## 7 Conclusions  
Vibration hazard control is the same as rock fragmentation and is the goal pursued in open-pit blasting. Meanwhile, reliable and accurate blasting vibration prediction models and referenceable blasting design parameters are important for the control of blasting-induced ground vibration. To accurately predict and control blasting vibrations, this paper proposed the PSO-LSSVM prediction model and the MOPSO optimization model. The following conclusions can be drawn:  
1. The PSO-LSSVM model outperformed GA-BP, unoptimized LSSVM, and BP in terms of the prediction efficiency and accuracy of PPV, with better prediction error (RMSE, MAE) and goodness of fit (\(r\)). More specifically, the hyperparameter-optimized PSO-LSSVM reduced the prediction error (RMSE, MAE) by more than 55% and improved the goodness of fit (\(r\)) by more than 10%, compared with the least-efficient one (unoptimized BP).
2. With the multi-objective optimization function of PSO, a relatively optimal blasting design was found based on existing blasting tests. When considering the PPV of the sensitive area (\(R\) = 100 m, \(H\) = 90 m) and the Br, the blasting design parameters for Zhoushan mine were taken as \(W\) = 173.68 kg, PF = 0.38 kg/m\({}^{3}\), \(S\) = 5.96 m, \(B\) = 3.19 m, and \(H_{0}\) = 1.91 m, corresponding to a PPV of 0.893 cm/s and Br of 9.8%. Therefore, it can provide engineers with a more specific and reliable blasting vibration control reference.
3. In order to predict and control the PPV more accurately, more experimental data and influencing factors should be considered. Furthermore, reliable agent models are a requirement for more accurate multi-objective optimization results.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13127166/s1](https://www.mdpi.com/article/10.3390/app13127166/s1)]([https://www.mdpi.com/article/10.3390/app13127166/s1](https://www.mdpi.com/article/10.3390/app13127166/s1)).  
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [PERSON] The first draft of the manuscript was written by [PERSON] and [PERSON] and all authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Solution** & \(W\) **(kg)** & **PF (kg/m\({}^{3}\))** & \(S\) **(m)** & \(B\) **(m)** & \(H_{0}\) **(m)** & **PPV (cm/s)** & **Br (\%)** \\ \hline A & 169.95 & 0.29 & 6.33 & 3.21 & 1.26 & 0.683 & 0.196 \\ B & 173.68 & 0.38 & 5.96 & 3.19 & 1.91 & 0.893 & 0.098 \\ C & 180.32 & 0.41 & 5.02 & 3.04 & 2.35 & 1.109 & 0.041 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Three sets of classical solutions for the Pareto front.  
Figure 11: Pareto solution for two-objective optimization.  
**Funding:** Project supported by the Central South University School-Enterprise Joint Project \"Analysis of Blasting Production Data of Dahuang Mountain Tuff Mine and full operation chain optimization study\" (2022 XQLH080); supported by the Central South University-Hongda Blasting Engineering Group Postgraduate Joint Training Base (2020 pyjd91).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are available in the Supplementary Materials.  
**Acknowledgments:** The team of authors express their gratitude to the editors and reviewers for valuable recommendations that have been taken into account to improve significantly the quality of this article. We also thank [PERSON] and [PERSON] for providing the field guidance.  
**Conflicts of Interest:** The authors declare no conflict of interest.