## 5 Conclusions  
In this paper, we addressed the concept of neuroevolution, where the algorithms FGA, ICA, SHLO, SLO, TLBO, vs., and VOA were used to find the architecture, weights, and biases of neural networks. Using a search procedure, we identified three best-performing algorithms and combined them using three proposed ensemble strategies: hybrid cascade, hybrid single elite solution, and hybrid multiple elite solutions. The proposed ensemble strategies are easy to implement because they do not involve changes in the logic of the algorithms. Instead, the proposed strategies involve simple methods of generating populations and transferring them to the algorithms. We used the MMA dataset to train neural networks with variable structures using each individual algorithm and the proposed ensembles constructed with the same algorithms. The training performance of individual optimizers was compared with that of the ensemble of optimizers, and we observed that hybrid multiple elite solutions outperformed all optimizers in convergence speed. We believe this performance is due to a more diverse population that we create at each iteration of the hybrid multiple elite solutions ensemble. Using a larger number of iterations, one of the individual optimizers, i.e., ICA, achieves a prediction accuracy similar to that of the ensemble. However, ICA has a very slow convergence. Furthermore, we have analyzed the effect of using an unbalanced computational effort for weak optimizers, and the experimental results demonstrate that a hybrid multiple elite solutions ensemble is a stable strategy. Our experimental results show that the hy \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Ensemble**} & \multicolumn{3}{c}{**Average Results for 30 Independent Runs**} \\  & **RMSE** & **RMSE** & **No.** \\  & **Training** & **Testing** & **Evals** \\ \hline Cascade-balanced & 0.00655 & 0.01159 & 39,136 \\ Cascade-ICA & 0.00702 & 0.01234 & 38,224 \\ Cascade-TLBO & 0.00629 & 0.01111 & 39,767 \\ Cascade-SHLO & 0.00699 & 0.01240 & 39,654 \\ \hline SingleElite-balanced & 0.00646 & 0.01142 & 39,225 \\ SingleElite-ICA & 0.00685 & 0.01207 & 38,348 \\ SingleElite-TLBO & 0.00607 & 0.01070 & 39,735 \\ SingleElite-SHLO & 0.00650 & 0.01153 & 39,628 \\ \hline MultipleElite-balanced & 0.00582 & 0.01029 & 39,245 \\ MultipleElite-ICA & 0.00591 & 0.01048 & 38,261 \\ MultipleElite-TLBO & 0.00571 & 0.01015 & 39,735 \\ MultipleElite-SHLO & 0.00584 & 0.01040 & 39,603 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of ensembles with a balanced number of iterations and an unbalanced number of iterations for weak optimizers. brid multiple elite solutions ensemble is the strategy that generates neural network-based regression models that provide the best representation of the underlying process behind MMA, and which have the potential to generate the most dependable related predictions. Furthermore, given that there is no precise phenomenological model for this process, the predictions provided by the optimal neural network prove to be of real use in industrial practice, successfully replacing a series of experiments that consume time, materials, and energy. In addition, the proposed model can be easily introduced in an online control procedure for optimal control. Additionally, to our knowledge, such a neural network optimization strategy has not been used before for such a process, while performing better than other well-established biologically inspired optimizers. A future research direction is to evaluate the performance of the proposed ensembles of optimizers on a larger number of optimization problems. The proposed ensemble strategies can be seen as adaptive optimizers that combine the characteristics of individual optimizers. Therefore, we believe this approach would provide competitive results because an ensemble is always constructed with a subset of optimizers performing better on a given optimization problem. Conceptualization, S.C. and F.L. ; methodology, S.-A.F., F.L. and M.G. ; software, S.-A.F. and M.G.