Comparison of optimization methods for a fed-batch reactor

In the optimization of a fed-batch reactor, a large number of local optima were discovered. By using sequential quadratic programming (SQP) rapid convergence to various local optima was obtained, but very good initial starting conditions had to be used to ensure obtaining the global optimum. Iterative dynamic programming (IDP) exhibits greater reliability in obtaining the global optimum. Good initial starting points are not necessary to obtain convergence to the vicintiy of the global optimum. Also the use of the direct search procedure as proposed by Luus and Jaakola yields rapid convergence to the vicinity of the global optimum, if the number of stages is small, such as 10. As the number of stages is increased, obtaining the global optimum becomes more difficult with SQP and LJ optimization. However, the global optimum for 20 stages can be readily obtained with IDP when a sufficient number of grid points are used at each time stage.