Evolutionary clustering (EC) refers to the applications of evolutionary optimization algorithms such as genetic algorithm to data clustering. Although multi-objective evolutionary clustering algorithms were proposed to simultaneously consider different cluster properties such as compactness and separation, these techniques usually suffer from a reasonable initial population and a pre-defined number of clusters. Besides, the effectiveness of evolutionary operators is decreased in dealing with the clustering problem. On the other side, complex networks play an essential role in different fields of machine learning. In a complex network, points are considered as nodes, and the dataset is shown as a connected weighted graph. Also, complex networks tend to present a modular structure. This paper applies two concepts of complex networks including node centrality and community modularity to introduce a novel multi-objective evolutionary clustering. The proposed centrality modularity-based multi-objective evolutionary clustering (CMMOEC) takes the advantage of nodes similarity to find the best initial population of clustering solutions and provide new structural-based modularity to determine the optimal number of clusters automatically. Moreover, the proposed modularity is used to design a new recombination and mutation operator so that it generates offspring solutions that satisfy more diversity. Experiments carried out on several artificial and real-world datasets with different structures. The performance of the proposed algorithm is evaluated by the Adjusted Rand Index (ARI). Simulation results indicate that the proposed algorithm satisfies better performance in comparison to traditional methods.

进化聚类（EC）是指进化优化算法（例如遗传算法）在数据聚类中的应用。尽管提出了多目标进化聚类算法来同时考虑不同的聚类属性，例如紧密性和分离性，但是这些技术通常遭受合理的初始种群和预定义数目的聚类的困扰。此外，进化算子处理聚类问题的效率降低。另一方面，复杂的网络在机器学习的不同领域中起着至关重要的作用。在复杂的网络中，点被视为节点，而数据集则显示为连接的加权图。而且，复杂的网络倾向于呈现模块化的结构。本文应用了复杂网络的两个概念，包括节点中心性和社区模块化，以介绍一种新颖的多目标进化聚类。所提出的基于中心性模块化的多目标进化聚类（CMMOEC）利用节点相似性来找到最佳的初始聚类解决方案种群，并提供新的基于结构的模块化来自动确定最佳的聚类数量。此外，所提出的模块性用于设计新的重组和变异算子，从而生成满足更多多样性的后代解决方案。在具有不同结构的几个人工和真实数据集上进行了实验。拟议算法的性能通过调整兰德指数（ARI）进行评估。