### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 16 |

Volume | 2005-8 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2005-8 |

### Fingerprint

### Keywords

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

### Cite this

*Maximin Latin Hypercube Designs in Two Dimensions*. (CentER Discussion Paper; Vol. 2005-8). Tilburg: Operations research.

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

Research output: Working paper › Discussion paper › Other 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.

N1 - Pagination: 16

PY - 2005

Y1 - 2005

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 -