<p>The influence maximization problem (IM) involves identifying <i>K</i> seed nodes in a given network capable of producing the maximum influence range. A great stream of literature has devoted to the construction of diffusion models and seed determination approaches. The majority of existing studies focus on networks with stable structures; in this manner, the impact of typological changes on the influence diffusion process remains to be investigated. Meanwhile, network systems are inevitably subject to perturbations or even structural damages during operation. Investigating the robustness of the influence diffusion process (RIM problem) holds substantial practical significance. Related studies indicate that the cascading failure may incur severe perturbances over the connectivity, but its impact on the attached diffusion process has not been touched upon. In order to solve the RIM problem under cascading failures. In this paper, we investigate the robust influence maximization (RIM) problem under cascading failures caused by link-based attacks. A numerical metric is designed for comprehensively assessing the robust influence performance of selected seeds. The failure model is also analyzed to give reasonable parameters in the destruction process. In addition, a Memetic algorithm with niches and population recombination strategy is designed to search for seeds with stable influence aiming at solving the RIM problem, named NMA-RIM_CF-L. Finally, experiments on synthetic and authentic networks validate the competitiveness of NMA-RIM_CF-L with respect to existing approaches.</p>