## 5 Conclusions  
This paper utilized the RF and improved weighted RF models to predict the blast-induced PPV. Thus, a dataset of a total of 102 samples collected from an open granite mine was used to develop the target regular RF model. The input parameters used for modeling included BS, HD, ST, PF, MC, and DI, while the output was the PPV. Then, five techniques, i.e., refined weights based on the accuracy (R\({}^{2}\) and the RMSE) of decisions trees as well \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**Training**} & \multicolumn{5}{c}{**Testing**} \\ \cline{3-10}  & & **R\({}^{2}\)** & **RMSE** & **MAE** & **VAF** & **R\({}^{2}\)** & **RMSE** & **MAE** & **VAF** \\ \hline Present & & & & & & & & & \\ paper & RF-WOA & 0.986 & 0.118 & 0.093 & 98.603 & 0.932 & 0.246 & 0.188 & 95.032 \\ \hline
[64] & \begin{tabular}{l} GEP \\ NLMR \\ \end{tabular} & 0.914 & 0.920 & 0.755 & 91.304 & 0.874 & 0.963 & 0.851 & 87.107 \\  & \begin{tabular}{l} NLMR \\ \end{tabular} & 0.829 & 1.365 & 1.125 & 80.878 & 0.790 & 1.498 & 1.221 & 69.261 \\ \hline \multirow{4}{*}{[1]} & \begin{tabular}{l} RF \\ CART \\ \end{tabular} & 0.940 & 0.770 & 0.620 & 92.970 & 0.830 & 1.460 & 1.190 & 82.170 \\  & \begin{tabular}{l} CART \\ CHAID \\ \end{tabular} & 0.670 & 1.670 & 1.320 & 67.030 & 0.560 & 2.390 & 1.840 & 54.600 \\  & \
\begin{tabular}{l} CHAID \\ ANN \\ SVM \\ \end{tabular} & 0.910 & 0.860 & 0.540 & 91.300 & 0.680 & 1.900 & 1.470 & 67.790 \\  &
\begin{tabular}{l} ANN \\ SVM \\ \end{tabular} & 0.890 & 0.960 & 0.750 & 89.140 & 0.840 & 1.410 & 1.130 & 83.710 \\ \hline
[65] &
\begin{tabular}{l} RF \\ BN \\ \end{tabular} & 0.930 & - & - & - & 0.903 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of the evaluation metrics of the models that used the same datasets. as the optimization results of three metaheuristics algorithms (WOA, GWO, and TSA), were employed to enhance the performance of the regular RF model by reassigning the new weights of decision trees. The results concluded that the optimal hyperparameters of the regular RF model are 51 decision trees and 7 of maximum depth. Subsequently, the performance evaluation results of the five weighted RF models showed that all improved RF models outperformed the regular RF model. Moreover, the RF-WOA model shows the best performance among these five models, as evidenced by the fact that the RF-WOA model has the R\({}^{2}\) values of 0.986 and 0.932, the RMSE values of 0.118 and 0.246, the MAE values of 0.093 and 0.188, and the VAF values of 98.603 and 95.032 for the training and testing sets, respectively. Additionally, compared with the models developed in published articles that also used the same dataset, the RF-WOA model still shows the best accuracy, proving that the RF-WOA model developed in this study has better performance, adaptability, and robustness. Furthermore, the sensitivity analysis revealed that the PF model shows a great significant correlation with the PPV prediction, and the results of the PDPs indicated that when the PF is less than 0.46, the PPV maintains a small fluctuation. At the same time, when the PF exceeds 0.46, there is a significant increasing trend of PPV, and when the PF exceeds 0.63, the increasing trend of the PPV gradually shrinks, which suggests that governing the magnitude of the PPV by managing the PF is an effective and practical measure for the case of this project. Conceptualization, B.H. and A.S.M. ; methodology, B.H., S.H.L. ; software, B.H. and M.M.S.S. ; validation, B.H., A.S.M. ; formal analysis, B.H. and S.H.L. ; investigation, B.H. ; writing--original draft preparation, B.H., M.M.S.S., S.H.L., A.S.M. and D.V.U. ; writing--review and editing, B.H., M.M.S.S., S.H.L., A.S.M. and D.V.U. ; supervision, S.H.L., A.S.M. and M.M.S.S. ; funding acquisition, M.M.S.S. All authors have read and agreed to the published version of the manuscript.