Identifying critical nodes in multiplex complex networks by using memetic algorithms

The problem of dismantling multiplex complex networks, i.e., finding a minimal set of critical nodes to achieve maximum disruption, has received extensive attention because many real-world complex systems can more properly be represented as multiplex complex networks. However, most related studies mainly focus on the single-layer network dismantling, which ignores the inter-layer relationships of the real-world complex systems. Meanwhile, most of the existing network dismantling methods provide a set of critical nodes only considering a single predetermined measure such as degree centrality, betweenness centrality, or collective influence. Unfortunately, this approach is not universally valid, especially in the context of multiplex complex networks. In our study, a memetic algorithm (MA) that combines a group-based global search with an individual-based local search is proposed for identifying critical nodes in the multiplex complex networks, which may lead to a set of critical nodes considering different measures. In addition, we design an efficient crossover operator and a local search operator novelly considering the influence of node neighborhoods. We conduct extensive experiments by synthetic and real-world multiplex complex networks with different inter-layer linking properties, showing that the proposed MA method has better critical node identification capability than that of several state-of-the-art methods. We also analyze the characteristics of nodes found by our MA, indicating that the critical node set is not composed of a single predetermined metric, but a combination of nodes with multiple metrics. MA shows excellent performance in enhancing the robustness of beneficial networks and dismantling deleterious networks, especially in disassortative link networks.