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Nested maximin Latin hypercube designs

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  • Rennen, G.

    (Tilburg University)

  • Husslage, B.G.M.

    (Tilburg University)

  • Dam, E.R. van

    (Tilburg University)

  • Hertog, D. den

    (Tilburg University)

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.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-3736835.

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Date of creation: 2010
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Publication status: Published in Structural and Multidisciplinary Optimization (2010) v.41, p.371-395
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-3736835

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Web page: http://www.tilburguniversity.edu/

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  1. Husslage, B.G.M. & Rennen, G. & Dam, E.R. van & Hertog, D. den, 2006. "Space-Filling Latin Hypercube Designs for Computer Experiments (Replaced by CentER DP 2008-104)," Discussion Paper 2006-18, Tilburg University, Center for Economic Research.
  2. Husslage, B.G.M. & Dam, E.R. van & Hertog, D. den, 2005. "Nested Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-79, Tilburg University, Center for Economic Research.
  3. Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den & Melissen, H., 2005. "Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-8, Tilburg University, Center for Economic Research.
  4. 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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Cited by:
  1. 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.
  2. Ray-Bing Chen & Ying-Chao Hung & Weichung Wang & Sung-Wei Yen, 2013. "Contour estimation via two fidelity computer simulators under limited resources," Computational Statistics, Springer, vol. 28(4), pages 1813-1834, August.
  3. 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.
  4. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.

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