## 4 Results and Discussion  
Results of the ANN predictions of the species concentrations are presented first. The parity plot giving the predicted versus actual values for the concentrations of butanol is presented in Figure 5. Very similar results were obtained for the concentrations of the other seven species, so their graphs are not shown. In this graph, points represented by red, blue, and gray symbols correspond to the training (30 solutions), validation (10 solutions), and testing (1000 solutions) data, respectively. The testing data was generated by randomly choosing the five decision variables subjected to the same minimum and maximum bounds of the training and validation datasets. The graph on the left of Figure 5 presents the predictions obtained by the ANNs when the decision variables for training and validation were selected using a wider range (Table 1). Results show that the predicted concentrations have a high degree of scatter, especially at the lower concentrations. The residuals are heteroskedastic for the initial range, as the variance of the error is not constant, and two sections with distinct variability prevail in Figure 5a. There are many solutions with zero concentrations in the actual fermenter, corresponding to operating conditions where the microorganisms were washed out, i.e., the culture was not able to sustain itself through the fermenter due to high dilution rates and high cell retention factor \(\alpha_{\theta/12}\). Figure 4: Multiobjective optimization and analysis of the integrated fermentation–membrane pervaporation system flowchart: (A) ANN metamodels of the four objective functions; (B) process simulator with ANN metamodels providing the eight initial species concentrations; and (C) process simulator with arbitrary initial concentrations. Figures 6 and 7 present the parity plots of the first two objectives obtained with the same set of decision variables. The predictions based on the ANNs for the wider range of decision variables are also relatively scattered, especially at very low values. A similar plot was obtained for the third objective (sugar conversion), whereas predictions of the number of membrane modules showed a perfect regression (data not shown). On the other hand, at higher values of butanol productivity, overall butanol concentration, and sugar conversion, the predictions seem to be acceptable. Nevertheless, they could certainly be improved, provided the ranges of the operating conditions are refined to eliminate solutions that were generated in the lower range of the first three objectives, which in reality would never be part of the final Pareto domain. Indeed, these solutions are clearly dominated when compared to the solutions with higher objective values. To refine the ranges of the decision variables, the genetic algorithm was used to generate the Pareto domain from the four ANN metamodels of the objectives. The obtained Pareto domain allowed for reducing the ranges of the decision variables to those of the second row of Table 1. It was then possible to generate new sets of training and validation data, which were used to generate the 12 new ANNs. The parity plots of the butanol concentration for the first two objectives are presented on the right graphs of Figures 5-7. It is obvious that the new ANNs show much better predictions than those obtained with the wider ranges of decision variables. It is believed that these predictions should provide sufficient accuracy to use the ANNs with confidence for directly obtaining the Pareto domain or providing good initial species concentrations. The overall coefficients of determination (R2) are included on each graph and clearly indicate a significant improvement of the metamodels when the reduced ranges are used. Moreover, for all variables, the numerous low values and zeros present with the wider ranges of decision variables disappeared for the ANN predictions obtained with the reduced decision variable ranges.