LAUSR

The critical node detection based on cascade model is a very important way for analyzing network vulnerability and has recently attracted the attention of many researchers in complex network area. Most of existing works aim to design effective attack strategies which lead to maximal damage to the network (i.e. the destructiveness of the attack), while the number of initial attacked nodes (i.e. $k$) should be given by decision makers in advance. In this paper, we transform the critical node detection based on cascade model as a bi-objective optimization problem (named BCVND), where the destructiveness of the attack and the cost of the attack (i.e. $k$) are optimized simultaneously. The main advantage for the problem transformation is that this multi-objective optimization can provide decision makers with a holistic view for analyzing the network vulnerability. To solve BCVND, we propose an effective multi-objective evolutionary approach termed as MO-BCVND. In MO-BCVND, a cost-reduced population initialization strategy is proposed to increase the population diversity and an adaptive local search strategy is also designed to speed up the population convergence. Finally, the experimental results on 12 real-world complex networks clearly demonstrate the effectiveness of the proposed algorithm compared with the state-of-the-art baselines.