Advanced Search
MyIDEAS: Login

Bounds for maximin Latin hypercube designs

Contents:

Author Info

  • Dam, E.R. van

    (Tilburg University)

  • Rennen, G.

    (Tilburg University)

  • Husslage, B.G.M.

    (Tilburg University)

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.

(This abstract was borrowed from another version of this item.)

Download Info

If 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.
File URL: http://arno.uvt.nl/show.cgi?fid=95224
Download Restriction: no

Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-378636.

as in new window
Length:
Date of creation: 2009
Date of revision:
Publication status: Published in Operations Research (2009) v.57, p.595-608
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-378636

Contact details of provider:
Web page: http://www.tilburguniversity.edu/

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
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.:
as in new window
  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. Husslage, B.G.M., 2006. "Maximin Designs for Computer Experiments," Open Access publications from Tilburg University urn:nbn:nl:ui:12-189738, Tilburg University.
  3. 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.
  4. 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.
  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. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. 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.
  2. 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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-378636. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Economists Online Support).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.