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约束聚类问题找到了新的有前景的方法。其典型的成对约束常可用于指导数据划分。然而，许多问题具有聚类级别约束，例如容量聚类问题（CCP），其中每个点具有权重，且每个聚类中所有点的总权重之和受限于预设容量。本文针对CCP提出了一种新方法——神经容量聚类，该方法通过学习一个神经网络，从其他问题实例的最优或接近最优的过往解数据集中预测点与聚类中心的分配概率。在推理阶段，所得分数随后被用于类似k-means的迭代过程，以在容量约束下优化分配。在我们的人工数据集和两个真实世界数据集实验中，该方法优于文献中几种最先进的数学求解器和启发式求解器。此外，我们将该方法应用于容量车辆路径问题（CVRP）的“先聚类后路径”求解框架中，并在著名的Uchoa基准测试上展示了具有竞争力的结果。