## 5 Optimization Results and Discussion
(2, black) The optimal operation of the FBR (this paper), with a time-step-wise optimally varied feed [GLC], and feed flow rate, with the control variable limits of Equation (12). (3, red) The optimal operation of the FBR (this paper), with a constant but optimal feed [GLC], and feed flow rate (FL), with the control variable limits of Equation (11). (4, green) The optimal operation of the FBR (this paper), with a constant but Pareto-optimal feed [GLC], and feed flow rate (\(\mathrm{F_{L}}\); see Figures 3–5), with the control variable limits of Equation (12). unevenness in curve 2 is linked to the variable feeding with GLC of the optimally operated FBR (see the feeding plots in the top part of the figure). 8. The HSMDM prediction of the biomass dynamics in the bulk phase (curve 1 in Figure 9c,d) fits the experimental data of [PERSON] very well [72], thus proving its adequacy. The comparative plots of the biomass dynamics in the FBR bulk phase in all operating alternatives are presented in (Figure 9c). They reveal similar significantly increasing trajectories. In the best optimal operation cases, the biomass growth is more intense, due to a significantly higher GLC uptake, and a better GLC use during the batch, thus offering more favourable biomass growth conditions. Their maximum increase was limited during the bioreactor optimization in Equation (12), to avoid hydrodynamic problems. 9. The TRP concentration dynamics in the bulk phase are comparatively plotted in (Figure 10) for all the investigated optimal operating alternatives of the FBR, and compared to the nominal (non-optimal) operation, with the constant feeding of (Table 1) of [PERSON] [72] [that is, the experimental blue curve 1, and the experimental data (\(\bullet\), blue)]. As can be observed, the applied HSMDM of this paper fits the experimental  
Figure 7: Model-based simulated trajectories () for the key species involved in the TRP-operon expression module (TRP, OR, MRNA, E) in the modified _E. coli_ T5 strain for the FBR operated in two alternative forms: (1, blue) Curves simulated with the HSMDM (this paper, and Maria [11]) compared to the experimental data (\(\bullet\), blue) of [PERSON] [72] under the nominal, non-optimal operation of the FBR of (Table 1), which involves a constant feed [GLC], and constant feed flow rate FL. (2, black) The optimal operation of the FBR (this paper), with a time-step-wise optimally varied feed [GLC], and feed flow rate, with the control variable limits of Equation (12). (3, red) The optimal operation of the FBR (this paper), with a constant but optimal feed [GLC], and feed flow rate (FL), with the control variable limits of Equation (11). (4, green) The optimal operation of the FBR (this paper), with a constant but Pareto-optimal feed [GLC], and feed flow rate (FL; see Figures 3–5), with the control variable limits of Equation (12). data fairly well. From all the optimal FBR operation alternatives (curves 2-4), only the Pareto-optimal operation with a constant feeding exhibits a slightly better TRP productivity (curve 4). * The rough classification given in Table 5 for the different FBR operating alternatives (i.e., poor, worst, good, best) is based on the TRP production maximization, on the substrate (GLC) minimum consumption, and on the minimum increase in the liquid volume. By analyzing the optimization algorithms applied in this paper, and the above (1-10) remarks regarding the obtained optimization results, the present work includes a significant number of novel elements, as follows:  
* It proves the advantages and feasibility of using the HSMDM in solving difficult biochemical engineering problems, such as the determination of an optimal operation strategy for an industrial bioreactor (FBR). Figure 8: Top curves: The time-step-wise optimal feeding strategy of GLC in the bioreactor \(c_{glc,j}^{feat}\) (j = 1,...5 time-arcs) for FBR operated in different ways, using a modified \(E\). _coli_ T5 strain [32].