Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
SIAM Journal on Numerical Analysis
A generalized discrepancy and quadrature error bound
Mathematics of Computation
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Constructing uniform designs: A heuristic integer programming method
Journal of Complexity
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A uniform design scatters its design points evenly on the experimental domain according to some discrepancy measure. In this paper all the design points of a full factorial design can be split into two subdesigns. One is called the complementary design of the other. The complementary design theories of characterizing one design through the other under the four commonly used discrepancy measures are investigated. Based on these complementary design theories, some general rules for searching uniform designs through their complementary designs are proposed. An efficient method to check if a design has repeated points is introduced and a modified threshold-accepting algorithm is proposed to search uniform or nearly uniform designs without replications. The new algorithm is shown to be more efficient by comparing with other existing methods. Many new uniform or nearly uniform designs without replications are tabulated and compared.