Multiobjective dynamic optimization of a nonvaporizing nylon 6 batch reactor

Abstract

Multiobjective dynamic optimization has been carried out on a nonvaporizing nylon 6 batch reactor. Three objective functions have been identified, viz., minimization of the concentration of unreacted monomer in the product, minimization of the dimer concentration, and minimization of the reaction time, for producing polymer having a specified value, μ_{n, d}, of the number average chain length. Two problems have been studied in this paper, each consisting of two objective functions taken from the above set. Pareto solutions have been generated using an algorithm based on Pontryagin's minimum principle and the method of Lagrangian multipliers. The effects of various physical and computational parameters have been studied, and methods have been developed to overcome the numerical difficulties that arise during the solution. The Pareto sets so generated can be coupled with the surrogate worth trade-off (SWT) method, which facilitates interaction with a decision maker (DM). The optimal temperature histories obtained for the two problems studied are quite different and suggest that one must solve the three-dimensional problem in which the vector objective function incorporates all three objective functions. Results from the present study could be used as starting guesses to converge rapidly on the solution of the three-dimensional problem.