1. Introduction

Table 1. Selected studies on prediction of environmental side effects.

2. Research Methodology

2.1. Multilayer Perception Neural Network (MLPNN)

ANNs as computational structures to solve difficult problems, are employed for different applications in various fields [1]. Simulated by the human brain's learning strength, ANN is included in the category of artificial intelligence methods. Structurally, ANN can implicate hidden layer(s) between the input and output layer [50], [51]. Among the different structures for ANNs, MLPNN has been commonly utilized [52].

The fundamental elements of ANN are the artificial neurons (nodes) and their neural connections [53], which are mathematically simulated based on artificial neurons of the human brain. Figure 1 presents the general architecture of the neural networks and its operation. The MLPNN computation can be formulated as follows [1]:

$$Y_i=f\left({\theta }_i+{\displaystyle \sum _{j=1}^n{w}_{ij}\cdot X_j}\right)$$

(1)

where Y_i is the output variable, f is the transfer function, θ_i is the bias at the hidden layer, w_ij the connection weight between the input variable and the hidden layer, n is the number of neurons in the hidden layer, and X_j is the input variable.

Figure 1. Typical structure of the MLPNN.

Figure 1. Typical structure of the MLPNN.

ANN should be trained to predict target(s). Firstly, the input neurons (independent variables) as neural signals are imported into the input layer. Then, ANN processes the information received from the input neurons and transmits them into the next computational steps (hidden layers). In the next step, the weights of the connections are processed to be applied in the hidden layer. Input neuron weights are calculated using transfer functions. The hidden neurons transmit signals to output layer nodes and actualize the prediction of the targeted output(s). An ANN model with an architecture of two hidden layers is capable to solve complex problems. Various algorithms may be employed in the process of ANN learning. Nevertheless, the feedforward backpropagation algorithm as the most efficient learning procedure is considered for this research.

2.2. Grasshopper Optimization Algorithm (GOA)

The GOA, as an evolutionary computation method, is a nature-inspired algorithm developed by imitating grasshoppers' swarming behavior while exploring food sources [54]. The algorithm's salient advantages include fast convergence capabilities, deep exploration, and the precision results. The principal feature of the grasshoppers' swarm is its behavior organized in adult and nymph. Swarms of larvae jump and treat similar to a tumbling cylinder. In this evolutionary algorithm, two-phase of exploration and exploitation are implemented similarly to other optimization algorithms. In the exploration phase, the search agents are employed to search the various areas in the solution space. Whereas, in the exploitation phase, the agents are encouraged to move nearby to improve the current obtained solutions.

Mathematically, the GOA simulates the motion of the grasshopper in the search space as follows [54]:

$$X_i=S_i+G_i+A_i$$

(2)

where X_i, S_i, G_i, and A_i are swarming behavior in the search space (position of the i^th grasshopper), the advantage of social interaction gained by the i^th grasshopper, gravity force on i^th grasshopper, and wind advection effects on the i^th grasshopper, respectively.

The social interaction has principally operated as the main portion of grasshopper behavior approach, which can be computed by:

$$S_i={\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne i\end{array}}^{N}s(d_{ij})}{\widehat{d}}_{ij}$$

(3)

where, N indicates the total number of population (grasshopper), d_ij is the distance between i^th and j^th grasshoppers which can be calculated by $d_{ij}=\left|x_j-x_i\right|$, ${\widehat{d}}_{ij}$ indicates a unit vector from the i^th grasshopper to the j^th grasshopper calculated by ${\widehat{d}}_{ij}=\frac{x_j-x_i}{d_{ij}}$, and the strength of social forces (s) is determined by the following equation [54]:

$$s(r)=f{e}^{\frac{-r}{l}}-e^{-r}$$

(4)

where, f is the attraction intension and l is the attraction length scale. GOA includes three various regions, namely, comfort, repulsion, and attraction zones. Attraction intension and the attraction length affect the comfortable distance or comfort zone, which occurs in various social interactions in grasshopper’s social communication (see Figs. 2b and 2c). In this research, we have considered f = 0.5 and l = 1.5 as was proposed by Saremi et al. [54]. Notably, the function $s$ separates the area between grasshoppers into the comfort zone, attraction, and repulsion regions. The interaction among grasshoppers regarding soothe region is schematically shown in Figure 3.

Figure 2. Function s for, a) l = 1.5 and f = 0.5, b) l = 1.5 and different f, c) f = 0.5 and different l [54].

Figure 2. Function s for, a) l = 1.5 and f = 0.5, b) l = 1.5 and different f, c) f = 0.5 and different l [54].

Figure 3. Individual’s adaptive communication in grasshoppers artificial [54].

Figure 3. Individual’s adaptive communication in grasshoppers artificial [54].

The second component in Eq. (2), (G_i) is computed as follows:

$$G_i=-g{\widehat{e}}_g$$

(5)

where ${\widehat{e}}_g$ is a unit vector toward the center of earth and $g$ represents the gravitational constant.

A_i component in Eq. (2) is calculated as follows:

$$A_i=u{\widehat{e}}_w$$

(6)

where ${\widehat{e}}_w$ is the unity vector in the wind direction and $u$ is wander coefficient.

Substituting the triple components in Eq. (2):

$$X_i={\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne i\end{array}}^{N}s\left(\left|x_j-x_i\right|\right)\frac{x_j-x_i}{d_{ij}}}-g{\widehat{e}}_g+u{\widehat{e}}_w$$

(7)

It should be noted, the X_i is not applied in grasshopper’s optimization and simulation. This is because swarm immediately attain their comfort region; Therefore, the individuals do not experience converge to the optimal solution, and exploration and extraction are not carried out to achieve a precise estimation of global optimum. Particular modifications were added to the abovementioned equation to solve this problem [54].

$$X_i=c\left({\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne i\end{array}}^{N}c\frac{u{b}_d-l{b}_d}{2}s\left(\left|x_j^d-x_i^d\right|\right)\frac{x_j-x_i}{d_{ij}}}\right)+{\widehat{T}}_d$$

(8)

where ub_d and lb_d indicates the upper and lower bounds, respectively, in the d^th dimension. Also, ${\widehat{T}}_d$ represents target value of d^th dimension. $c$ represents decreasing factor to shrink the soothe region, repulsion and attraction zones.

The aim of utilizing parameter $c$is to decline the exploration and intensify the exploitation and is defined by:

$$c=c_{max}-t\frac{c_{max}-c_{min}}{t_{max}}$$

(9)

where c_max and c_min represent the maximum and minimum values of $c$; t, and t_max, are the current iteration, and the maximum number of iterations, respectively. In this research, the values of c_max and c_min were set as 0.95 and 2e-6, respectively.

3. Case Study: Anguran Lead-Zinc Mine

Figure 4. Location map of Anguran mine and two snapshots of blasting rounds.

Figure 4. Location map of Anguran mine and two snapshots of blasting rounds.

Table 1. Most influential parameters affecting fly-rock and back-break.

4. Results and Discussions

4.1. Regression-Based Mine-to-Crusher Cost Model

Minimizing the operating cost from blasting to the crusher is the most important objective, compare to fly-rock and back-break, because all industrial activities seek to reduce operating costs. For the sake of this goal, the cost of any feasible pattern in the Anguran mine should be calculated. Thus, a multi-variable linear regression analysis was developed to develop a model for the total operating costs.

In this paper, the total cost (TC) includes the costs of drilling, blasting, bench cleaning, loading, hauling, crushing, loader working, hydraulic hammer, secondary blasting, additional secondary crushing and the cost of compensating adverse consequences. Descriptive statistics of costs are summarized in Table 3.

The input variables for modeling the costs are L, B, S, HA, St, BRH, Pf, CD, described in Table 2. The regression model is presented in Table 4, which shows that all input variables are significant. None of the variance inflation factors (VIF) is more than five to be removed from the model. The results show that about 95% of the variation in operating cost (from blasting to crushing) can be explained by the proposed regression model. The obtained regression model is formulated as Eq. (10).

(10)

4.3. Optimization of the Blasting Pattern

The developed multi-objective optimization problem (MOP) was implemented to minimize operating costs, fly-rock, and back-break simultaneously considering triple objective functions developed accurately. In this study, the high-speed evolutionary method named the multi-objective grasshopper optimization algorithm (MOGOA), was used for solving the proposed model at an agreeable time using MATLAB software. The conceptual model of multi-objective optimization is as follows:

As seen, there are three objective functions; f(X) is the objective function related to the mine-to-crusher costs, g(Y) and h(Z) are the objective functions related to the back-break and fly-rock, respectively. The main GOA parameters are: population size = 85; c_min = 0.95; and c_max = 2e-6 and the initial population was generated randomly.

The algorithm was implemented with different initial generations from 10 to 500. The Pareto fronts (PF) resulting from the various generations in MOGOA are illustrated in Figure 7. In multi-objective optimization, there may not be one global optimum solution. Instead, a set of non-dominant solutions can be found, such that any of these solutions can be the best solution according to the decision maker’s opinion. A non-dominant solution is a solution that is not worse than other solutions in all objectives and it is better than other solutions in at least one objective. The Pareto set of non-dominant solutions for the case study of this research is presented in Table 7.

Figure 7. The Optimal Front resulted from the various generations in MOGOA.

Figure 7. The Optimal Front resulted from the various generations in MOGOA.

According to the obtained results, 11 non-dominant blasting patterns for Anguran mine were presented (Table 8), where any of those can be one solution to the problem, and the mine engineers select and perform one according to mine’s need and purpose. For example, the mine may consider implementing a pattern with the minimum costs, then model #1 is the best pattern, while still back break and fly-rock are satisfactory.

Optimizing the blasting pattern in order to reduce mining costs, especially in Anguran mine, which has a significant extraction tonnage, has a considerable role in the economic cycle of the country. Therefore, the most effective and efficient solution should be adopted to reduce the mining costs by spending less money. In this regard, we obtained 11 non-dominant blasting patterns that simultaneously reduce the mining costs and environmental side effects due to mine blasting. As can be seen in Table 7, blasting pattern #11 created the minimum value of fly-rock and back-break by 38.53 m (reduction of 67%) and 0.49 m (reduction of 25%), respectively. This pattern is an environmentally friendly policy due to the significant reduction of undesirable environmental effects induced by mine blasting. However, this model is unprofitable for the project because it requires an investment of 49,442.78 $ per blast to reach a usable product. In fact, pattern #11 increase mine to crusher costs by approximately 20%, which is a considerable money. Reciprocally, blasting pattern #1 is the most economical policy for the mining operation with the cost of 41157.28 $ per blast. In constant, the maximum values of fly-rock and back-break are generated by pattern #1. Hence, this pattern is not in accordance with environment-friendly policies. Noteworthy, the maximum value of BRH is related to pattern #11 as shown in Table 8. This means that this pattern can be used to increase the crushing feed and the supply processing plant feed and supply cycle can be established when faced with the reduction of fragmented materials.

5. Conclusions

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