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

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 accurac...

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