A Two-Phase Multiobjective Evolutionary Algorithm for Enhancing the Robustness of Scale-Free Networks Against Multiple Malicious Attacks.

Designing robust networks has attracted increasing attentions in recent years. Most existing work focuses on improving the robustness of networks against a specific type of attacks. However, networks which are robust against one type of attacks may not be robust against another type of attacks. In the real-world situations, different types of attacks may happen simultaneously. Therefore, we use the Pearson's correlation coefficient to analyze the correlation between different types of attacks, model the robustness measures against different types of attacks which are negatively correlated as objectives, and model the problem of optimizing the robustness of networks against multiple malicious attacks as a multiobjective optimization problem. Furthermore, to effectively solve this problem, we propose a two-phase multiobjective evolutionary algorithm, labeled as MOEA-RSFMMA. In MOEA-RSFMMA, a single-objective sampling phase is first used to generate a good initial population for the later two-objective optimization phase. Such a two-phase optimizing pattern well balances the computational cost of the two objectives and improves the search efficiency. In the experiments, both synthetic scale-free networks and real-world networks are used to validate the performance of MOEA-RSFMMA. Moreover, both local and global characteristics of networks in different parts of the obtained Pareto fronts are studied. The results show that the networks in different parts of Pareto fronts reflect different properties, and provide various choices for decision makers.