## 1 Introduction
The results confirmed that ANFIS and ANN outperformed the empirical models in terms of providing a prediction, while ANFIS was found to be more feasible than ANN in this regard. [PERSON] et al. [8] predicted the PPV using ANN combined with the K-nearest neighbors (KNN) method. In their study, a common empirical model introduced by United States Bureau of Mines (USBM) was also applied. Based on their results, the hybrid of ANN and KNN predicted PPV with higher accuracy compared to the ANN and USBM models. [PERSON] et al. [23] used an extreme gradient boosting (XGBoost) model to predict ground vibration. For comparison aims, SVM, random forest (RF), and KNN models were also used in their study. Based on the results, it was found that the XGBoost model was more accurate than SVM, RF, and KNN models in predicting ground vibration. In another study, a Gaussian process regression (GPR) model was employed to predict ground vibration by [PERSON] et al. [24]. They showed the superiority of the GPR for predicting the blast-induced ground vibration compared to empirical models. Recently, [PERSON] et al. [25] predicted blast-induced ground vibration using a hybrid model of ANN and the k-means clustering algorithm (HKM). Their results were then compared with support vector regression (SVR) results. They showed that the HKM-ANN model can predict ground vibration more effectively than ANN and SVR models. Overall, it could be seen that machine learning models are capable of producing better prediction results. However, there are some disadvantages to ML techniques such as ANN. One of them is slow convergence and the other is the trap in local minima. Generally, the optimization algorithm is used to improve the convergence rate and isolation from the local optimum phenomenon. The two categories of optimization algorithms can be defined as global optimization methods which do not follow the derivative. They are the stochastic metaheuristic algorithm and the deterministic optimization algorithm. Stochastic metaheuristic algorithms are interpreted using simplicity stating and are therefore used for many engineering problems, while the deterministic optimization algorithm guarantees convergence in complexity problems due to its theoretical features. However, deterministic methods, such as the DIRECT method [26], obtain superiority in the analytical approach, while heuristic methods have presented more flexible and efficient approaches [27; 28]. In this paper, both metaheuristic and deterministic algorithms are used to improve the ANN results. The aim of the present study is to develop two stochastic metaheuristic algorithms, namely PSO and biogeography-based optimization (BBO), as well as one deterministic optimization algorithm, namely the DIRECT method, to improve the performance of the ANN model in predicting the PPV. For comparison aims, minimax probability machine regression (MPMR), the extreme learning machine (ELM), and three common empirical methods were also employed. It is worth mentioning that this was the first time that BBO-ANN and DIRECT-ANN models were applied to predict PPV, which can be a contribution of the present paper to the body of knowledge in this field of study.