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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)

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 ℓ1 distance measure for certain values of n.

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Bibliographic Info

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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Web page: http://center.uvt.nl

Related research

Keywords: Latin hypercube design; maximin; space-filling; mixed integer programming; trav- elling salesman problem; graph covering.;

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References

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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.
  2. Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den & Melissen, H., 2005. "Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-8, Tilburg University, Center for Economic Research.
  3. Husslage, B.G.M., 2006. "Maximin Designs for Computer Experiments," Open Access publications from Tilburg University urn:nbn:nl:ui:12-189738, Tilburg University.
  4. Driessen, L., 2006. "Simulation-Based Optimization for Product and Process Design," Open Access publications from Tilburg University urn:nbn:nl:ui:12-182338, Tilburg University.
  5. Stinstra, E., 2006. "The Meta-Model Approach for Simulation-based Design Optimization," Open Access publications from Tilburg University urn:nbn:nl:ui:12-189750, Tilburg University.
  6. Husslage, B.G.M. & Rennen, G. & Dam, E.R. van & Hertog, D. den, 2006. "Space-Filling Latin Hypercube Designs for Computer Experiments (Replaced by CentER DP 2008-104)," Discussion Paper 2006-18, Tilburg University, Center for Economic Research.
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Citations

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Cited by:
  1. Husslage, B.G.M. & Rennen, G. & Dam, E.R. van & Hertog, D. den, 2008. "Space-Filling Latin Hypercube Designs For Computer Experiments (Revision of CentER DP 2006-18)," Discussion Paper 2008-104, Tilburg University, Center for Economic Research.
  2. 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.

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