In the research of complex networks, how to find a set of nodes in the network with the most extensive range in the propagation process, i.e., the Influence Maximization (IM) problem, is one of the focal topics. Existing studies mainly consider the information dissemination process on networks and how to select diffusive nodes efficiently, but little attention has been paid to changes related to the network structure. In reality, networked systems are exposed to uncertain interferences and even destructive sabotages, and cascading failures are one common destruction that can cause networks to collapse even if only a small number of nodes fail. In the case of various complex environmental factors, how to select robust and influential nodes, i.e., the robust influence maximization (RIM) problem, is of great importance in promoting the realistic application of the influence maximization problem. This paper investigates the RIM problem under cascading failures to address the shortcomings in previous studies. Based on existing research, a new performance evaluation metric, , is designed to assess the level of robust influence in a numerical form. For solving the seed determination problem, a Memetic algorithm towards the RIM problem under cascading failures, MA-RIM, is designed to find nodes with stable information propagation capability guided by . Experiments have been conducted on both synthetic and realistic networks to validate the performance of the algorithm. Results indicate that MA-RIM can obtain competitive candidates over existing approaches, and seeds with robust and influential abilities are generated to solve diffusion dilemmas.

中文翻译：

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使用模因算法从级联故障下的网络中查找稳健且有影响力的节点

在复杂网络的研究中，如何找到网络中传播过程中范围最广的一组节点，即影响最大化（IM）问题，是焦点问题之一。现有的研究主要考虑网络上的信息传播过程以及如何有效地选择扩散节点，而很少关注与网络结构相关的变化。事实上，网络系统会受到不确定的干扰，甚至是破坏性的破坏，而级联故障是一种常见的破坏，即使只有少量节点发生故障，也可能导致网络崩溃。在各种复杂环境因素的情况下，如何选择鲁棒且有影响力的节点，即鲁棒影响最大化（RIM）问题，对于促进影响最大化问题的实际应用具有重要意义。本文研究了级联故障下的 RIM 问题，以解决先前研究的不足。基于现有研究，设计了一种新的绩效评估指标，以数字形式评估稳健影响力的水平。为了解决种子确定问题，设计了一种针对级联故障下 RIM 问题的 Memetic 算法 MA-RIM，以寻找具有稳定信息传播能力的节点。在合成网络和现实网络上进行了实验，以验证算法的性能。结果表明，MA-RIM 可以获得比现有方法有竞争力的候选者，并生成具有强大且有影响力的能力的种子来解决扩散困境。