Towards a better understanding of the epoxy-polymerization process using multi-objective evolutionary computation

The epoxy-polymerization process can be better understood by investigating the underlying optimization problem involving a number of conflicting objectives and more than 20 decision parameters. A combination of minimization or maximization of objectives, such as the number average molecular weight, polydispersity index and reaction time, are considered in this paper. The first two objectives are related to the properties of a polymer, whereas the third objective is related to productivity of the polymerization process. The decision variables are addition quantities of various reactants, e.g. the amount of addition for bisphenol-A (a monomer), sodium hydroxide and epichlorohydrin at different time steps (modeled in a semi-batch operation), whereas the satisfaction of all species balance equations is treated as constraints. A multi-objective evolutionary algorithm (the elitist non-dominated sorting genetic algorithm or NSGA-II) is used to obtain a set of non-dominated solutions in a single simulation run. The results show a substantial improvement (with about 300% more productivity) over the benchmark condition (reported by performing a one-time addition of reactants in the beginning in a batch process). Importantly, this study brings out a salient aspect of using an evolutionary approach to multi-objective problem solving. The availability of multiple optimal trade-off solutions allows a process engineer to have salient information about the polymerization process. Changes in the distribution of various polymer species in the course of polymerization process as observed among various Pareto-optimal solutions are identified and explained for this purpose. Such information provide important information about optimal operating conditions corresponding to different trade-offs among objectives, which are otherwise difficult to obtain. The systematic approach of starting from the two-objective problems to capture the essential features of interesting optimal operating conditions to finally solving the three-objective problem associated with the epoxy-polymerization problem in discovering the optimal trade-off interactions should motivate further such studies on other chemical process optimization problems. Overall, this paper demonstrates how fundamental optimization principles can be used systematically and reliably to find optimum operating conditions for complex chemical process operations.