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Minimax Designs for Finite Design Regions

Summary: [This abstract is based on the author's abstract.] The problem of choosing a design that is representative of a finite candidate set is an important problem in computer experiments. The minimax criterion measures the degree of representativeness because it is the maximum distance of a candidate point to the design. This article proposes a method for finding minimax designs for finite design regions. We establish the relationship between minimax designs and the classical set covering location problem (SCLP) in operations research, which is a binary linear program. In particular, we prove that the set of minimax distances is the set of discontinuities of the function that maps the covering radius to the optimal objective function value. We show that solving the SCLP at the points of discontinuities, which can be determined, gives minimax designs. These results are employed to design an efficient procedure for finding minimax designs for small-sized candidate sets. A heuristic procedure is proposed to generate near-minimax designs for large candidate sets. Supplementary materials for this article are available online.

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  • Topics: Design of Experiments, Software Quality
  • Keywords: Design of experiments (DOE),Gaussian process, Heuristics, Linear models, Computer models, Physical modeling, Minimax
  • Author: Tan, Matthias H. Y.;
  • Journal: Technometrics