A bilevel-optimization-driven evolutionary algorithm for community detection in multilayer networks with significant topological differences

Community detection in multilayer networks (MNCDs) is an important research topic in the field of network science. Although significant differences (e.g., variations in node sets or edge sets) often exist between different network layers, few studies have adequately considered these factors in MNCD. In this paper, we propose a novel multilayer collaborative optimization model, that employs a bilevel optimization architecture for MNCD with significant topological differences. At the upper level, we innovatively introduce the concept of consensus information, which integrates the community division results from all network layers to form a consensus, thereby providing a global MNCD perspective. At the lower level, we develop a multi-objective evolutionary algorithm based on cross-layer information (MCOEA) to address MNCD hierarchically. With modularity and newly designed cross-layer normalized mutual information (CLNMI) as two objective functions, MCOEA can effectively mitigate the negative impact of interlayer topological differences on community detection results by fully leveraging cross-layer information. Extensive experimental results on many real-world multilayer networks demonstrate the superiority of our approach over several state-of-the-art MNCD methods.