Importance of the first design matrix in experimental simplex optimization
Öberg, T.
Presentation vid 5th Scandinavian Symposium on Chemometrics, Lahti, Finland, 17-21 augusti, 1997.

Abstract
Simplex optimization is a popular and efficient optimization technique applied in many fields of chemistry and chemical engineering. During the last decades a number of studies on modifications and improvement of the original algorithm have been published. The first design matrix is however one aspect of simplex optimization that has raised substantially less interest. It has been suggested that this issue be of minor or no importance at all.

We have carried out a study to investigate the influence of the first design matrix on the simplex optimization results under practical conditions. Typical for this situation is that the number of experiments should be kept to a minimum, and that there is noise in the recorded response.

Various first design matrices were tested with both the basic and a modified simplex algorithm on two polynomial models with added noise. The results from this study suggests that the first design matrix have a far more important role for the final outcome than previously thought. Applying the principles of statistical experimental design will yield the most efficient design matrix for starting a simplex optimization procedure.

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