Abstract: Enhancing the robustness of complex networks is crucial for their resilience against external attacks and cascading failures. Existing evolutionary algorithms face limitations in addressing optimization issues related to network structures, particularly concerning convergence and optimization speed. In response to this challenge, this paper proposes an innovative adaptive complex network robustness optimization algorithm (SU-ANet). To mitigate the substantial time cost associated with robustness computations, a robustness predictor based on an attention mechanism is introduced as an offline surrogate model, replacing frequent robustness computations in local search operator. Throughout the evolutionary process, the algorithm comprehensively considers global and local information, aiming to avoid falling into local optima while simultaneously broadening the search space. The design of crossover operators involves edge exchanges between each individual and global best candidates, as well as a random individual, to balance the algorithm's convergence and diversity. Additionally, the algorithm employs a parameter self-adaptive mechanism to automatically adjust operator execution probabilities during the evolutionary process, alleviating the impact of parameter design uncertainty on algorithm performance. Experimental validation on both artificially synthesized networks and real-world networks demonstrates that the proposed algorithm exhibits superior search capabilities and higher evolutionary efficiency.

Key words: complex networks, evolutionary algorithm, adaptive parameter, robustness, surrogate model

摘要： 提升复杂网络的鲁棒性对于网络抵御外部攻击和级联失效具有重要现实意义。现有进化算法在解决网络结构优化问题时存在局限，特别是在收敛性和优化速度方面有待提升。针对这一问题，本文提出了一种创新的自适应复杂网络鲁棒性优化算法（SU-ANet）。为降低鲁棒性计算所带来的巨大时间开销，构建了基于注意力机制的鲁棒性预测器作为离线代理模型，以代替局部搜索算子中频繁的鲁棒性计算。在进化过程中，算法全面考虑了的全局和局部信息，旨在避免陷入局部最优，同时拓宽解空间的搜索范围。通过设计交叉算子，每个个体与全局最优候选解和随机个体进行连边互换，以平衡算法的收敛性和多样性。此外，算法采用参数自适应机制自动调整算子执行概率，从而缓解参数设计对算法性能带来的不确定性。通过在人工合成网络和真实网络上的实验证明，本文提出的算法具有更好的搜索能力和更高的进化效率。

关键词: 复杂网络, 进化算法, 参数自适应, 鲁棒性, 代理模型