One-dimensional nested maximin designs

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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 particularly useful as training and test sets for fitting and validating metamodels, respectively. Furthermore, nested designs can be used to deal with linking parameters and sequential evaluations. In this paper, we introduce one-dimensional nested maximin designs. We show how to nest two designs optimally and develop a heuristic to nest three and four designs. These nested maximin designs can be downloaded from the website http://www.spacefillingdesigns.nl. Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14.64 and 19.21%, when nesting two and three designs, respectively.
Original languageEnglish
Pages (from-to)287-306
JournalJournal of Global Optimization
Volume46
Issue number2
Publication statusPublished - 2010

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Maximin
Black Box
Nested Design
Nest
Design for All
Computer Experiments
Evaluation
Test Set
Process Optimization
Metamodel
Design
Linking
Heuristics
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title = "One-dimensional nested maximin designs",
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 particularly useful as training and test sets for fitting and validating metamodels, respectively. Furthermore, nested designs can be used to deal with linking parameters and sequential evaluations. In this paper, we introduce one-dimensional nested maximin designs. We show how to nest two designs optimally and develop a heuristic to nest three and four designs. These nested maximin designs can be downloaded from the website http://www.spacefillingdesigns.nl. Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14.64 and 19.21{\%}, when nesting two and three designs, respectively.",
author = "{van Dam}, E.R. and B.G.M. Husslage and {den Hertog}, D.",
note = "Appeared earlier as CentER Discussion Paper 2004-66",
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One-dimensional nested maximin designs. / van Dam, E.R.; Husslage, B.G.M.; den Hertog, D.

In: Journal of Global Optimization, Vol. 46, No. 2, 2010, p. 287-306.

Research output: Contribution to journalArticleScientificpeer-review

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