Optimized U-type designs on flexible regions

Authors:
D. K. J. Lin;C. Sharpe;P. Winker
Affiliations:
Pennsylvania State University, USA;University of Giessen, Germany;University of Giessen, Germany
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

The concept of a flexible region describes an infinite variety of symmetrical shapes to enclose a particular region of interest within a space. In experimental design, the properties of a function on the region of interest are analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. The generation of design points on a flexible region is investigated. A recently proposed discrepancy measure, the central composite discrepancy, is used for this purpose. The optimization heuristic Threshold Accepting is applied to generate low-discrepancy U-type designs. The proposed algorithm is capable of constructing optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two-dimensional case indicate that by using an optimization heuristic in combination with an appropriate discrepancy measure produces high-quality experimental designs on flexible regions.