## 3 Results and Discussions  
MATLAB codes were developed for the MFO algorithm, which has been executed repeatedly 30 times. Each time, there are 100 solutions in an archive, and one best solution is selected using the TOPSIS [25] method; hence, the 30 best solutions obtained by the MFO algorithm are shown in Table 6 for response L (crack length) and similarly for other responses; D (crack depth) and W (crack width) are presented in Tables 7 and 8. Out of these 30 solutions, the best one is selected again using the TOPSIS method for all of the responses. It is confirmed from Figure 4 that the highest closeness values are obtained for the MFO algorithm as compared to the DFO [26] and PSO [27] algorithms. The convergence plot for three different performance measures is shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**SI. No. **} & \multicolumn{3}{c}{**RMSE**} & \multicolumn{3}{c}{**MAE**} & \multicolumn{3}{c}{**R\({}^{2}\)**} & \multirow{2}{*}{**TOPSIS**} \\ \cline{2-2} \cline{5-10}  & **Total** &  
Figure 4: _Cont._  
Figure 4a-c. represent the statistical distribution of closeness values obtained for 30 runs from Minitab 19 software using MFO, DFO and PSO algorithms for response L. Similar representation for responses D and W are illustrated in Figure 4d-f. and Figure 4g-i. respectively. It is observed that all of the \(p\)-values are greater than 0.05, which shows that the closeness values are normally distributed. This confirmed that the results obtained by the MFO, DFO, and PSO algorithms are accepted. Figure 5a-c. illustrate the closeness values obtained for various responses using MFO, DFO, and PSO algorithms for responses L, D and W respectively. It is understood that, in most of the runs, the MFO has the highest closeness value as compared to the DFO and PSO algorithms. Based on the highest closeness value, the best SVR model has been selected for each response, L, D, and W, and presented in Table 9. Using these models, the predicted response values are calculated and represented in Figure 6. The actual training data set of responses, L, D, and W, with their predicted values are plotted in Figure 6a-c. A similar representation is shown for the testing data set in Figure 6d-f. The predicted values of L and W are closer to the actual value in the training data set compared with response D. In the testing data set, out of 29 samples of response W, almost all predicted values are closer to the actual values, whereas in L, out of 20 samples, 14 are closer, and in D, it is only 7 out of 25. It is inferred that the SVR models developed to predict the response values of L and W are more accurate compared to D.  
Figure 4: Statistical analysis of closeness values for (**a**) Response L-MFO; (**b**) Response L-DFO; (**c**) Response L-PSO; (**d**) Response D-MFO; (**e**) Response D-DFO; (**f**) Response D-PSO; (**g**) Response W-MFO; (**h**) Response W-DFO; (**i**) Response W-PSO. The probability plots shown in Figure 7a-c. reveal that the results obtained using MFO for 30 runs are normally distributed for trainrig data set of responses L, D and W. Figure 7d-f. represent probability plots for testing data set of responses L, D and W, it also show the results are normally distributed; hence, the developed SVR models are appropriate. The three performance measures of SVR models for responses, L, D, and W, are presented in Figure 8a-c. It is reported that RMSE values of 0.071, 0.0767, and 0.0678 were obtained in the testing data set of responses L, D, and W, respectively. Lesser MAE values of 0.0624, 0.0672, and 0.0583 and higher \(R^{2}\) values of 0.9996, 0.9909, and 0.9999 were reported in the testing data set. Figure 9 illustrates the convergence plot of performance measures for three responses, L, D, and W, for the total, training, and testing data sets.