Abstract
The aim of network structural balance is to find proper partitions of nodes that guarantee equilibrium in the system, which has attracted considerable attention in recent decades. Most of existing studies focus on reducing imbalanced components in complex networks without considering the tolerance of these balanced networks against attacks and failures. However, as indicated by some recent studies, the robustness of structurally balanced networks is also important in real applications, which should be emphasized in balancing processes. Currently, it remains challenging to define suitable robustness measures for signed networks, and few performance enhancement strategies have been designed. In this paper, two measures are designed to numerically evaluate the robustness of structurally balanced networks. Furthermore, the simultaneous enhancement on these two measures is modeled as a multiobjective optimization problem, and a multiobjective evolutionary algorithm, MOEA/D-RSB, is developed to successfully solve this problem. Experiments on synthetic and real-world networks demonstrate the good performance of MOEA/D-RSB in finding robust balanced candidates. In addition, the features of partitions with different robustness performances are analyzed to show the impact of different balancing strategies on network robustness. The obtained results are valuable in dealing with some problems arising in social and natural dynamics.