In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to efficiently partition the graph into clusters, ensuring that nodes within a cluster are closely linked by positive edges while minimizing negative edge connections between them. To tackle this challenge, we first develop a scalable multilevel algorithm based on label propagation and FM local search. Then we develop a memetic algorithm that incorporates a multilevel strategy. This approach meticulously combines elements of evolutionary algorithms with local refinement techniques, aiming to explore the search space more effectively than repeated executions. Our experimental analysis reveals that this our new algorithms significantly outperforms existing state-of-the-art algorithms. For example, our memetic algorithm can reach solution quality of the previous state-of-the-art algorithm up to four orders of magnitude faster.

翻译：本研究针对符号图中的图聚类这一复杂问题展开研究。符号图以正负权重边为特征，分别表示节点间的吸引与排斥关系。主要目标是将图高效地划分为若干簇，确保同一簇内的节点通过正边紧密连接，同时最小化簇间的负边连接。为应对这一挑战，我们首先开发了一种基于标签传播与FM局部搜索的可扩展多层次算法。随后，我们构建了一种融合多层次策略的模因算法。该方法将进化算法要素与局部优化技术精细结合，旨在比重复执行策略更有效地探索搜索空间。实验分析表明，我们的新算法显著优于现有先进算法。例如，我们的模因算法能以较先前先进算法快四个数量级的速度达到同等解的质量。