Last-Mile Restoration for Multiple Interdependent Infrastructures

This paper considers the restoration of multiple interdependent infrastructures after a man-made or natural disaster. Modern infrastructures feature complex cyclic interdependencies and require a holistic restoration process. This paper presents the first scalable approach for the last-mile restoration of the joint electrical power and gas infrastructures. It builds on an earlier threestage decomposition for restoring the power network that decouples the restoration ordering and the routing aspects. The key contributions of the paper are (1) mixed-integer programming models for finding a minimal restoration set and a restoration ordering and (2) a randomized adaptive decomposition to obtain highquality solutions within the required time constraints. The approach is validated on a large selection of benchmarks based on the United States infrastructures and state-of-the-art weather and fragility simulation tools. The results show significant improvements over current field practices. Background and Motivation Restoring critical infrastructure after a significant disruption (e.g., a natural or man-made disaster) is an important task with consequences on both human and economic welfare. Damaged components must be prioritized and repaired, to restore service as quickly as possible without causing additional instability. Last-mile restoration considers infrastructure damages at the city or the state scale and is particularly complex as it amounts to solving a pickup and delivery routing problem, whose objective function minimizes loss of service over time in an interdependent infrastructure. It contrasts with humanitarian relief efforts which are more concerned with effectively establishing one-time supply chains. Last-mile restoration has attracted increased attention in recent years but the majority of the research is devoted to single infrastructures, e.g., the power network or potable water supply. However, modern infrastructures exhibit multiple, often cyclic, interdependencies. For instance, the gas network may fuel an electric generator or a gas compressor may consume electricity to increase the pressure in Copyright c © 2012, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. pipelines. Therefore, it is critical to restore these infrastructures jointly to maximize the level of service over time. This paper proposes the first last-mile restoration approach of multiple complex interdependent infrastructures. It uses mixed-integer programs (MIP) for modeling interdependent power and gas networks, combining the linearized DC model for the power network and a flow model for the gas network. The models are then integrated into the multistage last-mile restoration approach proposed in (Van Hentenryck, Coffrin, and Bent 2011) for the power network, which is used to advise federal agencies when hurricanes of category 3 or above approach the United States. The infrastructure interdependencies induce computational difficulties for MIP solvers in the prioritization step, which we address by using a randomized adaptive decomposition (RAD) approach. The RAD approach iteratively improves a restoration order by selecting smaller restoration subproblems which are solved independently. The proposed approach was evaluated systematically on a large collection of benchmarks generated with state-of-the-art hazard and fragility simulation tools on the infrastructure of the United States. The results demonstrate the scalability of the approach, which finds very high-quality solutions to large lastmile restoration problems and brings significant improvements over current field practices. The rest of the paper describes the modeling of multiple interdependent infrastructures and our approach for lastmile restoration of such infrastructures. It presents the experimental results and concludes with a discussion of related work in restoration of interdependent infrastructures. Infrastructure Modeling Power and gas infrastructures can be modeled and optimized at various levels of abstraction. Linear approximations are typically used for applications involving topological changes, a design choice followed by this paper as well. This section presents a demand maximization model for interdependent power and gas infrastructures, which is a key building block for the restoration models. The Power Infrastructure The power infrastructure is modeled in terms of the Linearized DC Model (LDCM), a standard tool in power systems (e.g., (Murillo-Sánchez and Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence