Community structure recovery optimization for partial disruption, functionality, and restoration in interdependent networks*

Community structures exist in different infrastructure networks such as water, gas, and power networks among others, where each network is split into multiple sets of components. Such sets are sparsely connected but have densely connected components within each one of them. However, critical networks often depend on each other to function properly. Consequently, such interdependencies can both improve efficiency of the collection of networks but also increase their vulnerability to a disruptive event. In this paper, we address the interdependent network restoration problem from community structures perspective. That is, how to restore community structures in a set of infrastructure networks, that are physically interdependent, following a disruptive event. Accordingly, we develop an optimization model using mixed integer programming that aims to enhance the resilience of the set of infrastructure networks considering their physical interdependency. The model prioritizes the restoration tasks for each infrastructure network, according to their influence on the performance of their respected networks, and allocates and schedules the selected restoration tasks to the available work crews. Furthermore, we present a numerical experiment for the developed optimization model with a real set of interdependent infrastructure networks in Shelby County, TN, USA, considering multiple hypothetical earthquake scenarios of different magnitudes.