## 4 Results and Discussion
The main change in the ranges was the cell retention factor, which now assumes a unique value of 0.1, allowing elimination of the fermenter washout and retention of a higher microorganism concentration within the fermenter. A Pareto domain was obtained for each of the three strategies described in Figure 4 using the same generic algorithm. In strategy A, the Pareto domain was obtained from the ANN metamodels of the entire process where the four objectives are predicted from the five decision variables. In strategy B, the phenomenological simulator of continuous fermentation integrated with a pervaporation unit was used with the initial estimates of the concentrations of the eight species in the fermenter being predicted with the eight ANN metamodels. Each concentration estimate was predicted from the five decision variables. Finally, in strategy C, the Pareto domain was circumscribed akin to strategy B, except the initial estimates of the concentrations were set arbitrarily. It is obvious that strategies B and C led to similar Pareto domains, since the phenomenological simulator of the continuous integrated fermentation was used in both cases until convergence was achieved. With the initial ranges of the decision variables, strategy A was used to determine the Pareto domain (not shown), which made reducing the ranges of the decision variables possible. With the 12 ANN metamodels developed with the decision variables of the reduced ranges, Pareto domains with a population of 5000 solutions were obtained with strategies A, B and C. All Pareto-optimal solutions were then ranked with the NetFlow method. The method's relative weights and the three threshold  
Figure 6: Predicted versus actual butanol productivity for (**a**) initial ranges and (**b**) reduced ranges of the five decision variables. Figure 7: Predicted versus actual overall process butanol concentration for (**a**) initial ranges and (**b**) reduced ranges of the five decision variables. values for each of the four objective functions are summarized in Table 2. The plots of the four objective functions and two of the decision variables are presented in Figures 8-11. The Pareto domain is plotted with four distinct regions: (1) best-ranked solution (green point), (2) solutions ranked in the first 5% (red points), (3) solutions ranked in the next 45% (blue points), and (4) solutions of the remaining 50% (black points). Figure 8a depicts the overall concentration of butanol as a function of butanol productivity, as determined by the genetic algorithm using the four ANN metamodels. The best-ranked solution is located at a butanol productivity of 10.95 kg/m\({}^{3}\cdot\)h and an overall butanol concentration of 21.74 kg/m\({}^{3}\) (Table 3, column A). When the decision variables associated with the optimal solution obtained with the ANN were used in the phenomenological simulator to validate this optimal point, values of 12.14 kg/m\({}^{3}\cdot\)h and 24.04 kg/m\({}^{3}\) were obtained, respectively. This is comparable to the best-ranked solution obtained by the genetic algorithm using the phenomenological simulator, as depicted in Figure 8b, where butanol productivity of 11.83 kg/m\({}^{3}\cdot\) was obtained (Table 3, column C). Figure 8 shows the positive correlation between butanol productivity and overall butanol concentration at a constant dilution rate. The dilution rate increases diagonally (left to right) from a lower bound of 0.5 h\({}^{-1}\) to an upper bound of 1.4 h\({}^{-1}\). The empty portion depicted in the Pareto domain of Figure 8b corresponds to an inoperable range due to the constraints that exist between elevated dilution rate, butanol concentration, and flow rates to achieve steady state. The metamodel failed to recognize these limitations and instead filled the empty region accordingly by interpolating the data. This observation is expected, as a metamodel is based on input-output observations without accounting for the intrinsic constraints of the system.