Network robustness optimization is crucial for enhancing the resilience of industrial networks and social systems against malicious attacks. Existing studies typically evaluate the robustness by simulating the sequential removal of nodes or edges and recording the residual connectivity at each step. However, the attack simulation is computationally expensive and becomes impractical for large-scale networks. Therefore, this paper proposes a multiobjective evolutionary algorithm assisted by a graph isomorphism network (GIN)-based surrogate model to efficiently optimize network robustness. First, the robustness optimization task is formulated as a multiobjective problem that simultaneously considers network robustness against attacks and the structural modification cost. Then, a GIN-based surrogate model is constructed to approximate the robustness, replacing the expensive simulation assessments. Finally, the multiobjective evolutionary algorithm is employed to explore promising network structures guided by the surrogate model, which is continuously updated via online learning to improve both prediction accuracy and optimization performance. Experimental results in various synthetic and real-world networks demonstrate that the proposed algorithm reduces the computational cost of the robustness evaluation by about 65% while achieving comparable or even superior robustness optimization performance compared with those of baseline algorithms. These results indicate that the proposed method is practical and scalable and can be applied to enhance the robustness of industrial and social networks.
Li et al. (Mon,) studied this question.