## 4 Results and Discussion
Nevertheless, the best-ranked solution and the solutions ranked in the first 5% were well identified with the metamodels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Objective**} & \multirow{2}{*}{**Relative Weight**} & \multicolumn{3}{c}{**Thresholds**} \\ \cline{3-5}  & & **Indifference** & **Preference** & **Veto** \\ \hline Butanol productivity & 0.35 & 0.75 & 1.50 & 3.00 \\ Butanol concentration & 0.35 & 0.75 & 1.50 & 3.00 \\ Sugar conversion & 0.25 & 0.04 & 0.08 & 0.16 \\ Number of membrane modules & 0.05 & 1.00 & 2.00 & 4.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial and reduced ranges of the decision variables. Figure 8: Plots of the Pareto-optimal overall butanol concentration versus butanol productivity for the integrated fermentation–membrane pervaporation system: (**a**) ANN metamodels; (**b**) actual integrated acetone–butanol–ethanol (ABE) fermentation simulation. Sugar conversion as a function of the butanol productivity of the Pareto domain is depicted in Figure 9. Figure 9a was obtained by the genetic algorithm using the ANN metamodels, while Figure 9b presents the Pareto domain obtained using the phenomenological simulator. Both Pareto domains are nearly identical, which clearly indicates that the ANN metamodels were able to adequately model and well predict the relationship between conversion and butanol productivity. The sugar conversion corresponding to the best-ranked solution is 0.96 and 0.93 for the metamodel and phenomenological simulator, respectively. The same sugar conversion was obtained when the decision variables of the best-ranked solution identified with the ANN metamodels was used in the phenomenological simulator (Table 3). The first three objective functions need to be maximized, whereas the fourth objective, the number of membrane modules in series, needs to be minimized. A trade-off between all four objectives needs to prevail in order to determine the optimal operating conditions for the decision variables via the NetFlow ranking algorithm. Figure 10a depicts the number of membrane modules, also a decision variable, as a function of butanol productivity as determined by the ANN metamodels. The best-ranked solution suggests seven membrane modules, which is the same value as the best-ranked solution obtained with the phenomenological simulator depicted in Figure 10b. An increase in the number of membrane modules is accompanied by an increase in the overall membrane area, which in turn leads to higher solvent recovery, higher sugar conversion, and alleviation of product inhibition. The first two decision variables, the dilution rate and the feed sugar concentration, are plotted in Figure 11. Both strategies led to very similar graphs. The best-ranked solution shows that the optimal trade-off was obtained for a feed sugar concentration of 125 kg/m\({}^{3}\) and a dilution rate of 0.5 h\({}^{-1}\) for both strategies. The third decision variable, the cell retention factor, was kept constant at 0.1. A small value of the cell retention factor implies that a higher microorganism concentration prevails inside the fermenter. The optimal operating conditions as determined with the Pareto domains obtained with the three strategies described in Figure 4 are summarized in Table 3. The two sub-columns of Table 3 for strategy A correspond to the first three objectives predicted with the five decision variables by the ANN metamodel and the phenomenological simulator, respectively. The latter is recorded for validation purposes.