# Multi-Objective Edge Node Deployment Method Based on Improved Heuristic Algorithms for Smart Mines
## 6 Results and Discussion  
### Analysis of the Results of the Fixed Equipment Edge Node Placement Algorithm  
We have selected the randomized algorithm [32] and the k-means algorithm [33; 34] as benchmark algorithms for comparison. A comparison of IBGA with benchmark algorithms and GA [35; 36] is performed based on completion time and deployment cost. On the production line platform, a sequence of operations is executed. This includes monitoring the position of the materials box, tracking the status of materials, assembling the cylinder to move the materials box to the processing position upon detection, performing the loading operation, updating the product status, and activating the cylinder to push the materials box along the conveyor belt in a series of five tasks. Based on expert input, a minimum of five strategically placed nodes were required to ensure the smooth execution of each task. Each node was assumed to have sufficient resources to handle any task assigned to it successfully. Multiple experiments were conducted on the production line platform with different edge node placements in each scenario. Device coverage and objective function values were obtained through the algorithm, and the results are presented in Table 5. To reduce the impact of random errors, the results of 50 experiments were averaged. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Value** \\ \hline T & Maximum number of iterations of IBGA & 500 \\ M & Number of populations of IBGA & 200 \\ \(P_{cro}\) & Crossover rate of IBGA & 0.6 \\ \(P_{alt}\) & Variation rate of IBGA & 0.05 \\ T & Maximum number of iterations of ISCSO & 500 \\ MF & Number of populations of ISCSO & 200 \\ b & Spiral shape constant & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters set in the algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Value** \\ \hline MN & Number of mobile devices & [5; 10; 20] \\ MX & Number of potential candidate locations & [5; 10; 20] \\ \(md_{in}\) & Amount of data input per task & [80; 150] Kb \\ \(md_{out}\) & Amount of data output per task & [1; 50] Kb \\ \(my\) & Load per task & [80; 1000] MHz \\ \(mfre\) & The main frequency of the edge node & 3.6 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Notations used in mobile device edge node placement. The optimal number of nodes to be deployed in this scenario can be obtained by analyzing the experimental results in Table 5. As the number of edge nodes increases, the system's device coverage expands accordingly. In each time slot, the number of tasks processed by the system rises, leading to a reduction in task response time. This reduction outweighs the increase in cost, resulting in a gradual decrease in the objective function value. However, when the number of nodes exceeds 9, the reduction in task response time becomes less significant compared to the increase in cost, leading to a subsequent rise in the value of the objective function. Figure 10 illustrates the detailed delay and cost outcomes. Hence, with nine nodes, the achieved solution attains the optimal objective, boasting a high coverage rate and representing the optimal deployment solution at that juncture, as illustrated in Figure 9. Figure 9a depicts the initial node positions generated by the IBGA algorithm and Figure 9b shows the optimal node deployment scheme generated by IBGA after a certain number of iterations. Figure 9c further illustrates the algorithm's stability, achieved after 200 iterations. Figure 10 illustrates the impact of the four deployment strategies on the service time as the number of edge nodes increases while keeping the number of endpoints constant. As shown in Figure 10a, the service time of all four methods steadily decreases with the increasing number of \(SE_{s}\).