Generating exact D-optimal designs for polynomial models

This paper compares several optimization algorithms that can be used to generate exact D-optimal designs (i.e., designs for a specified number of runs) for any polynomial model. The merits and limitations of each algorithm are demonstrated on several low-order polynomial models, with numerical results verified against analytical results. The efficiencies -- with respect to estimating model parameters --of the D-optimal designs are also compared to the efficiencies of one commonly used class of experimental designs: fractional factorial designs. In the examples discussed, D-optimal designs are significantly more efficient than fractional factorial designs when the number of runs is close to the number of parameters in the model.