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 used to deal with linking parameters and sequential evaluations. In this paper we discuss one-dimensional nested maximin designs. We show how to nest two designs optimally and develop a heuristic to nest three and four designs. Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14.64 percent and 19.21 percent, when nesting two and three designs, respectively.
Highlights
Maximin designs play an important role in the area of black-box evaluation and optimization
√ Note that the obtained lower bound is tight since we can take c2 arbitrarily close to 2. The interpretation of this lower bound is that for all values of n1 and n2, by nesting the sets X1 and X2 we will never lose more than 14.64%, with respect to the “restriction free” maximin distance. In practice this implies that a linking parameter can be included in the maximin designs, or the designs can be used as training and test sets, at a cost of using designs that are at most 14.64% worse with respect to space-fillingness
Such designs play an important role in the design of computer experiments in black-box evaluation and optimization processes
Summary
Maximin designs play an important role in the area of (deterministic) black-box evaluation and optimization. There are three main reasons for nesting maximin designs: training and test sets, linking parameters, and sequential evaluations. To start with the first, consider the problem of fitting and validating a particular metamodel This approximation model is fitted to the obtained data, i.e., the responses obtained when evaluating the design points in the training set. Our aim is to determine x j and Ii such that every set Xi is as much as possible space-filling with respect to the maximin criterion To this end we define di as the minimal scaled distance among all points in the set Xi , i.e., di = min j,k∈Ii , j =k (ni − 1)|x j − xk | for all i.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
