Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature cluster-level constraints, e.g. the Capacitated Clustering Problem (CCP), where each point has a weight and the total weight sum of all points in each cluster is bounded by a prescribed capacity. In this paper we propose a new method for the CCP, Neural Capacited Clustering, that learns a neural network to predict the assignment probabilities of points to cluster centers from a data set of optimal or near optimal past solutions of other problem instances. During inference, the resulting scores are then used in an iterative k-means like procedure to refine the assignment under capacity constraints. In our experiments on artificial data and two real world datasets our approach outperforms several state-of-the-art mathematical and heuristic solvers from the literature. Moreover, we apply our method in the context of a cluster-first-route-second approach to the Capacitated Vehicle Routing Problem (CVRP) and show competitive results on the well-known Uchoa benchmark.

翻译：近期关于深度聚类的研究为受约束聚类问题提出了新的有前景方法。此类方法通常利用成对约束来引导数据划分。然而许多问题涉及聚类级约束，例如容量约束聚类问题（CCP），其中每个点具有权重，且每个簇内所有点的权重总和需受预设容量限制。本文提出了一种针对CCP的新方法——神经容量聚类，该方法通过学习一个神经网络，基于其他问题实例的最优或近最优历史解数据集，预测各点归属于聚类中心的概率。在推理过程中，所得分数通过类似k-means的迭代程序，在容量约束下优化聚类分配。在人工数据集及两个真实世界数据集上的实验表明，我们的方法优于文献中多种最先进的数学求解器与启发式求解器。此外，我们将该方法应用于"先聚类后路径"框架下的容量车辆路径问题（CVRP），并在著名的Uchoa基准测试中展现出竞争性结果。