Optimized U-type Designs on Flexible Regions
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 is analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. This paper investigates the generation of design points on a flexible region. It uses a recently proposed new measure of discrepancy for this purpose, the Central Composite Discrepancy. The optimization heuristic Threshold Accepting is used to generate low discrepancy Utype designs. The proposed algorithm is capable to construct optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two dimensional case indicate that using an optimization heuristic in combination with an appropriate discrepancy measure, it is possible to produce high quality experimental designs on flexible regions.
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