Crisp and fuzzy optimization of a fed-batch fermentation for ethanol production

An efficient method is introduced to simultaneously determine the optimal feed rate, fed glucose concentration, and fermentation time to crisp and fuzzy optimization problems. In the optimization problems, two approaches, a computational method and an experiment, are employed to validate the optimal solution. Good agreement was found between experimental and computed results. In real optimization, it is usually required that the decision maker limit the total amount of glucose fed into the process to obtain maximization of the production rate. The restriction of the total amount of supplied glucose is, in general, not crisp. The fuzzy goal attainment method is applied to formulate such a trade-off optimization problem. An optimal trade-off solution with 61.63% satisfactory grade is obtained by the fuzzy goal attainment approach.