On algorithmic construction of maximin distance designs

ABSTRACT

Maximin distance designs are useful for conducting expensive computer experiments. In this article, we compare some global optimization algorithms for constructing such designs. We also introduce several related space-filling designs, including nested maximin distance designs, sliced maximin distance designs, and general maximin distance designs with better projection properties. These designs possess more flexible structures than their analogs in the literature. Examples of these designs constructed by the algorithms are presented.

KEYWORDS:

• Computer experiment
• Global optimization
• Nested design
• Projectional property
• Quasi-Monte Carlo
• Sliced design
• Space-filling design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K05

Acknowledgments

The authors thank the AE and the referee for their constructive suggestions that lead to improvement of this article.

Funding

This work is supported by Funding from Chinese Ministry of Science and Technology (Grant No. 2016YFF0203801), Research Funding from BUCEA (Grant No. 21082716014, 00331616031), Science and Technology Plan Project of Beijing Municipal Education Commission (Grant No. KM201410016003), and National Natural Science Foundation of China (Grant No. 11471172, 11671386, 11601027). Xiong is also grateful to the support of Key Laboratory of Systems and Control, Chinese Academy of Sciences.