Maximin Latin hypercube designs in two dimensions

Maximin Latin hypercube designs in two dimensions

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Article ID: iaor20081518
Country: United States
Volume: 55
Issue: 1
Start Page Number: 158
End Page Number: 169
Publication Date: Jan 2007
Journal: Operations Research
Authors: , , ,
Keywords: programming: branch and bound, programming: integer
Abstract:

The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n × 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 I or I1. Furthermore, for the distance measure I2, 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.

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