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Maximin Latin hypercube designs in two dimensions

Author

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  • van Dam, E.R.

    (Tilburg University, School of Economics and Management)

  • den Hertog, D.

    (Tilburg University, School of Economics and Management)

  • Husslage, B.G.M.

    (Tilburg University, School of Economics and Management)

  • Melissen, H.

Abstract

The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n × 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 l (infinity) or l 1 . Furthermore, for the distance measure l 2 , we obtain maximin Latin hypercube designs for n (le) 70 and approximate maximin Latin hypercube designs for other values of n . All these maximin Latin hypercube designs can be downloaded from the website http://www.spacefillingdesigns.nl. We show that 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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • van Dam, E.R. & den Hertog, D. & Husslage, B.G.M. & Melissen, H., 2007. "Maximin Latin hypercube designs in two dimensions," Other publications TiSEM b4eb1336-e9d8-441a-ac87-0, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:b4eb1336-e9d8-441a-ac87-0d8696680d09
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
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    JEL classification:

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

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