Application of mathematical optimization methods in microbiology

Mathematical methods of experiment design have so far found little use in the optimization of microbiological processes. The conventional optimization procedure is still the transformation of functional relationship of n variables into n unidimensional optimizations; furthermore, the Box-Wilson gradient method is often used. This paper presents a review of methods used in other fields, and their application in microbiological practice. The methods are classified according to whether they require, besides the simple determination of the objective function (direct search methods), also the finding of its first (gradient methods) or second derivative (Newton-Raphson method). A modified Rosenbrock's method of direct optimum search and the gradient Box-Wilson method were used in parallel for the optimization of yeast growth on methanol. Their comparison showed that Rosenbrock's method is more suitbale for multiparameter systems.