Maximin Latin Hypercube Designs in Two Dimensions

CentER Discussion Paper No. 2005-08

15 Pages Posted: 23 Feb 2005

See all articles by Edwin van Dam

Edwin van Dam

Tilburg University - Department of Econometrics & Operations Research

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Hans Melissen

Delft University of Technology - Faculty of Information Technology and Systems

Date Written: January 2005

Abstract

The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n non-attacking 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 l1. Furthermore, for the distance measure l2 we obtain maximin Latin hypercube designs for n less than/equal to 70 and approximate maximin Latin hypercube designs for the values of n. We show 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.

Keywords: Branch-and-bound, circle packing, Latin hypercube design, mixed integer programming, non-collapsing, space-filling

Suggested Citation

van Dam, Edwin and Husslage, Bart and den Hertog, Dick and Melissen, Hans, Maximin Latin Hypercube Designs in Two Dimensions (January 2005). CentER Discussion Paper No. 2005-08. Available at SSRN: https://ssrn.com/abstract=670641 or http://dx.doi.org/10.2139/ssrn.670641

Edwin Van Dam (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Bart Husslage

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Hans Melissen

Delft University of Technology - Faculty of Information Technology and Systems ( email )

P.O. Box 5031
2600 GA Delft
Netherlands

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