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：本研究针对具有正负加权边（分别表示节点间的吸引与排斥）的符号图聚类这一复杂问题展开研究。核心目标是高效地将图划分为若干簇，确保簇内节点通过正边紧密相连，同时最小化簇间负边连接。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，随后设计了融合多层次策略的模因算法。该方法将进化算法与局部细化技术有机结合，旨在比重复执行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最先进算法。例如，模因算法达到先前最先进算法解质量的速度可提升四个数量级。