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

Keywords

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

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    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). Operations research.