The effective BRKGA algorithm for the k-medoids clustering problem

¹ National School of Statistical Sciences, Rio de Janeiro, Brazil
² Fluminense Federal University, Rio de Janeiro, Brazil
³ Brazilian Institute of Geography and Statistics, Rio de Janeiro, Brazil

^* Corresponding author: jambrito@gmail.com

Received: 7 May 2022
Accepted: 4 August 2022

Abstract

This paper presents a biased random-key genetic algorithm for k-medoids clustering problem. A novel heuristic operator was implemented and combined with a parallelized local search procedure. Experiments were carried out with fifty literature data sets with small, medium, and large sizes, considering several numbers of clusters, showed that the proposed algorithm outperformed eight other algorithms, for example, the classics PAM and CLARA algorithms. Furthermore, with the results of a linear integer programming formulation, we found that our algorithm obtained the global optimal solutions for most cases and, despite its stochastic nature, presented stability in terms of quality of the solutions obtained and the number of generations required to produce such solutions. In addition, considering the solutions (clusterings) produced by the algorithms, a relative validation index (average silhouette) was applied, where, again, was observed that our method performed well, producing cluster with a good structure.