## 1 Introduction  
Blasting operation is one of the most frequently used techniques in rock excavation. However, this technique may result in several environmental impacts, including air over-pressure, back break, fly-rock, and ground vibration [1; 2; 3; 4; 5; 6; 7; 8]. Typically, these impacts are the results of wasting a huge amount of explosive energy. The existing literature on surface mining and blasting operation confirmed that ground vibration is one the most undesirable phenomena and can damage surrounding structures [9; 10; 11; 12]. These include damage of nearby rock masses, underground workings, slopes, railroads, roads, the existing groundwater conduits, and the adjacent area ecology [13; 14; 15; 16]. Therefore, an accurate estimation of ground vibration helps engineers to reduce the environmental impacts of blasting. Once explosive material is detonated in a blast hole, a chemical reaction of the explosive may produce high-pressure gas. The produced gas pressure then crushes the surrounding rock mass of the blast hole, and the explosion pressure fades or bursts rapidly. Then, in the ground, wave motion is created by the strain waves conveyed to the nearby rocks [17]. The waves of strain run as an elastic wave once the intensity of the stress wave decreases to the ground level [18]. These waves are recognized as ground vibration. Typically, two factors are used to record ground vibration, including frequency and peak particle velocity (PPV). PPV is an index which is critically important to control the damage criteria. Thus, the PPV is used to measure ground vibrations [13; 19; 20]. Several empirical vibration predictors were proposed during the past years to predict PPV created by blasting [17; 21; 22; 23; 24]. Among these predictors, two factors, including maximum charge per delay and distance from the blast face, were used to obtain the PPV values. As the high degree of PPV estimation is needed to identify blast safety area, the abovementioned empirical approaches are not sufficient. The PPV estimation is also influenced by several other parameters, including burden, powder factor, spacing, and stemming. The lack of these parameters in the estimation of PPV may be the main reason for the insufficiency of the abovementioned empirical approaches [25]. PPV prediction was not limited to empirical predictors; several statistical techniques were also proposed for this purpose [26; 27; 28]. One of the main advantages of these techniques over the empirical ones is that these techniques consider more predictors, including those related to blasting design, rock mass property, and explosive material [3; 29; 30]. The main disadvantage of the statistical techniques is that the implementation of these techniques may be problematic if newly available data differ from the original data [9; 31]. Recently, several soft computing and machine learning (ML) techniques were widely used to solve civil and mining engineering problems, as well as the ground vibration resulting from blasting [32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. These techniques include artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), fuzzy inference system (FIS), support vector machine (SVM), particle swarm optimization (PSO), imperialism competitive algorithm (ICA), gene expression programming (GEP), genetic programming (GP), and genetic algorithm (GA). A summary of the previous studies that used soft computing and ML techniques to predict PPV is presented in Table 1. Several studies acknowledged the better performance of ANN compared to empirical and statistical techniques, as well as other techniques [67; 68]. On the other hand, several studies obtained more accurate results using the fuzzy models (e.g., ANFIS and FIS) compared to previous ones [12; 69; 70]. Several studies compared ML techniques to determine the best model. For example, [PERSON] [31] compared the ANN and FIS models, and [PERSON] et al. [71] compared the SVM and ANN models.