The Capacitated Centered Clustering Problem (CCCP)—a multi-facility location model—is very important within the logistics and supply chain management fields due to its impact on industrial transportation and distribution. However, solving the CCCP is a challenging task due to its computational complexity. In this work, a strategy based on Gaussian mixture models (GMMs) and dispersion reduction is presented to obtain the most likely locations of facilities for sets of client points considering their distribution patterns. Experiments performed on large CCCP instances, and considering updated best-known solutions, led to estimate the performance of the GMMs approach, termed as Dispersion Reduction GMMs, with a mean error gap smaller than 2.6%. This result is more competitive when compared to Variable Neighborhood Search, Simulated Annealing, Genetic Algorithm and CKMeans and faster to achieve when compared to the best-known solutions obtained by Tabu-Search and Clustering Search.

中文翻译：

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基于高斯混合模型和色散减少的能力化中心聚类问题求解策略

容量集中式集群问题（CCCP）是一种多工厂位置模型，由于其对工业运输和分销的影响，在物流和供应链管理领域中非常重要。然而，由于其计算复杂性，解决CCCP是一项具有挑战性的任务。在这项工作中，提出了一种基于高斯混合模型（GMM）和分散减少的策略，以考虑到客户点集的分布模式来获得最可能的设施点位置。在大型CCCP实例上进行的实验，并考虑了更新的最著名解决方案，导致估计了GMM方法（称为“色散降低GMM”）的性能，平均误差差距小于2.6％。与可变邻域搜索，模拟退火，