Failure Mitigation and Restoration in Interdependent Networks via Mixed-Integer Optimization

We propose a new optimization model for determining optimal mitigation and restoration strategies for coupled interdependent networks in the context of preserving and/or restoring the maximum flow through the entire networked system, subject to cascading node failures that may be caused by disruptions of a subset of “seed nodes” at an initial time step. Previous related studies mainly focused on “static” strategies to mitigate cascading failures. However, our model allows one to identify “dynamic” strategies for step-by-step failure propagation, given initial seed node disruptions. Moreover, the proposed model accounts for backup arc capacity and node fortification to mitigate the impact of further failure cascades on network performance. The objective is to restore network performance during a finite recovery planning horizon at total minimal cost. We formulate this problem by mixed-integer optimization, and derive valid inequalities using the substructure of the problem. We report a summary of computational experiments to demonstrate the strength and effectiveness of the inequalities when compared to solving the problem with a commercial optimization solver.