Neural Capacitated Clustering

TL;DR

This paper introduces Neural Capacitated Clustering, a neural network-based approach for solving the Capacitated Clustering Problem, outperforming existing methods and applying successfully to related routing problems.

Contribution

It proposes a novel neural network method that learns from past solutions to efficiently address cluster-level capacity constraints.

Findings

Outperforms state-of-the-art solvers on artificial and real datasets.

Achieves competitive results on the Capacitated Vehicle Routing Problem.

Demonstrates effectiveness of neural approach in constrained clustering tasks.

Abstract

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.