## 5 Validation Model
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Model** & \(R^{2}\) & **MSE** & **RMSE** & **MAE** & **MAE** & **MSRE** & **RMSE** & **RRMSE** & **MBE** & **erMAX** & **SD** & \(t\)**-_Stat_ & \(U_{\text{ss}}\)** \\ \hline \hline \multicolumn{10}{c}{Evaluation index for prediction of maximum shear strain increment} \\ \hline GA–BP & 0.993 & 3.752 & 1.937 & 1.694 & 0.053 & 0.005 & 0.071 & 0.430 & \(-\)0.016 & 0.146 & 1.937 & 0.024 & 3.835 \\ \hline RF & 0.311 & 353 & 18.808 & 16.721 & 0.883 & 1.331 & 1.153 & 51.700 & \(-\)11.306 & 2.224 & 15.844 & 2.257 & 34.429 \\ \hline DT & 0.897 & 46.503 & 6.819 & 5.426 & 0.220 & 0.117 & 0.341 & 1.412 & 1.038 & 0.768 & 6.740 & 0.462 & 13.423 \\ \hline GBM & 0.978 & 9.528 & 3.087 & 2.398 & 0.081 & 0.013 & 0.112 & 0.671 & \(-\)1.313 & 0.240 & 2.793 & 1.410 & 5.828 \\ \hline LR & 0.872 & 33.550 & 5.792 & 3.592 & 0.090 & 0.017 & 0.129 & 1.141 & 0.285 & 0.238 & 5.785 & 0.148 & 11.461 \\ \hline GR & \(-\)0.124 & 433.634 & 20.824 & 12.749 & 0.271 & 0.139 & 0.373 & 4.197 & 12.012 & 0.743 & 17.010 & 2.118 & 37.644 \\ \hline \multicolumn{10}{c}{Evaluation index for prediction of safety factor} \\ \hline GA–BP & 0.930 & 0.026 & 0.161 & 0.142 & 0.086 & 0.012 & 0.110 & 0.796 & \(-\)0.020 & 0.235 & 0.160 & 0.373 & 0.317 \\ \hline RF & 0.430 & 0.117 & 0.342 & 0.245 & 0.125 & 0.026 & 0.161 & 18.390 & \(-\)0.027 & 0.308 & 0.359 & 0.235 & 0.694 \\ \hline DT & 0.305 & 0.099 & 0.315 & 0.218 & 0.132 & 0.039 & 0.197 & 1.931 & \(-\)0.012 & 0.529 & 0.315 & 0.110 & 0.623 \\ \hline GBM & 0.825 & 0.025 & 0.160 & 0.111 & 0.079 & 0.014 & 0.118 & 1.049 & 0.064 & 0.267 & 0.146 & 1.322 & 0.303 \\ \hline LR & 0.444 & 0.112 & 0.335 & 0.232 & 0.134 & 0.047 & 0.216 & 1.860 & \(-\)0.076 & 0.624 & 0.326 & 0.702 & 0.654 \\ \hline GR & \(-\)0.475 & 0.231 & 0.480 & 0.280 & 0.196 & 0.119 & 0.344 & 3.143 & \(-\)0.172 & 1.019 & 0.449 & 1.148 & 0.920 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Design Parameters** & **Optimization** & **Comparison** & **Evaluation Indicators** & **Optimization** & **Comparison** \\  & **Solutions** & **Program** & **Solutions** & **Program** \\ \hline Wrapping thickness (m) & \(1.1983\) & \(1.200\) & \(\begin{array}{c}\text{Maximum lateral}\\ \text{displacement}\\ \text{(mm)}\end{array}\) & \(-47.0218\) & \(-50.623\) \\ Slope ratio of reinforced & \(1.9962\) & \(2.000\) & \(\begin{array}{c}\text{Maximum vertical}\\ \text{displacement (mm)}\end{array}\) & \(-71.8192\) & \(-91.658\) \\ Modulus of elasticity of the & \(\begin{array}{c}\text{Maximum stress in the XZ}\\ \text{fill (MPa)}\end{array}\) & \(31.3183\) & \(25.000\) & \(\begin{array}{c}\text{Maximum lateral}\\ \text{displacement (kPa)}\end{array}\) & \(-113.5368\) & \(-115.76\) \\ Reinforcement strip length (m) & \(10.010\) & \(10.000\) & \(\begin{array}{c}\text{Maximum shear strain}\\ \text{ increment (-)}\end{array}\) & \(32.4313\) & \(38.68\) \\ Modulus of elasticity of \(\begin{array}{c}\text{reinforcement strip (GPa)}\end{array}\) & \(1784.354\) & \(1000.000\) & \(\begin{array}{c}\text{Safety factor (-)}\end{array}\) & \(1.6283\) & \(1.410\) \\ Interfacial friction angle (\({}^{\circ}\)) & \(4.986\) & \(5.000\) & \(\begin{array}{c}\text{Embankment cost}\end{array}\) & \(7639.05\) & \(7625.93\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of optimization programs. From Figure 6, which shows the prediction of the five evaluation indexes, it can be seen that the predicted values by the GA-BP neural network and GBM are closer to the actual values, which is also the same as for the results analyzed in Table 10. The statistical error data indicate that the conclusion can be drawn that the maximum error value of the GA-BP neural network is 8.62%, which occurs at the maximum shear strain increment of sample no. 3, and that the rest of the error is less than 5%; the maximum error of the GBM is 24.08%, which occurs at the maximum shear strain increment of sample no.