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.

中文翻译：

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使用多目标进化算法的有符号网络中的稳健结构平衡

网络结构平衡的目的是找到保证系统平衡的适当节点划分，这在近几十年来引起了相当大的关注。大多数现有研究都集中在减少复杂网络中的不平衡组件，而没有考虑这些平衡网络对攻击和故障的容忍度。然而，正如最近的一些研究表明，结构平衡网络的鲁棒性在实际应用中也很重要，在平衡过程中应该强调这一点。目前，为签名网络定义合适的健壮性措施仍然具有挑战性，并且设计的性能增强策略很少。在本文中，设计了两种措施来数值评估结构平衡网络的鲁棒性。此外，这两个措施的同时增强被建模为多目标优化问题，并且开发了多目标进化算法 MOEA/D-RSB 来成功解决这个问题。合成网络和真实世界网络的实验证明了 MOEA/D-RSB 在寻找稳健的平衡候选者方面的良好性能。此外，还分析了具有不同鲁棒性能的分区的特征，以展示不同平衡策略对网络鲁棒性的影响。获得的结果对于处理社会和自然动力学中出现的一些问题是有价值的。合成网络和真实世界网络的实验证明了 MOEA/D-RSB 在寻找稳健的平衡候选者方面的良好性能。此外，还分析了具有不同鲁棒性能的分区的特征，以展示不同平衡策略对网络鲁棒性的影响。获得的结果对于处理社会和自然动力学中出现的一些问题是有价值的。合成网络和真实世界网络的实验证明了 MOEA/D-RSB 在寻找稳健的平衡候选者方面的良好性能。此外，还分析了具有不同鲁棒性能的分区的特征，以展示不同平衡策略对网络鲁棒性的影响。获得的结果对于处理社会和自然动力学中出现的一些问题是有价值的。