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One-dimensional nested maximin designs

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Author Info

  • Edwin Dam

    ()

  • Bart Husslage

    ()

  • Dick Hertog

    ()

Abstract

The design of computer experiments is an important step in black box evaluation and optimization processes.When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually.These so-called nested designs are used to deal with linking parameters and sequential evaluations.In this paper we discuss one-dimensional nested maximin designs.We show how to nest two designs optimally and develop a heuristic to nest three and four designs.Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14:64 percent and 19:21 percent, when nesting two and three designs, respectively.

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File URL: http://hdl.handle.net/10.1007/s10898-009-9426-y
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Bibliographic Info

Article provided by Springer in its journal Journal of Global Optimization.

Volume (Year): 46 (2010)
Issue (Month): 2 (February)
Pages: 287-306

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Handle: RePEc:spr:jglopt:v:46:y:2010:i:2:p:287-306

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Web page: http://www.springer.com/business/operations+research/journal/10898

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Related research

Keywords: Computer simulation; Global optimization; Linking parameter; Maximin design; Mixed integer linear programming; Packing problem; Space-filling; Training and test set;

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References

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  1. Kleijnen, J.P.C. & Beers, W.C.M. van, 2003. "Application-driven Sequential Designs for Simulation Experiments: Kriging Metamodeling," Discussion Paper 2003-33, 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.
  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.
  4. 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.
  5. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
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Cited by:
  1. 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.
  2. János Pintér & Zoltán Horváth, 2013. "Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints," Journal of Global Optimization, Springer, vol. 57(1), pages 191-215, September.

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