## 2 Methods
### Bb-Ann
In the first step, the empirical models were used to predict PPV, and according to the results, their performances were not good enough. The R\({}^{2}\) values of 0.799, 0.747, and 0.724 obtained from Indian Standard, USBM and Ambraseys-Hendron models indicated that we need more accurate predictions. To consider all the attributes needed to predict the PPV, seven input parameters, namely \(B\), \(S\), \(ST\), \(PF\), \(W\), \(RMR\), and \(D\) were used in the modeling. Although the ELM, MPMR and PSO-ANN models, with the R\({}^{2}\) of 0.963, 0.971 and 0.972, respectively, were capable of predicting PPV with reasonable performances, the accuracy of DIRECT-ANN and BBO-ANN models were the best. Based

Figure 8: Convergence curve for PSO-ANN and BBO-ANN. Figure 9: Sensitivity analysis results. on the results, the DIRECT-ANN with R\({}^{2}\) of 0.981 and the BBO-ANN with R\({}^{2}\) of 0.988 possessed superior predictive ability compared to the other models. In other words, the effectiveness of the BBO and DIRECT methods for improving the ANN model's performance was confirmed. Additionally, sensitivity analysis showed that the W was the main parameter influencing PPV. These findings confirm that the BBO-ANN and DIRECT-ANN models are significant and reliable artificial intelligence techniques for producing precise predictions of PPV and can be used in various fields. Additionally, the use of deterministic optimization algorithms, such as the DIRECT method, to improve the ANN performance and other soft computing methods can be recommended. Conceptualization, M.H. ; Data curation, M.H. ; Investigation, G.L. ; Methodology, G.L., D.K., H.N.R. and B.R. ; Supervision, P.S. ; Validation, G.L. ; Writing--review & editing, M.H., G.L., D.K., H.N.R., B.R. All authors have read and agreed to the published version of the manuscript. This study was financially supported by the National Key Research and development program (2016 YFC0600901), and the Project 51574224 supported by NSFC. The authors declare no conflict of interest. ## Abbreviations

* Adaptive neuro-fuzzy inference system
* Artificial neural network
* Biogeography-based optimization
* Burden
* Coefficient of determination
* Degree of agreement
* Distance from the blasting-point
* Extreme gradient boosting
* Extreme learning machine
* Fuzzy system
* Gaussian process regression
* General regression neural network
* K-means clustering algorithm
* KNN
* Maximum weight charge per delay
* Mean absolute error
* Mean-square error
* Minimax probability machine regression
* Particle swarm optimization
* Peak particle velocity
* Powder factor
* Random forest
* Ratio of RMSE to the standard deviation of the observations
* Rock mass rating
* Root mean square error
* Single layer feed-forward Network
* Spacing
* Stemming
* Support vector machine
* Support vector regression
* United States Bureau of Mines

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