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Searching approximate global optimal Heilbronn configurations of nine points in the unit square via GPGPU computing

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  • Liangyu Chen

    (East China Normal University)

  • Yaochen Xu

    (East China Normal University)

  • Zhenbing Zeng

    (Shanghai University)

Abstract

In this paper we present a method of applying the GPGPU technology to compute the approximate optimal solution to the Heilbronn problem for nine points in the unit square, namely, points $$P_1,P_2,\ldots ,P_9$$ P 1 , P 2 , … , P 9 in $$[0,1]\times [0,1]$$ [ 0 , 1 ] × [ 0 , 1 ] so that the minimal area of triangles $$P_iP_jP_k\,(1\le i

Suggested Citation

  • Liangyu Chen & Yaochen Xu & Zhenbing Zeng, 2017. "Searching approximate global optimal Heilbronn configurations of nine points in the unit square via GPGPU computing," Journal of Global Optimization, Springer, vol. 68(1), pages 147-167, May.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:1:d:10.1007_s10898-016-0453-1
    DOI: 10.1007/s10898-016-0453-1
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    References listed on IDEAS

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    1. Liangyu Chen & Zhenbing Zeng & Wei Zhou, 2014. "An upper bound of Heilbronn number for eight points in triangles," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 854-874, November.
    2. Didier Henrion & Frédéric Messine, 2013. "Finding largest small polygons with GloptiPoly," Journal of Global Optimization, Springer, vol. 56(3), pages 1017-1028, July.
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