Year: 2026
Type: preprint
Abstract: We study a hierarchical clustering problem formulated as a sum of k-medoids objectives. This problem is related to the multi-period p-median problem, but instead of having nested facilities, we consider a hierarchy of nested assignments. We present two Benders formulations from the p-median literature and show how the obtained nested p-median solutions can be converted into hierarchical k-medoids solutions. We validate our methods on various instances. First, we show on small-scale instances that a standard Benders decomposition approach achieves speedups of up to three orders of magnitude over an existing branch-and-price method, while producing hierarchical k-medoids solutions that are at most 5% away from optimality. Second, we present an aggregated Benders heuristic that can handle instances with more than 13,000 observations.
Source: arXiv (Cornell University)
Author: Willemsen, Rick S. H.
Institution: Erasmus University Rotterdam
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223012761