Enhancing the Robustness of Networks Against Multiple Damage Models Using a Multifactorial Evolutionary Algorithm

Networked systems widely exist in the modern society, and these systems are always operated in the presence of attacks and errors. The robustness of a network indicates its tolerance against potential damages, which is crucial for the network's normal functionalities. Damage models including malicious attacks and cascading failures have been considered in previous studies. And the mitigation on these two destructive damages has attracted increasing attention, both single-objective and multiobjective optimization techniques are proposed to enhance the robustness of networks. The main weakness of these methods is that the obtained results can only handle one type of damages, either malicious attacks or cascading failures. In this way, multiple independent realizations are evitable to acquire robust candidates against different damages, which omits the inherent complementarities between the optimization of different objectives. Also, the design of networks with comprehensive robustness (CR) against both the two destructive damages is still pendent. For improving the efficiency in optimizing networks considering multiple damage models, in this article, evolutionary multitasking optimization is introduced into the optimization of network robustness. A multifactorial evolutionary algorithm (MFEA) for enhancing the CR of networks, called MFEA textsubscript CR, has been proposed. The algorithm is equipped with several dedicated genetic operators to find networks with robust structures against malicious attacks and cascading failures; meanwhile, the synergy between the optimization of the two objectives is exploited to improve the computational efficiency. Empirical studies demonstrate the competitive performance of ${\mathrm{ MFEA}}_{\mathrm{ CR}}$ over existing methods; the efficiency enhancement is remarkable via the simultaneous optimization of multiple objectives.