3. Process Optimization

Optimization has been defined as the procedure of locating the best of something or the best way of doing something (Mular, 1971). Several texts (Himmelblau, 1972; Ray and Szekeley, 1973; Box and Draper, 1969; and Lee, Adams, and Gaines, 1968) on the subject are available. Such techniques have been placed in two categories, namely, off-line optimization and on-line optimization. For the former, an optimization model is employed; for the latter, a black box approach is involved. The essence of an optimization problem becomes obvious, when a response surface is considered. Suppose that a response (in this case, a criterion of improvement such as profit per day; grade of concentrate per day) denoted by Y, depends only on two variables, X1 and X2, which can be manipulated and controlled. The relationship between Y, X1 and X2 may be represented graphically as shown in Fig. 1. The diagram is called a response surface and its height, Y, is determined by X1 and X2. Points associated with equal responses constitute response contours. The shape is that of a hill, and optimization is the procedure of ascending the hill to reach the top (maximum). In practice, a response surface is subject to disturbances which distort its shape and shift its location from time to time, so that the exact location of a maximum is imprecise. Generally, constraints (restrictions of some sort) on responses and manipulable variables serve to define a region of permissible operation.