In the case of multiple feeds, the best trajectories were determined for two separate feeds of glucose and glutamine. Again the number of intervals within
10 days and the number of the individuals of a generation were respectively selected as 10 and 1000 (i.e., m =10 and q = 1000). Note that the feed rate vector for this case is:
Vi(g) = [pii(g) Pi2(g) ■■■ Pi2m(g)} (i = 1,2,■■■,q) (2.10)
The feed rate vector of the glucose is the first m elements and the feed rate vector of glutamine is the last m elements. Each individual feed rate vector is constrained by the following conditions:
o < Pij(g)+Pi(j+m}(g) < 0.5 L/day 2 > m ZT=1Pij (g) +Pi(j+m}(g)] (i = 1, 2, ■■■,q; j = 1,2, ...,m) (/'ii)
Figure 2.5 shows that the glutamine was fed to the reactor first at a rate around 0.251 L/day for five days then followed by a zero rate. On the other hand, the glucose was added after three days at a low rate (0.02 L/day) then followed by a medium rate (0.045 L/day). These trajectories yielded a final MAb concentration of 196.0 mg/L, an improvement of 39% as compared to the optimal constant single-feed rate (0.136 L/day). Figures 2.6 and 2.7 show the corresponding histories of culture volume and MAb, respectively. The determination of the optimal varying feed rate trajectories for the multi-feed case required about three hours on a Pentium 100 using MATLAB GAOT software.
Table 2.2 shows the effect of m on the final level of MAb. It appears that there is not much difference in the final level of MAb for m in this range (five and 20). However, the computation time requires for m = 20 is about two times the time required for m = 10.
Glucose feed rate Glutamine feed rate
123456 Time (day)
Fig. 2.5. The optimal multi-feed rate profile (m = 10).
m |
Final level of MAb (mg/L) |
5 |
195.05 |
I0 |
I96.00 |
I5 |
196.16 |
20 |
196.27 |
Table 2.3 shows the comparison between GAs and DP. It is clearly shown that, for all feed rate cases, the GA-calculated feed trajectories yield a higher level of MAb than the DP-calculated feed trajectories.
Table 2.3 shows the comparison between GAs and DP. It is clearly shown that, for all feed rate cases, the GA-calculated feed trajectories yield a higher level of MAb than the DP-calculated feed trajectories.
Table 2.3. Comparison between GA and DP.
Feed rate MAb (mg/L)
Constant-feed (DP) I3i
Constant-feed (gA) 141.1
Single-feed (DP) 147
Single-feed (gA) 156.36
Multi-feed (DP) 158.5
Multi-feed (gA)_196.27
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