Nested Maximin Latin Hypercube Designs

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Abstract

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages21
Volume2009-06
Publication statusPublished - 2009

Publication series

NameCentER Discussion Paper
Volume2009-06

Fingerprint

Latin Hypercube Design
Maximin
Nested Design
Grid
Computer Experiments
Test Set
Black Box
Linking
Higher Dimensions
Design
Subset
Optimization
Evaluation
Approximation

Keywords

  • Design of computer experiments
  • Latin hypercube design
  • linking parameter
  • nested designs
  • sequential simulation
  • space-filling
  • training and test set

Cite this

Rennen, G., Husslage, B. G. M., van Dam, E. R., & den Hertog, D. (2009). Nested Maximin Latin Hypercube Designs. (CentER Discussion Paper; Vol. 2009-06). Tilburg: Operations research.
Rennen, G. ; Husslage, B.G.M. ; van Dam, E.R. ; den Hertog, D. / Nested Maximin Latin Hypercube Designs. Tilburg : Operations research, 2009. (CentER Discussion Paper).
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Rennen, G, Husslage, BGM, van Dam, ER & den Hertog, D 2009 'Nested Maximin Latin Hypercube Designs' CentER Discussion Paper, vol. 2009-06, Operations research, Tilburg.

Nested Maximin Latin Hypercube Designs. / Rennen, G.; Husslage, B.G.M.; van Dam, E.R.; den Hertog, D.

Tilburg : Operations research, 2009. (CentER Discussion Paper; Vol. 2009-06).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Nested Maximin Latin Hypercube Designs

AU - Rennen, G.

AU - Husslage, B.G.M.

AU - van Dam, E.R.

AU - den Hertog, D.

N1 - Subsequently published in Structural and Multidisciplinary Optimization, 2010 Pagination: 21

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Y1 - 2009

N2 - In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.

AB - In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.

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KW - linking parameter

KW - nested designs

KW - sequential simulation

KW - space-filling

KW - training and test set

M3 - Discussion paper

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T3 - CentER Discussion Paper

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ER -

Rennen G, Husslage BGM, van Dam ER, den Hertog D. Nested Maximin Latin Hypercube Designs. Tilburg: Operations research. 2009. (CentER Discussion Paper).