Importance of the First Design Matrix in Experimental Simplex Optimization

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, despite the observation of its importance for the speed of convergence by Nelder and Mead. This is probably due to the fact that Spendley et al already in their first presentation of the sequential simplex method were unable to show any consistent or major effect of orientation. Walters et al have likewise not been able to show any practical advantages of the tilted first simplex, suggested by Spendley et al, as compared to a cornered first simplex (a first-order Koshal design).