Optimization.

Abstract

Most research and development projects require the optimization of a system response as a function of several experimental factors. Familiar chemical examples are the maximization of product yield as a function of reaction time and temperature; the maximization of analytical sensitivity of a wet chemical method as a function of reactant concentration, pH, and detector wavelength; and the minimization of undesirable impurities in a pharamaceutical preparation as a function of numerous process variables. The "classical" approach to research and development involves answering the following three questions in sequence: What are the important factors? (Screening)In what way do these important factors affect the system? (Modeling)What are the optimum levels of the important factors? As R. M. Driver has pointed out, when the goal of research and development is optimization, an alternative strategy is often more efficient: What is the optimum combination of all factor levels? (Optimization)In what way do these factors affect the system? (Modeling in the region of the optimum)What are the important factors? The key to this alternative approach is the use of an efficient experimental design strategy that can optimize a relatively large number of factors in a small number of experiments. For many chemical systems involving continuously variable factors, the sequential simplex method has been found to be a highly efficient experimental design strategy that gives improved response after only a few experiments. It does not involve detailed mathematical or statistical analysis of experimental results. Sequential simplex optimization is an alternative evolutionary operation (EVOP) technique that is not based on traditional factorial designs. It can be used to optimize several factors (not just one or two) in a single study. Some research and development projects exhibit multiple optima. A familiar analytical chemical example is column chromatography which often possesses several sets of locally optimal conditions. EVOP strategies such as the sequential simplex method will operate well in the region of one of these local optima, but they are generally incapable of finding the global or overall optimum. In such situations, the "classical" approach can be used to estimate the general region of the global optimum, after which EVOP methods can be used to "fine tune" the system. For example, in chromatography the Laub and Purnell "window diagram" technique can often be applied to discover the general region of the global optimum, after which the sequential simplex method can be used to "fine tune" the system, if necessary. The theory of these techniques and applications to real situations will be discussed.