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

Kai Jia, Xiaojun Duan (), Zhengming Wang, Taihe Yi, Liang Yan and Xuan Chen
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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

Journal of Global Optimization, 2024, vol. 88, issue 1, No 7, 197 pages

Abstract: 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.

Keywords: Derivative-free optimization; DIRECT-type algorithm; Minimax design; Covering radius (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01297-6

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