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SUMMARY: A multiobjective optimization technique has been developed for free radical bulk polymerization reactors using genetic algorithm. The polymerization of methyl methacrylate in a batch reactor has been studied as an example. The two objective functions which are minimized are the total reaction time and the polydispersity index of the polymer product. Simultaneously, end-point constraints are incorporated to attain desired values of the monomer conversion (x m ) and the number average chain length (l n ). A nondominated sorting genetic algorithm (NSGA) has been adapted to obtain the optimal control variable (temperature) history. It has been shown that the optimal solution converges to a unique point and no Pareto set is obtained. It has been observed that the optimal solution obtained using the NSGA for multiobjective function optimization compares very well with the solution obtained using the simple genetic algorithm (SGA) for a single objective function optimization problem, in which only the total reaction time is minimized and the two endpoint constraints on x m and l n are satisfied.

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An on-line optimizing control scheme has been developed for bulk polymerization of free radical systems. The effects of random errors, as well as one kind of a major disturbance (heating system failure), have been studied. A model-based, inferential state estimation scheme was incorporated to estimate, on-line, the parameters of the model (and thereby, the monomer conversion and molecular weight of the polymer) using experimental data on temperature and viscosity. A sequential quadratic programming technique was used for this purpose. A major disturbance, such as heating system failure, leads to a deteriorated final product unless an on-line optimal temperature trajectory (history) is recomputed and implemented on the reactor. Genetic algorithm was used for this purpose. It has been found that, if the "sensing" of the major temperature deviation from the optimal value and rectification of the heating system is achieved well in advance of the onset of the Trommsdroff effect, use of a reoptimized temperature history is sufficient to produce the desired product without significantly altering reaction time. However, if such a disturbance occurs late, a single-shot intermediate addition of an optimal amount of initiator needs to be used in addition to changing the temperature history to produce polymers having the desired properties in the minimum reaction time. Other types of failures can similarly be handled using the methodology developed.