Maximin distance designs based on densest packings

Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algo...

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Bibliographic Details
Published in:Metrika 2021-07, Vol.84 (5), p.615-634
Main Authors: Yang, Liuqing, Zhou, Yongdao, Liu, Min-Qian
Format: Article
Language:English
Subjects:
Algorithms
Economic Theory/Quantitative Economics/Mathematical Methods
Experiments
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algorithms, and these methods will be infeasible when the run size or number of factors is large. In this paper, we propose some deterministic construction methods for maximin L 2 -distance designs in two to five dimensions based on densest packings. The resulting designs have large L 2 -distances and are mirror-symmetric. Some of them have the same L 2 -distances as the existing optimal maximin distance designs, and some of the others are completely new. Especially, the resulting 2-dimensional designs possess a good projection property.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-020-00788-w