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Bounds for Maximin Latin Hypercube Designs

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Author Info
Dam, E.R. van
Rennen, G.
Husslage, B.G.M. (Tilburg University, Center for Economic Research)

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Abstract

Latin hypercube designs (LHDs) play an important role when approximating computer simula- tion models. To obtain good space-filling properties, the maximin criterion is frequently used. Unfortunately, constructing maximin LHDs can be quite time-consuming when the number of dimensions and design points increase. In these cases, we can use approximate maximin LHDs. In this paper, we construct bounds for the separation distance of certain classes of maximin LHDs. These bounds are useful for assessing the quality of approximate maximin LHDs. Until now only upper bounds are known for the separation distance of certain classes of unrestricted maximin designs, i.e. for maximin designs without a Latin hypercube struc- ture. The separation distance of maximin LHDs also satisfies these ?unrestricted? bounds. By using some of the special properties of LHDs, we are able to find new and tighter bounds for maximin LHDs. Within the different methods used to determine the upper bounds, a vari- ety of combinatorial optimization techniques are employed. Mixed Integer Programming, the Travelling Salesman Problem, and the Graph Covering Problem are among the formulations used to obtain the bounds. Besides these bounds, also a construction method is described for generating LHDs that meet Baer?s bound for the ?1 distance measure for certain values of n.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-16.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200716

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 127(2), pages 197-211, July. [Downloadable!] (restricted)
  2. Husslage, Bart & Rennen, Gijs & Dam, Edwin R. van & Hertog, Dick den, 2006. "Space-filling Latin hypercube designs for computer experiments," Discussion Paper 18, Tilburg University, Center for Economic Research. [Downloadable!]
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This page was last updated on 2008-7-29.

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