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.
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The research of E. R. van Dam has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of B. G. M. Husslage has been financially supported by the Samenwerkings Orgaan Brabantse Universiteiten (SOBU).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Dam, E.R., Husslage, B. & den Hertog, D. One-dimensional nested maximin designs. J Glob Optim 46, 287–306 (2010). https://doi.org/10.1007/s10898-009-9426-y
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DOI: https://doi.org/10.1007/s10898-009-9426-y