## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Decision Variable/Objective**} & \multicolumn{3}{c}{**Strategy**} \\ \cline{2-4}  & **A** & **B** & **C** \\ \hline Dilution rate D (h\({}^{-1}\)) & 0.51 & 0.51 & 0.50 \\ Feed sugar concentration S\({}_{0}\) (kg/m\({}^{3}\)) & 125 & 122 & 125 \\ Cell retention factor \(\alpha_{\mathrm{g}/12}\) & 0.1 & 0.1 & 0.1 \\ Number of membrane modules N\({}_{\mathrm{Mod}}\) & 7 & 7 & 7 \\ Number of membrane stacks N\({}_{\mathrm{Stack}}\) & 2500 & 2480 & 2389 \\ Butanol productivity (kg/m\({}^{3}\).h) & 10.95 1 & 21.14 2 & 12.10 & 11.83 \\ Butanol concentration (kg/m\({}^{3}\)) & 21.74 1 & 24.04 2 & 23.68 & 23.65 \\ Sugar conversion & 0.96 1 & 0.96 2 & 0.95 & 0.93 \\ Computation time (s) & 5.6 & 8353 & 14052 \\ Number of actual model evaluations & 81 & 21573 & 21347 \\ \hline \hline \end{tabular}  
* Values determined by the genetic algorithm using the ANN metamodels. 2 Values determined by the phenomenological simulator for validation using decision variables of Column A.  
\end{table} 
Table 3: Decision variables and objectives of best solutions of Pareto domains with a population of 5000 individuals obtained with strategies A, B and C (see Figure 4). Figure 11: Plots of feed sugar concentration versus dilution rate for the integrated fermentation–membrane pervaporation system: (**a**) ANN metamodels; (**b**) actual integrated system simulation. Figure 10: Plots of the numbers of membrane modules versus butanol productivity for the integrated fermentation–membrane pervaporation system: (**a**) ANN metamodels; (**b**) actual integrated system simulation. Figure 9: Plots of sugar conversion versus butanol productivity for the integrated fermentation–membrane pervaporation system: (**a**) ANN metamodels; (**b**) actual integrated system simulation. Table 3 also provides the computation time needed to circumscribe the Pareto domain for each strategy. It only took 5.6 s to determine the complete Pareto domain with the ANN metamodels, whereas it took about 1500 and 2500 times more computation time with strategies B and C, respectively. It is clear that there is a net advantage to using the ANN metamodels for circumscribing the Pareto domain. This computational time advantage would be even more impressive if the time to perform a single simulation was longer. Previous research has also clearly illustrated the advantage of using neural networks as surrogate models for the optimization of processes [21; 22]. In this investigation, the number of evaluations using the phenomenological model for circumscribing the Pareto domain is given in Table 3. It took 81 simulations for the two iterations (initial and reduced ranges of decision variables) to derive the ANN metamodels, including the simulation for validating the optimum solution identified by strategy A. On the other hand, it took more than 250 times the number of evaluations for strategies B and C.  
The use of ANN metamodels in strategy B for estimating the initial species concentrations is to accelerate the convergence to steady state. However, only mitigated results were obtained, the main reason being the stringent concentration tolerance for convergence, combined with the accuracy of ANNs. Figure 12 presents variation of butanol and microorganism concentration as a function of time. These results show that for many operating conditions, the time to convergence is significantly improved. For some operating conditions, the concentrations within the fermenter oscillate in a quasi-steady state. This phenomenon, referred to as a chemical feedback loop, sometimes occurs for some chemical systems, such as the oxidation of malonic acid by bromate ions catalyzed by cerium [23]. In the current fermentation system integrated with a pervaporation unit, the dynamics of production and consumption of intermediate metabolites, butyric and acetic acids, and the ABE solvents along with their partial recovery induces this oscillatory behavior under some particular decision variables.