## 3 Results
### Results Summary  
After comparing the six best results emerging from the six models considered, Table 9 summarizes the emerging training results of all algorithms used in the present study to predict the surface roughness of aluminum Al6061 machined on a CNC machine. The generalization of the model, described by the testing regression value, was considered an indicator of the prediction performance. It appears that the selection of hyperparameters can potentially enhance the robustness of the models. Through the parametric analysis performed in this study, it is demonstrated that the prediction performance of the surface roughness would depend on the model configuration, which cannot be estimated a priori. It is interesting to note that ANN was the most robust approach, yielding a testing regression value of 0.9984. This can be attributed to the flexibility of the approach, which allows for the retraining and rearrangement of training and testing data to enhance the robustness of the model. This was not the case for the other proposed approach, for which testing data were selected intuitively. Nevertheless, the results revealed that the training of ANN and ANFIS with GA yields relatively higher regression values of 0.8475 and 0.8102, compared to the testing regression values of 0.7992 and 0.8026 obtained with ANN-PSO and ANFIS-PSO, respectively. Many other studies have shown same result with ANN performing better than ANFIS, but both similarly exhibiting outstanding performance in terms of accuracy [14; 33; 34]. Figure 22 illustrates a example of a comparison between ANFIS-GA's test results and the experimentally measured results. The testing input data of ANFIS-GA provided the following surface roughness: 0.9932, 0.9254, 0.6742, 0.7509, 0.6981, 0.9933, 0.9933, 1.2101, and 1.1160. Meanwhile, the experimental procedure yielded 1.08, 0.93, 0.6, 0.5, 0.74, 1.08, 1.01, 1.16, and 1.04. Both sets of outcome data were compared, and variances were noted and are displayed below. The largest variation was 33.4 percent, and the lowest was 0.5 percent, with roughly 90% of the resulting data falling within a 12-percentage-point range.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & **RMSE** & **Training R\({}^{2}\)** & **Testing R\({}^{2}\)** & **Training Function** \\ \hline ANN & 0.03653 & 0.8587 & 0.9984 & \begin{tabular}{c} Training algorithm: Levenberg–Mauardt \\ Number of layers: 1 \\ Number of neurons: 12 \\ \end{tabular} \\ \hline ANFIS & 0.01911 & 0.9914 & 0.9058 & \begin{tabular}{c} Triangular MF shape \\ Grid partition FIS generator \\ Hybrid optimization method \\ \end{tabular} \\ \hline ANN-PSO & 0.02098 & 0.9938 & 0.7992 & \begin{tabular}{c} Size of the population: 200 \\ Number of neurons: 9 \\ Acceleration values: \(c_{1}=1.5\) and \(c_{2}=2.25\) \\ \end{tabular} \\ \hline ANN-GA & 0.124 & 0.514 & 0.8475 & \begin{tabular}{c} Size of the population: 75 \\ Number of neurons: 5 \\ \end{tabular} \\ \hline ANFIS-PSO & 0.01476 & 0.9923 & 0.8026 & \
\begin{tabular}{c} Size of population: 50 \\ Acceleration factors: \(c_{1}=1.0\) and \(c_{2}=2.25\) \\ \end{tabular} \\ \hline ANFIS-GA & 0.01097 & 0.9939 & 0.8102 &
\begin{tabular}{c} Size of population: 50 \\ Mutation rate (Mu): 0.2 \\ Cross-over percentage: 0.4 \\ \end{tabular} \\ \hline \end{tabular}
\end{table}
Table 9: Results summary.