## 4 Numerical Experiment and Analysis
\[S=\sqrt{\frac{\sum{(F-\overline{F})^{2}}}{\text{n}-1}}\]  
In the above equation, \(F\) represents the convergence results of repeated inversions based on different reconstruction models. \(\overline{F}\) is the average value of \(F\). n is the number of repeated inversion operations of each reconstruction model, and n = 5. As shown in Table 1, after 500 generations of iterations, the mean values of the convergence outcomes of the objective functions achieved by the SGA and MPGA with numerous repeated evolutionary searches were 15.885 dB/m and 6.037 dB/m, respectively. The standard deviations were 0.272 dB/m and 0.114 dB/m. In conclusion, the MPGA has stronger stability compared with the SGA, also proving the accuracy of the global search performance of the MPGA. Figure 5: Cont. Figure 5: Evolution curves of objective function f obtained based on different reconstruction models. (**a**) Evolution curve of objective function inversion based on the SIRT algorithm. (**b**) Evolution curve of objective function inversion based on the SGA-SIRT hybrid intelligent optimization algorithm. (**c**) Evolution curve of objective function inversion based on the MPGA-SIRT hybrid intelligent optimization algorithm. As shown in Table 2, after five iterations, the mean values of the final convergence results obtained via the SIRT, SGA-SIRT, and MPGA-SIRT were 7.948 dB/m, 3.492 dB/m, and 3.075 dB/m, with standard deviations of 0.574 dB/m, 0.182 dB/m, and 0.071 dB/m, respectively. Therefore, MPGA-SIRT offers better performance in terms of both accuracy and stability. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Optimization Models**} & \multicolumn{5}{c}{**Repetitive Sequence**} & \multirow{2}{*}{**Average Value**} & \multirow{2}{*}{**Standard Deviation**} \\ \cline{2-2} \cline{5-6}  & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** \\ \hline SGA & 15.451 & 15.801 & 16.011 & 16.144 & 16.018 & 15.885 & 0.272 \\ MPGA & 5.882 & 6.038 & 6.046 & 6.015 & 6.205 & 6.037 & 0.114 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Convergence results with repetitive sequence obtained via the SGA and MPGA [dB/m]. Figure 6: Tomography inversion results obtained using different reconstruction models. (**a**) Tomography inversion result obtained via the SIRT algorithm. (**b**) Tomography inversion result obtained via the SGA-SIRT algorithm. (**c**) Tomography inversion result obtained via the MPGA-SIRT algorithm. Figure 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Inversion Models**} & \multicolumn{5}{c}{**Repetitive Sequence**} & \multirow{2}{*}{**Average Value**} & \multirow{2}{*}{**Standard Deviation**} \\ \cline{2-2} \cline{5-8}  & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** & & \\ \hline SIRT & 7.129 & 8.059 & 7.667 & 8.263 & 8.624 & 7.948 & 0.574 \\ SGA-SIRT & 3.448 & 3.811 & 3.411 & 3.353 & 3.438 & 3.492 & 0.182 \\ MPGA-SIRT & 3.072 & 3.066 & 2.961 & 3.156 & 3.119 & 3.075 & 0.071 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Convergence results with repetitive sequence for different inversion models [dB/m]. Figure 8: Convergence results of objective function \(f\) obtained based on different reconstruction models with repeated tests. Figure 7: Evolution curves of objective function f obtained based on different reconstruction models with repeated tests. (**a**) Evolution curves of objective function based on SIRT with repeated tests. (**b**) Evolution curves of objective function based on SGA-SIRT with repeated tests. (**c**) Evolution curves of objective function based on MPGA-SIRT with repeated tests.