## 3 Results and Discussions
#### Quantitative Comparison of MFO with DFO and PSO Algorithms  
The performance of the MFO algorithm is compared with the DFO and PSO algorithms using two quantitative metrics, namely diversity and spacing [28]. Diversity indicates the spread of the Pareto solutions produced by an algorithm. The higher the value of diversity confirmed the better performance of the algorithm. The mathematical representation is given in Equation (18). Spacing is a straightforward method to compute the distance between the point and its closest neighbor. The minimum value of spacing indicates the better performance of the algorithm. The value of spacing is calculated using Equation (19). Table 10 represents the diversity and spacing values of the MFO, DFO, and PSO algorithms. \[Div=\sum_{i=1}^{np}(P_{imax}-P_{imin})^{2} \tag{18}\]  
where  
\(P_{imax}\)--Maximum value of ith performance measures  
\(P_{imin}\)--Minimum value of ith performance measures  
\(np\)--number of performance measures  
\[SP=\sqrt{\frac{1}{np-1}}\sum_{i=1}^{np}(\overline{D}-D_{i})^{2} \tag{19}\]  
where  
\[\overline{D}=\frac{\sum_{i=1}^{np}D_{i}}{np}\]  
\[D_{i}=\min_{i=1,2,...np}\left\{\sum_{j=1}^{nr}abs\Big{(}P_{ij}-P_{kj}\Big{)} \right\}_{k=i+1,...np}\]  
where \(nr\)--Number of runs, \(I\)--index for a no. of performance measures, \(J\)--index for a no. of runs. It is understood from Table 10 that the diversity value of the MFO algorithm is high compared to both the DFO and PSO algorithms in all of the three-response values, L, D, and W. Furthermore, the spacing value is less in the MFO algorithm for all three responses. Hence, it is confirmed that the MFO algorithm outperformed compared with both the DFO and PSO algorithms. The statistical analysis of three performance measures for training, testing, and total data sets for the MFO, DFO, and PSO algorithms are represented in Tables 11-13. The best values of three performance measures, RMSE, MAE, and \(R^{2}\) are 0.0544, 0.0527, and 0.9999, respectively, for response L in the MFO algorithm, whereas in the DFO algorithm, the values are 0.0626, 0.0539, and 0.9993, and in the PSO algorithm, the values are 0.0626, 0.0538, and 0.9993. It is confirmed that the MFO algorithm is good compared to the DFO and PSO algorithms in predicting the response L. This is true for response W in the DFO algorithm, but in the PSO algorithm, both the RMSE and MAE \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Response** & **Algorithms** & **Diversity** & **Spacing** \\ \hline \multirow{3}{*}{L} & MFO & 0.0652 & 0.0053 \\  & DFO & 0.0644 & 0.0054 \\  & PSO & 0.0648 & 0.0057 \\ \hline \multirow{3}{*}{D} & MFO & 0.0679 & 0.0026 \\  & DFO & 0.0664 & 0.0058 \\  & PSO & 0.0653 & 0.0062 \\ \hline \multirow{3}{*}{W} & MFO & 0.0685 & 0.0063 \\  & DFO & 0.0676 & 0.0066 \\  & PSO & 0.0680 & 0.0073 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of performance of algorithms using performance indicators. values are lower compared with the MFO algorithm. In the case of response D in the DFO and PSO algorithms, the RMSE and MAE values are a little bit low compared to the MFO algorithm, but in the meantime, the \(R^{2}\) value is higher than in the DFO and PSO algorithms. In overall performance, the SVR models developed by the MFO algorithm outperformed compared to the DFO and PSO algorithms.