Maximin Latin hypercube designs in two dimensions
成果类型：
Article
署名作者：
van Dam, Edwin R.; Husslage, Bart; den Hertog, Dick; Melissen, Hans
署名单位：
Tilburg University; Delft University of Technology
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1060.0317
发表日期：
2007
页码：
158-169
关键词：
摘要：
The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n x n chessboard such that the minimal distance between pairs of rooks is maximized. Maximin Latin hypercube designs are important for the approximation and optimization of black-box functions. In this paper, general formulas are derived for maximin Latin hypercube designs for general n, when the distance measure is l(infinity) or l(1). Furthermore, for the distance measure l(2), we obtain maximin Latin hypercube designs for n <= 70 and approximate maximin Latin hypercube designs for other values of n. All these maximin Latin hypercube designs can be downloaded from the website http://www.spacefillingdesigns.nl. We show that the reduction in the maximin distance caused by imposing the Latin hypercube design structure is small. This justifies the use of maximin Latin hypercube designs instead of unrestricted designs.