## Evolutionary Optimization

An alternative to the one-variable-at-a-time approach is the technique of evolutionary optimization. Evolutionary optimization (EVOP), also known as method of steepest ascent, is based upon the techniques developed by Spindley, et al. The method is an iterative process in which a simplex figure is generated by running one more experiment than the number of variables to be optimized. It gets its name from the fact that the process slowly evolves toward the optimum. A simplex process is designed to find the optimum by ascending the reaction surface along the lines of the steepest slope, i.e., path with greatest increase in yield.

The procedure starts by the generation of a simplex figure. The simplex figure is a triangle when two variables are optimized, a tetrahedron when three variables are optimized, increasing to an n+1 polyhedron, where n is the number of variables to be optimized. The experimental point with the poorest response is eliminated and a new point generated by reflection of the eliminated point through the centroid of the simplex figure. This process is continued until an optimum is reached. In Fig. 2, experimental points 1, 2, and 3 form the vertices of the original simplex figure. Point 1 was found to have the poorest yield, and therefore was eliminated from the simplex figure and a new point (B) generated. Point 3 was then eliminated and the new point (C) generated. The process was continued until the optimum was reached. The EVOP process is a systematic method of adjusting the variables until an optimum is reached.

Rub 2

3.75 .Stof Apparent/'' Optimum/

Figure 1. Example of one-variable-at-a-time approach. Contour plot of yield.

Run 1

Apparent/'' Optimum/