Multiobjective formulation for protection allocation in interdependent infrastructure networks using an attack-diffusion model

Interdependent networks are a collection of individual networks that contain nodes that have interdependent relationships with nodes of other networks. Recognizing that many real-life networks are interdependent, approaches that were previously developed to study vulnerability in single networks are being extended to interdependent network applications (e.g., intentional attack of selected nodes). As such, this study proposes an approach for finding the best set of protection strategies for a given set of interdependent networks exposed to random or intentional attacks through the development of a multiobjective optimization formulation. A simple diffusion model [susceptible-infected-recovered (SIR)], based on cellular automata is used to describe the dynamics of the spread of the disruptive event through each individual network, and Monte Carlo simulation enables simulating the stochastic evolution of the disruption between the nodes of the interdependent networks. Several criteria considering the results of the propagation dynamics in each network or in the whole set of interdependent networks are proposed to assess the security characteristics of the network, and Pareto-optimal solutions are derived using the multiobjective evolutionary Nondominated Sorting Genetic Algorithm (NSGA-II). An example using the topology of an Italian electric power network and the set of communities previously defined illustrates the approach.