The number of intervals within 10 days and the number of individuals of a generation were selected respectively, as m = 10 and q = 1000. Figure 2.2 shows the best feed rate trajectory, Figure 2.3 and Figure 2.4 present the corresponding histories of the culture volume and the concentration of MAb, respectively. Figure 2.2 shows that the reactor operates as a batch culture for two days before operating in a fed-batch mode. After the batch period of two days, the feeding pattern steadily decreased. This optimal feed rate pattern yielded the final MAb concentration of 155.28 mg/L. The final MAb concentration yielded by the optimal constant feed rate was found to be 141.1 mg/L and its corresponding optimal constant feed rate was 0.136 L/day. Comparing the final MAb concentrations obtained by the optimal varying feed rate and the optimal constant feed rate, the optimal varying feed rate trajectory improved the final MAb concentration by 10%. The time required for the search of the optimal varying feed rate trajectory was about 30 min on a Pentium 100 using MATLAB Genetic Algorithms for Optimization Toolbox (GAOT).
Table 2.1 shows the effect of m on the final level of MAb. It appears that the larger the number of intervals, the higher the final MAb value. However, the larger the number of intervals, the longer the computation time per generation. The computation time required for m = 20 is about two times the time required for m = 10.
0.35
0.05
0123456789 10
Time (day)
Fig. 2.2. The optimal single-feed rate profile (m = 10).
Table 2.1. Effect of m on the final level of MAb (single-feed case).
m Final level of MAb (mg/L)
5 153.91
10 155.28
15 155.95
20 156.36
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