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Maximin Latin hypercube designs in two dimensions

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  • Dam, E.R. van

    (Tilburg University)

  • Hertog, D. den

    (Tilburg University)

  • Husslage, B.G.M.

    (Tilburg University)

  • 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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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-196763.

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Date of creation: 2007
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Publication status: Published in Operations Research (2007) v.55, p.158-169
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-196763

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

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  1. 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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Cited by:
  1. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
  2. Prescott, Philip, 2009. "Orthogonal-column Latin hypercube designs with small samples," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1191-1200, February.
  3. Rennen, G. & Husslage, B.G.M. & Dam, E.R. van & Hertog, D. den, 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
  4. Siem, A.Y.D. & Hertog, D. den, 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Discussion Paper 2007-68, Tilburg University, Center for Economic Research.
  5. 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.
  6. Dam, E.R. van & Rennen, G. & Husslage, B.G.M., 2007. "Bounds for Maximin Latin Hypercube Designs," Discussion Paper 2007-16, Tilburg University, Center for Economic Research.
  7. Crombecq, K. & Laermans, E. & Dhaene, T., 2011. "Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling," European Journal of Operational Research, Elsevier, vol. 214(3), pages 683-696, November.

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