An Improved Continuous-Encoding-Based Multiobjective Evolutionary Algorithm for Community Detection in Complex Networks

Community detection is a fundamental and widely studied field in network science. To perform community detection, various competitive multiobjective evolutionary algorithms (MOEAs) have been proposed. It is worth noting that the latest continuous encoding (CE) method transforms the original discrete problem into a continuous one, which can achieve better community partitioning. However, the original CE ignored important structural features of nodes, such as the clustering coefficient (CC), resulting in poor initial solutions and reduced the performance of community detection. Therefore, we propose a simple scheme to effectively utilize node structure feature vectors to enhance community detection. Specifically, a CE and CC-based (CE-CC) MOEA called CECC-Net is proposed. In CECC-Net, the CC vector performs the Hadamard product with a continuous vector (i.e., a concatenation of the continuous variables $\mathbf{x}$ associated with the edges), resulting in an improved initial individual. Then, applying the nonlinear transformation to the continuous-valued individual yields a discrete-valued community grouping solution. Furthermore, a corresponding adaptive operator is designed as an essential part of this scheme to mitigate the negative effects of feature vectors on population diversity. The effectiveness of the proposed scheme was validated through ablation and comparative experiments. Experimental results on synthetic and real-world networks demonstrate that the proposed algorithm has competitive performance in comparison with several state-of-the-art EA-based community detection algorithms.