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This thesis deals with the problem proposed by Ye and Zhou (2007): Is a Q-optimal minimax design still symmetric if the requirement of ∫ χ xm(x)dx = 0 is removed? We have shown that for the simple linear regression, considering only the variance, a Q-optimal minimax design is necessarily symmetric; we have also made an attempt of addressing the symmetry problem considering only the bias which is much more difficult to achieve. However, the numerical results using three different algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Expected Improvement Algorithm (EIA), indicate that the claim is true. We have also applied the three algorithm on a non-linear cases correspondingly and make the comparison.

Comparison of Three Methods of Generating Robust Statistical Designs