There are many target methods that are efficient to tackle the robustness and immunization problem, in particular, to identify the most influential nodes in a certain complex network. Unfortunately, owing to the diversity of networks, none of them could be accounted as a universal approach that works well in a wide variety of networks. Hence, in this paper, from a percolation perspective, we connect the immunization and robustness problem with an evolutionary algorithm, i.e., a framework of an evolutionary algorithm for investigation of influential nodes in complex networks, in which we have developed procedures of selection, mutation, and initialization of population as well as maintaining the diversity of population. To validate the performance of the proposed framework, we conduct intensive experiments on a large number of networks and compare it to several state-of-the-art strategies. The results demonstrate that the proposed method has significant advantages over others, especially on empirical networks in most of which our method has over 10% advantages of both optimal immunization threshold and average giant fraction, even against the most excellent existing strategies. Additionally, our discussion reveals that there might be better solutions with various initial methods.

中文翻译：

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复杂网络中影响节点调查的进化算法框架

有许多目标方法可以有效地解决鲁棒性和免疫问题，特别是识别某个复杂网络中最具影响力的节点。不幸的是，由于网络的多样性，它们都不能被视为在各种网络中都能很好地工作的通用方法。因此，在本文中，从渗透的角度来看，我们将免疫和鲁棒性问题与进化算法联系起来，即用于研究复杂网络中影响节点的进化算法框架，其中我们开发了选择、变异的程序，以及种群的初始化以及维持种群的多样性。为了验证所提议框架的性能，我们对大量网络进行了密集实验，并将其与几种最先进的策略进行了比较。结果表明，所提出的方法比其他方法具有显着优势，尤其是在经验网络中，我们的方法在大多数经验网络中具有超过 10% 的最佳免疫阈值和平均巨量分数优势，即使是针对最优秀的现有策略。此外，我们的讨论表明，各种初始方法可能有更好的解决方案。