An Interactive Co-Evolutionary Framework for Multi-Objective Critical Node Detection on Large-Scale Complex Networks

Multi-objective evolutionary algorithms (MOEAs) have been proved to be competitive for solving the critical node detection problem (CNDP) on complex networks in both non-cascading scenario and cascading scenario. With the continuous expansion of network scale, the search space of the existing MOEAs will increase exponentially. To this end, we propose an interactive co-evolutionary framework (ICoEF) to solve the multi-objective critical node detection on large-scale complex networks, where a set of local populations as well as a global population are interactively evolved to detect the critical nodes with high qualities. Specifically, we first use a community detection algorithm to divide the original network into multiple local communities, where each local community generates a local population for quickly finding local solutions independently. Then, the latent good solutions can be easily obtained by combining the returned local solutions. After that, one global population generated by the original network can refine these latent good solutions by using the proposed two-stage replacement search strategy. Through the above local and global evolutionary interaction, a set of high-quality solutions can be finally obtained. Experiments on synthetic and real-world networks demonstrate the superiority of the proposed framework over several state-of-the-art baselines in both non-cascading and cascading scenarios.