Robust Design of Interdependent Networks Considering Intra-Network Support Flow

Cyber-physical systems comprise multiple interdependent networks supporting each other. A node in an interdependent network fails when it cannot receive a sufficient volume of support from normal nodes in the other interdependent networks. Meanwhile, each node loses its support capability if it cannot terminate intra-network flow named “support flow”, which corresponds to the flow of electric power in the power grid and the flow of control messages in the computer network. This means that each sink node of the support flow is regarded as being in a failure state when it is disconnected with all the normal source nodes of the support flow in the same network. This criterion of the sink node failure increases the possibility of an initial node failure invoking a cascading failure with a wide range. This paper proposes a robust design method for the interdependent networks that takes the support flow into account. The proposed method can derive the optimum interdependency to minimize the greatest impact of the cascading failures induced from a given set of the initial node failures. The robust design problem is formulated using a mixed integer linear programming model and two kinds of metaheuristic methods are proposed to solve the problem efficiently even when numerous initial node failures are specified. Several characteristics of the risk of the cascading failures are revealed from the results of the proposed robust design. Simulation experiments demonstrate the effectiveness of the proposed metaheuristic methods.