Bounds for maximin Latin hypercube designs
AbstractLatin 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 âunrestrictedâ 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 Baerâs bound for the â1 distance measure for certain values of n.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-378636.
Date of creation: 2009
Date of revision:
Publication status: Published in Operations Research (2009) v.57, p.595-608
Contact details of provider:
Web page: http://www.tilburguniversity.edu/
Other versions of this item:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Husslage, B.G.M., 2006. "Maximin Designs for Computer Experiments," Open Access publications from Tilburg University urn:nbn:nl:ui:12-189738, Tilburg University.
- Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den & Melissen, H., 2005.
"Maximin Latin Hypercube Designs in Two Dimensions,"
2005-8, Tilburg University, Center for Economic Research.
- 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.
- 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.
- 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.
- Rennen, G. & Husslage, B.G.M. & Dam, E.R. van & Hertog, D. den, 2009.
"Nested Maximin Latin Hypercube Designs,"
2009-06, Tilburg University, Center for Economic Research.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Economists Online Support).
If references are entirely missing, you can add them using this form.