构造超球体中极大极小距离设计的保距抽样法  

Distance preserving sampling method for construction of maximin distance designs in hyperspheres

作　　者：周正 周永道 Zheng Zhou;Yongdao Zhou

机构地区：[1]南开大学统计与数据科学学院,天津300071

出　　处：《中国科学：数学》2020年第5期751-758,共8页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871288)资助项目。

摘　　要：极大极小距离设计常用于计算机实验,其安排实验点使得任意两实验点间的最小距离最大化.本文基于球覆盖的思路,提出保距抽样法构造单位球体中的极大极小距离设计.相较于致密堆积法,该方法实现了对任意实验次数的设计构造,且避免了水平重复.相较于贪心算法和序贯优化法,该方法能够得到极小距离更大的设计结果,同时具有更低的算法复杂度.Maximin distance designs are commonly used in computer experiments.They arrange the design points on the experiment domain such that the minimum distance of any two points is maximized.In this paper,we propose the distance preserving sampling method to construct maximin distance designs in the unit hypersphere based on sphere covering.Compared with the construction method based on densest packing,this method can construct a design with any number of runs and avoid the repetition of levels.Compared with the greedy algorithms and sequential optimization,the distance preserving sampling method can obtain designs with larger minimum distance and has lower computational complexity.

关 键 词：致密堆积 贪心算法 序贯设计 球覆盖 

分 类 号：O212.2[理学—概率论与数理统计]