Neural Capacitated Clustering
This addresses constrained clustering with cluster-level capacity limits, relevant for logistics and optimization, but is incremental as it builds on deep clustering and k-means approaches.
The paper tackles the Capacitated Clustering Problem (CCP) by proposing Neural Capacitated Clustering, a method that uses a neural network trained on past solutions to predict point assignments, which outperforms state-of-the-art solvers on artificial and real-world datasets and shows competitive results on the Capacitated Vehicle Routing Problem (CVRP) benchmark.
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.