The robustness of complex networks is of great significance. Great achievements have been made in robustness optimization based on single measures, however, such networks may still be vulnerable to multiple attack scenarios. Therefore, recently, multiobjective robustness optimization of networks has received increasing attention. Nevertheless, several challenges remain to be addressed, including the different computational complexities in evaluating the objectives, insufficient diversity in the obtained networks, and high computational costs of the search process. In this article, we address the aforementioned challenges by developing a computationally efficient multiobjective optimization algorithm. Based on the unique features of complex networks, a new parallel fitness evaluation method guided by a network property parameter is designed and embedded in a reference vector-guided multiobjective evolutionary algorithm. In addition, a surrogate ensemble with heterogeneous inputs is constructed based on graph embedding information to efficiently estimate multiple robustness of networks. The proposed algorithm is validated on synthetic and real-world network data and our results show that the designed algorithm outperforms the state-of-the-art method with a marked improvement on the computational efficiency. Compared with other single-objective optimization methods, the proposed algorithm demonstrates a considerable exploitation ability.

中文翻译：

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一种用于多目标网络鲁棒性优化的计算高效进化算法

复杂网络的鲁棒性具有重要意义。基于单一措施的鲁棒性优化取得了很大的成就，但这种网络可能仍然容易受到多种攻击场景的影响。因此，最近，网络的多目标鲁棒性优化受到越来越多的关注。尽管如此，仍有一些挑战有待解决，包括评估目标的不同计算复杂性、所获得网络的多样性不足以及搜索过程的高计算成本。在本文中，我们通过开发计算效率高的多目标优化算法来解决上述挑战。基于复杂网络的独特特征，设计了一种新的由网络属性参数引导的并行适应度评估方法，并将其嵌入到参考向量引导的多目标进化算法中。此外，基于图嵌入信息构建了具有异构输入的代理集成，以有效地估计网络的多重鲁棒性。所提出的算法在合成和真实世界的网络数据上进行了验证，我们的结果表明，所设计的算法优于最先进的方法，并显着提高了计算效率。与其他单目标优化方法相比，该算法展示了相当大的开发能力。基于图嵌入信息构建具有异构输入的代理集成，以有效估计网络的多重鲁棒性。所提出的算法在合成和真实世界的网络数据上进行了验证，我们的结果表明，所设计的算法优于最先进的方法，并显着提高了计算效率。与其他单目标优化方法相比，该算法展示了相当大的开发能力。基于图嵌入信息构建具有异构输入的代理集成，以有效估计网络的多重鲁棒性。所提出的算法在合成和真实世界的网络数据上进行了验证，我们的结果表明，所设计的算法优于最先进的方法，并显着提高了计算效率。与其他单目标优化方法相比，该算法展示了相当大的开发能力。