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One-dimensional nested maximin designs

Listed author(s):
  • Edwin Dam


  • Bart Husslage


  • Dick Hertog


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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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
DOI: 10.1007/s10898-009-9426-y
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  1. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
  2. Husslage, B.G.M. & van Dam, E.R. & den Hertog, D. & Stehouwer, H.P. & Stinstra, E., 2003. "Collaborative metamodelling : Coordinating simulation-based product design," Other publications TiSEM 0196e58f-78a8-4653-a48b-8, Tilburg University, School of Economics and Management.
  3. 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.
  4. 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.
  5. 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.
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