Multi-Objective Optimization of the Robustness of Complex Networks Based on the Mixture of Weighted Surrogates

Network robustness is of paramount importance. Although great progress has been achieved in robustness optimization using single measures, such networks may still be vulnerable to many attack scenarios. Consequently, multi-objective network robustness optimization has recently garnered greater attention. A complex network structure plays an important role in both node-based and link-based attacks. In this paper, since multi-objective robustness optimization comes with a high computational cost, a surrogate model is adopted instead of network controllability robustness in the optimization process, and the Dempster-Shafer theory is used for selecting and mixing the surrogate models. The method has been validated on four types of synthetic networks, and the results show that the two selected surrogate models can effectively assist the multi-objective evolutionary algorithm in finding network structures with improved controllability robustness. The adaptive updating of surrogate models during the optimization process leads to better results than the selection of two surrogate models, albeit at the cost of longer processing times. Furthermore, the method demonstrated in this paper achieved better performance than existing methods, resulting in a marked increase in computational efficiency.