Relaxed correlation clustering (RCC) is a vertex partitioning problem that aims at minimizing the so-called relaxed imbalance in signed graphs. RCC is considered to be an NP-hard unsupervised learning problem with applications in biology, economy, image recognition and social network analysis. In order to solve it, we propose two linear integer programming formulations and a local search-based metaheuristic. The latter relies on auxiliary data structures to efficiently perform move evaluations during the search process. Extensive computational experiments on existing and newly proposed benchmark instances demonstrate the superior performance of the proposed approaches when compared to those available in the literature. While the exact approaches obtained optimal solutions for open problems, the proposed heuristic algorithm was capable of finding high quality solutions within a reasonable CPU time. In addition, we also report improving results for the symmetrical version of the problem. Moreover, we show the benefits of implementing the efficient move evaluation procedure that enables the proposed metaheuristic to be scalable, even for large-size instances.

松弛相关聚类（RCC）是一个顶点分区问题，旨在最大程度地减少带符号图中所谓的松弛不平衡。RCC被认为是NP难的无监督学习问题，在生物学，经济，图像识别和社交网络分析中都有应用。为了解决该问题，我们提出了两种线性整数规划公式和一种基于局部搜索的元启发式方法。后者依靠辅助数据结构在搜索过程中有效执行运动评估。与现有文献相比，现有和新提出的基准实例的大量计算实验证明了所提出方法的优越性能。尽管精确的方法为未解决的问题获得了最佳解决方案，提出的启发式算法能够在合理的CPU时间内找到高质量的解决方案。此外，我们还报告了该对称问题的改进结果。此外，我们展示了实施有效的移动评估程序的好处，该程序使所提出的元启发式方法即使在大型实例中也可扩展。