Nested maximin Latin hypercube designs
AbstractIn 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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Bibliographic InfoPaper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-3736835.
Date of creation: 2010
Date of revision:
Publication status: Published in Structural and Multidisciplinary Optimization (2010) v.41, p.371-395
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Web page: http://www.tilburguniversity.edu/
Other versions of this item:
- C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
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- Dam, E.R. van & Rennen, G. & Husslage, B.G.M., 2009.
"Bounds for maximin Latin hypercube designs,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-378636, Tilburg University.
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- Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den & Melissen, H., 2005.
"Maximin Latin Hypercube Designs in Two Dimensions,"
2005-8, Tilburg University, Center for Economic Research.
- Edwin Dam & Bart Husslage & Dick Hertog, 2010.
"One-dimensional nested maximin designs,"
Journal of Global Optimization,
Springer, vol. 46(2), pages 287-306, February.
- Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den, 2010. "One-dimensional nested maximin designs," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3448696, Tilburg University.
- Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den, 2004. "One-Dimensional Nested Maximin Designs," Discussion Paper 2004-66, Tilburg University, Center for Economic Research.
- Dam, E.R. van & Hertog, D. den & Husslage, B.G.M. & Rennen, G., 2011. "Space-filling Latin hypercube designs for computer experiments," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4334874, Tilburg University.
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