For Objective 2, the rollout similarly accelerates the restoration of power to the food retailers, leading to a faster overall recovery of the food distribution network. Figures in the paper illustrate the mean and standard deviation of the number of households with electricity over time, as well as the performance gap between H and rollout for both objectives.

The authors discuss that the rollout algorithm consistently outperforms the base heuristic, even when the base is a naïve random policy, confirming the robustness of the approach. They also note that employing more informed heuristics (e.g., risk‑based “smart” policies) could further improve outcomes, and that integrating meta‑heuristics or stochastic modeling of repair success is an active research direction.

In conclusion, the study demonstrates that a rollout‑based ADP framework can generate near‑optimal, computationally tractable recovery schedules for large, interdependent infrastructure systems. While the demonstration focuses on the electrical power network after an earthquake, the methodology is generic and can be extended to other utility networks (water, transportation) and to different hazard types (floods, wildfires). The work provides a practical decision‑support tool for policymakers seeking to allocate scarce repair resources efficiently while meeting multiple community recovery objectives.