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Maximin Latin Hypercube Designs in Two Dimensions

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  • van Dam, E.R.

    (Tilburg University, Center For Economic Research)

  • Husslage, B.G.M.

    (Tilburg University, Center For Economic Research)

  • den Hertog, D.

    (Tilburg University, Center For Economic Research)

  • Melissen, H.

Abstract

The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n non-attacking rooks on an n x n chessboard such that the minimal distance between pairs of rooks is maximized.Maximin Latin hypercube designs are important for the approximation and optimization of black box functions.In this paper general formulas are derived for maximin Latin hypercube designs for general n, when the distance measure is l8 or l1. Furthermore, for the distance measure l2 we obtain maximin Latin hypercube designs for n = 70 and approximate maximin Latin hypercube designs for the values of n.We show the reduction in the maximin distance caused by imposing the Latin hypercube design structure is small.This justifies the use of maximin Latin hypercube designs instead of unrestricted designs.
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Suggested Citation

  • van Dam, E.R. & Husslage, B.G.M. & den Hertog, D. & Melissen, H., 2005. "Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-8, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:288828ce-b56b-41d8-9903-1a6a71215b26
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    References listed on IDEAS

    as
    1. Edwin R. van Dam & Bart Husslage & Dick den Hertog & Hans Melissen, 2007. "Maximin Latin Hypercube Designs in Two Dimensions," Operations Research, INFORMS, vol. 55(1), pages 158-169, February.
    2. Artan Dimnaku & Rex Kincaid & Michael Trosset, 2005. "Approximate Solutions of Continuous Dispersion Problems," Annals of Operations Research, Springer, vol. 136(1), pages 65-80, April.
    3. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 140(2), pages 197-211, July.
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    More about this item

    Keywords

    Branch-and-bound; circle packing; Latin hypercube design; mixed integer programming; non-collapsing; space-filling;
    All these keywords.

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

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