Maximin Latin Hypercube Designs in Two Dimensions

Research output: Working paperDiscussion paperOther research output

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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 l8 or l1. Furthermore, for the distance measure l2 we obtain maximin Latin hypercube designs for n = 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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages16
Volume2005-8
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-8

Fingerprint

Latin Hypercube Design
Maximin
Two Dimensions
Distance Measure
Black Box
Justify
Positioning
Optimization
Approximation

Keywords

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

Cite this

van Dam, E. R., Husslage, B. G. M., den Hertog, D., & Melissen, H. (2005). Maximin Latin Hypercube Designs in Two Dimensions. (CentER Discussion Paper; Vol. 2005-8). Tilburg: Operations research.
van Dam, E.R. ; Husslage, B.G.M. ; den Hertog, D. ; Melissen, H. / Maximin Latin Hypercube Designs in Two Dimensions. Tilburg : Operations research, 2005. (CentER Discussion Paper).
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van Dam, ER, Husslage, BGM, den Hertog, D & Melissen, H 2005 'Maximin Latin Hypercube Designs in Two Dimensions' CentER Discussion Paper, vol. 2005-8, Operations research, Tilburg.

Maximin Latin Hypercube Designs in Two Dimensions. / van Dam, E.R.; Husslage, B.G.M.; den Hertog, D.; Melissen, H.

Tilburg : Operations research, 2005. (CentER Discussion Paper; Vol. 2005-8).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Maximin Latin Hypercube Designs in Two Dimensions

AU - van Dam, E.R.

AU - Husslage, B.G.M.

AU - den Hertog, D.

AU - Melissen, H.

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N2 - 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 l8 or l1. Furthermore, for the distance measure l2 we obtain maximin Latin hypercube designs for n = 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.

AB - 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 l8 or l1. Furthermore, for the distance measure l2 we obtain maximin Latin hypercube designs for n = 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.

KW - Branch-and-bound

KW - circle packing

KW - Latin hypercube design

KW - mixed integer programming

KW - non-collapsing

KW - space-filling

M3 - Discussion paper

VL - 2005-8

T3 - CentER Discussion Paper

BT - Maximin Latin Hypercube Designs in Two Dimensions

PB - Operations research

CY - Tilburg

ER -

van Dam ER, Husslage BGM, den Hertog D, Melissen H. Maximin Latin Hypercube Designs in Two Dimensions. Tilburg: Operations research. 2005. (CentER Discussion Paper).