A Two-Phase Multiobjective Evolutionary Algorithm for Enhancing the Robustness of Scale-Free Networks Against Multiple Malicious Attacks
针对现实世界中多种攻击可能同时发生的情况，将不同攻击类型的鲁棒性度量作为目标，提出两阶段多目标进化算法MOEA-RSFMMA，在合成和真实网络上验证了其有效性，为决策者提供多种网络设计选择。
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.