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Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem

Author

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  • Rudolf Scitovski

    (University of Osijek)

  • Kristian Sabo

    (University of Osijek)

Abstract

In this paper, we propose an efficient method for searching for a globally optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n . 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.

Suggested Citation

  • Rudolf Scitovski & Kristian Sabo, 2019. "Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem," Journal of Global Optimization, Springer, vol. 74(1), pages 63-77, May.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:1:d:10.1007_s10898-019-00743-8
    DOI: 10.1007/s10898-019-00743-8
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    References listed on IDEAS

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    1. Ratko Grbić & Emmanuel Nyarko & Rudolf Scitovski, 2013. "A modification of the DIRECT method for Lipschitz global optimization for a symmetric function," Journal of Global Optimization, Springer, vol. 57(4), pages 1193-1212, December.
    2. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    3. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    4. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
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