Optimal U—Type Designs

Peter Winker; Kai Tai Fang

doi:10.1007/978-1-4612-1690-2_31

Optimal U—Type Designs

Peter Winker, Kai Tai Fang

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

Designs with low discrepancy are of interest in many areas of statistical work. U—type designs are among the most widely studied design classes. In this paper a heuristic global optimization algorithm, Threshold Accepting, is used to find optimal U—type designs (uniform designs) or at least good approximations to uniform designs. As the evaluation of the discrepancy of a given point set is performed by an exact algorithm, the application presented here is restricted to small numbers of experiments in low dimensional spaces. The comparison with known optimal results for the two—factor uniform design and good designs for three to five factors shows a good performance of the algorithm.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 1996
Subtitle of host publication	Proceedings of a Conference at the University of Salzburg, Austria, July 9-12, 1996
Editors	Harald Niederreiter, Peter Hellekalek, Gerhard Larcher, Peter Zinterhof
Publisher	Springer New York
Pages	436-448
Number of pages	13
Edition	1
ISBN (Electronic)	9781461216902
ISBN (Print)	9780387983356
DOIs	https://doi.org/10.1007/978-1-4612-1690-2_31
Publication status	Published - 14 Nov 1997
Externally published	Yes
Event	2nd International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 1996 - University of Salzburg, Salzburg, Austria Duration: 9 Jul 1996 → 12 Jul 1996 https://link.springer.com/book/10.1007/978-1-4612-1690-2?page=1#toc (Link to conference proceedings)

Publication series

Name	Lecture Notes in Statistics
Volume	127
ISSN (Print)	0930-0325
ISSN (Electronic)	2197-7186

Conference

Conference	2nd International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 1996
Country/Territory	Austria
City	Salzburg
Period	9/07/96 → 12/07/96
Internet address	https://link.springer.com/book/10.1007/978-1-4612-1690-2?page=1#toc (Link to conference proceedings)

Access to Document

10.1007/978-1-4612-1690-2_31

Cite this

Winker, P., & Fang, K. T. (1997). Optimal U—Type Designs. In H. Niederreiter, P. Hellekalek, G. Larcher, & P. Zinterhof (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 1996: Proceedings of a Conference at the University of Salzburg, Austria, July 9-12, 1996 (1 ed., pp. 436-448). (Lecture Notes in Statistics; Vol. 127). Springer New York. https://doi.org/10.1007/978-1-4612-1690-2_31

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abstract = "Designs with low discrepancy are of interest in many areas of statistical work. U—type designs are among the most widely studied design classes. In this paper a heuristic global optimization algorithm, Threshold Accepting, is used to find optimal U—type designs (uniform designs) or at least good approximations to uniform designs. As the evaluation of the discrepancy of a given point set is performed by an exact algorithm, the application presented here is restricted to small numbers of experiments in low dimensional spaces. The comparison with known optimal results for the two—factor uniform design and good designs for three to five factors shows a good performance of the algorithm.",

author = "Peter Winker and Fang, {Kai Tai}",

note = "Funding information: Research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 178, “Internationalisierung der Wirtschaft” at the University of Konstanz and a Hong Kong UGC grant. We are indebted to an anonymous referee for helpful comments. All remaining shortcomings are our owns. Publisher copyright: {\textcopyright} 1998 Springer Science+Business Media New York; 2nd International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 1996 ; Conference date: 09-07-1996 Through 12-07-1996",

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Winker, P & Fang, KT 1997, Optimal U—Type Designs. in H Niederreiter, P Hellekalek, G Larcher & P Zinterhof (eds), Monte Carlo and Quasi-Monte Carlo Methods 1996: Proceedings of a Conference at the University of Salzburg, Austria, July 9-12, 1996. 1 edn, Lecture Notes in Statistics, vol. 127, Springer New York, pp. 436-448, 2nd International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 1996, Salzburg, Austria, 9/07/96. https://doi.org/10.1007/978-1-4612-1690-2_31

Optimal U—Type Designs. / Winker, Peter; Fang, Kai Tai.
Monte Carlo and Quasi-Monte Carlo Methods 1996: Proceedings of a Conference at the University of Salzburg, Austria, July 9-12, 1996. ed. / Harald Niederreiter; Peter Hellekalek; Gerhard Larcher; Peter Zinterhof. 1. ed. Springer New York, 1997. p. 436-448 (Lecture Notes in Statistics; Vol. 127).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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N2 - Designs with low discrepancy are of interest in many areas of statistical work. U—type designs are among the most widely studied design classes. In this paper a heuristic global optimization algorithm, Threshold Accepting, is used to find optimal U—type designs (uniform designs) or at least good approximations to uniform designs. As the evaluation of the discrepancy of a given point set is performed by an exact algorithm, the application presented here is restricted to small numbers of experiments in low dimensional spaces. The comparison with known optimal results for the two—factor uniform design and good designs for three to five factors shows a good performance of the algorithm.

AB - Designs with low discrepancy are of interest in many areas of statistical work. U—type designs are among the most widely studied design classes. In this paper a heuristic global optimization algorithm, Threshold Accepting, is used to find optimal U—type designs (uniform designs) or at least good approximations to uniform designs. As the evaluation of the discrepancy of a given point set is performed by an exact algorithm, the application presented here is restricted to small numbers of experiments in low dimensional spaces. The comparison with known optimal results for the two—factor uniform design and good designs for three to five factors shows a good performance of the algorithm.

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Optimal U—Type Designs

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