Wanwisa Skolpap, Jeno M. Scharer, Peter L. Douglas, and Murray Moo-Young

pp. 1057 - 1064

Abstract

The fed-batch optimization of penicillin productivity was applied as an example of optimization
algorithm verification. The objective function of this problem was to optimize penicillin productivity by
determination of feed rate trajectory. This study compared the optimized results derived from the proposed
algorithm and from the iterative dynamic programming. Three decision variables for the proposed algorithm
comprised t_s (switching time from exponential to linear feeding schedules), K (constant in feed rate equation),
and ε (a multiplier on substrate requirement). Estimation of this set of decision variables employed Markov
chain Monte Carlo procedures (the Gibbs parameter sampling and the Metropolis-Hasting algorithm) using
an originally given set of initial values. The optimization procedure was divided into two time periods as
follows: i) the time period of exponential feeding policy, t < t_s and ii) the time period of linear feeding schedule,
t > t_s. The calculation procedure of the first period of fermentation time had been proposed by integrating
Pontryagin’s optimum principle and Luedeking-Piret equation. The feed rate profile during the later period
was obtained from the direct substitution of desired substrate requirement derived from Monod equation.
The optimal feed-rate profile corresponded to the values of decision variables as follows [t_s
 K ε] = [35.937 0.096 2.087]. The proposed algorithm was appropriate for the determination of optimal feed-rate trajectories in
any fed-batch problems provided that the product formation rate agrees with a Luedecking-Piret model.