## 4 Optimization of Blasting Parameters  
### The Optimization of Engineering Cases  
The lime mine area has an elevation ranging from 624 m to 1063 m, with a relative elevation difference of 439 m, indicating a medium-cut low-mountain landform. The terrain in the mining area exhibits higher elevations towards the north and lower elevations towards the south, characterized by steep slopes and well-developed vegetation. The highest mining point reaches +900 m, while the lowest mining point is at +701 m, resulting in a relative elevation difference of 199 m. The natural ore composition is relatively simple, consisting solely of limestone ore with predominant mineral components, including calcite, sparry calcite, and dolomite. The rock's physical and mechanical parameters are presented in Table 1. At the conclusion of mining operations, the step height measures 15 m, while the working step exhibits a slope angle of 75\({}^{\circ}\). The safety platform spans a width of 4 m, whereas the cleaning platform boasts an impressive width of 8 m. The road grade is classified as III and has a width of 8 m. With regard to longitudinal slopes, the maximum stands at 8%, while the average measures 6.4%. Additionally, a minimum turning curve radius of 15 m is required, and a relaxation slope section with a minimum length of 60 m must be implemented. To ensure optimal conditions for transportation within the mine site, mud-bound gravel pavement will be utilized along approximately 2.8 km worth of mining roads. Lastly, medium- and deep-hole multi-row hole-differential extrusion blasting techniques will be employed in conjunction with detonating tubes. Figure 6: Fitness step curve. Figure 7: The optimization algorithm determines the value of the optimal solution. During the calculation process for overall costs, actual consumption and production data from mine operations are taken into consideration. It can be concluded that the drilling cost per meter in the mine (\(m_{1}\)) amounts to CNV 22/m. The step height is set at 15 m with a hole depth (\(L\)) of 17 m. The bulk weight of ore (\(\gamma\)) stands at 2.62 ton/cubic meter. An emulsion explosive is used for blasting with a unit price (\(m_{2}\)) of CNV 7/kg. Additionally, the cost per meter for blasting equipment (\(m_{3}\)) reaches CNV 3.5/m. Transportation costs per ton of ore amount to \(m_{4}\) = CNV 2/ton. By analyzing lumpiness and consumption costs related to shipped ore statistics, values \(A_{1}\) = 0.298, \(A_{2}\) = 0.013, \(A_{3}\) = \(-\)0.0036, \(A_{4}\) = 0.032, and \(A_{5}\) = 0.48 can be obtained. By incorporating these variables into Formula (4), we can derive an overall consumption cost mathematical model specific to limestone mines. To solve this mathematical model effectively, the improved Gray Wolf algorithm is employed. The objective function associated with it is as follows:  
\[C=\frac{22\times 17}{15\times a\times b\times 2.62}+7q+\frac{3.5\times 17}{15 \times a\times b\times 2.62}+0.298X+0.013+2(-0.0036X^{2}+0.032X+0.48) \tag{13}\]  
The equation is defined as follows: \(X\) represents the average block size, \(a\) denotes the hole distance, \(b\) signifies the row distance, and \(q\) indicates the single explosive consumption. The development of the limestone mine joint has not been undertaken. Based on the average block formula and blasting experience formula, we derived the target constraint conditions. \[X=7\times q^{-0.8}\times 2.62^{-0.8}\times\left(15\times 2.62\times a\times b \times q\right)^{\frac{1}{6}}\times\left(1.15\right)^{\frac{2}{3}} \tag{14}\]  
\[a=mW_{1} \tag{15}\]  
\[b=a\sin 60^{\circ} \tag{16}\]  
\[q=\frac{Q}{aW_{1}H} \tag{17}\]  
The given formula incorporates the subsequent variables: \(a\) denotes the hole distance, \(b\) represents the row distance, \(q\) signifies the explosive consumption per unit, \(Q\) stands for the charge amount, and m represents the gun hole density coefficient. Typically, limestone exhibits a value ranging from 0.8 to 1.0 for this coefficient.