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A new partition method for DIRECT-type algorithm based on minimax design

Author

Listed:
  • Kai Jia

    (National University of Defense Technology)

  • Xiaojun Duan

    (National University of Defense Technology)

  • Zhengming Wang

    (National University of Defense Technology)

  • Taihe Yi

    (National University of Defense Technology)

  • Liang Yan

    (National University of Defense Technology)

  • Xuan Chen

    (National University of Defense Technology)

Abstract

This article presents a new DIRECT-type SCABALL (scattering balls) algorithm with a new partition method for derivation-free optimization problems. It does not focus on dividing the region of interest into specific geometric shapes, but rather scatters several balls to cover it. In SCABALL, several potential optimal regions are selected at each iteration, and they are covered by smaller balls sequentially. In this way, the SCABALL ensures the everywhere dense convergence. The center points and radii of the scattered balls significantly influence the efficiency of SCABALL; therefore, the minimax designs are used in the initial and sequential stages to obtain better coverage. The SCABALL parameters, including the number of balls and their radii, were analyzed by numerical investigation. We provided the empirical choices for those parameters and found that the balls’ radii can be contracted to balance efficiency and global convergence. Numerical experiments show that the SCABALL algorithm is locally biased and robust.

Suggested Citation

  • Kai Jia & Xiaojun Duan & Zhengming Wang & Taihe Yi & Liang Yan & Xuan Chen, 2024. "A new partition method for DIRECT-type algorithm based on minimax design," Journal of Global Optimization, Springer, vol. 88(1), pages 171-197, January.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:1:d:10.1007_s10898-023-01297-6
    DOI: 10.1007/s10898-023-01297-6
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    References listed on IDEAS

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    1. Qunfeng Liu & Guang Yang & Zhongzhi Zhang & Jinping Zeng, 2017. "Improving the convergence rate of the DIRECT global optimization algorithm," Journal of Global Optimization, Springer, vol. 67(4), pages 851-872, April.
    2. Anatoly Zhigljavsky & Jack Noonan, 2020. "Covering of High-Dimensional Cubes and Quantization," SN Operations Research Forum, Springer, vol. 1(3), pages 1-32, September.
    3. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    4. Jonas Mockus & Remigijus Paulavičius & Dainius Rusakevičius & Dmitrij Šešok & Julius Žilinskas, 2017. "Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 425-450, January.
    5. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
    6. Qunfeng Liu & Jinping Zeng & Gang Yang, 2015. "MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems," Journal of Global Optimization, Springer, vol. 62(2), pages 205-227, June.
    7. 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.
    8. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
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