Optimization of fed-batch reactors by the Luus-Jaakola optimization procedure

The presence of numerous local optima makes optimization of fed-batch reactors a challenging problem. In addition, the low sensitivity of the performance index on the control policy makes it very difficult to determine the optimal control policy accurately. As an alternative to iterative dynamic programming, we consider the application of the direct search optimization procedure of Luus and Jaakola (AIChE J. 1973, 19, 760-766) with the recent refinements involving the use of a quadratic penalty function with a shifting term to handle equality constraints. In using the optimization procedure in multipass fashion, we use the extent of variation of the variables in a pass to provide the region size for the beginning of the subsequent pass. In establishing the optimal control policies for three fed-batch reactor models, we show that this approach provides a good way of solving such optimization problems.