An effective construction method for multi-level uniform designs

Construction of main effects plans orthogonal through the block factor based on level permutation

“…To further distinguish geometrically nonisomorphic designs, uniformity is one of the mostly used criteria to compare the performance of geometrically nonisomorphic designs. More recently, Tang and Xu (2013), Tang, Xu, and Lin (2012) and Xu, Zhang, and Tang (2014) also used uniformity to compare fractional factorial designs via level permutations.…”

“…So we use the average discrepancy value (Tang & Xu, 2013;Tang et al, 2012;Xu et al, 2014) of all designs in P (D) to describe the performance of the result of the searching method. Recently, Tang and Xu (2013) derived the relation between average CD 2 values and generalized word length pattern.…”

“…Recently, Tang and Xu (2013) derived the relation between average CD 2 values and generalized word length pattern. Hence they first choose some GMA designs as the starting design to construct uniform fractional factorial designs.…”

“…However, to search for uniform POTBs, the starting design here is determined by Algorithm 1. We now use the same method in Tang and Xu (2013) to obtain the following expression of average CD 2 values, which will be used in the next section.…”

A Particle Swarm Optimization Algorithm Based on Uniform Design

“…Uniform Design can be the solution of the problem. Its aim to scatter design points uniformly on an experimental region [3]. UD can obtain the most information by the smallest number of tests, and greatly reduce direct influence of the initial population and the initial value of algorithm parameters on the results of parameter identification.…”