Application of the DIRECT algorithm to searching for an optimal k-partition of the set [Formula omitted] and its application to the multiple circle detection problem

• Published in: Journal of global optimization Vol. 74; no. 1; pp. 63 - 77
• Main Authors: Scitovski, Rudolf, Sabo, Kristian
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 15.05.2019; Springer Nature B.V
• Subjects: Algorithms; Global optimization; Mathematical optimization; Partitions (mathematics); Search algorithms
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-019-00743-8

In this paper, we propose an efficient method for searching for a globally optimal k-partition of the set [Formula omitted]. Due to the property of the DIRECT global optimization algorithm to usually quickly arrive close to a point of global minimum, after which it slowly attains the desired accuracy, the proposed method uses the well-known k-means algorithm with a initial approximation chosen on the basis of only a few iterations of the DIRECT algorithm. In case of searching for an optimal k-partition of spherical clusters, the method is not worse than other known methods, but in case of solving the multiple circle detection problem, the proposed method shows remarkable superiority.