# 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
The underlying reason is that, as the number of edge nodes increases, the available resources per node also increase, leading to a reduction in the average number of device requests allocated to each node, which in turn results in a decrease in latency.Among these strategies, the IBGA achieves a reduction in service time of 20.5-31.2% compared to the other algorithms, demonstrating a significantly lower service time. The results show that the IBGA algorithm performs best as the number of edge nodes increases. In Figure 10b, it is evident that the deployment cost increases for all four methods as the number of SEs increases. This is primarily due to the fact that deploying additional nodes incurs higher overall costs. The figure illustrates that the IBGA method consistently demonstrates a lower deployment cost compared to other algorithms, making it particularly well-suited for this scenario. The reason is that as the number of SEs increases, more nodes are deployed, leading to an increase in cost. However, the IBGA algorithm manages this growth more efficiently than the other approaches. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Edge Nodes** & **Average Device Coverage** & **Objective Function Value** \\ \hline
5 & 0.5895 & 0.6228 \\
6 & 0.7074 & 0.6220 \\
7 & 0.7800 & 0.6140 \\
8 & 0.8571 & 0.6020 \\
9 & 0.9614 & 0.5916 \\
10 & 0.9773 & 0.6080 \\
11 & 0.9841 & 0.6400 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results. Figure 9: Edge node deployment location. (**a**) Initial deployment location. (**b**) Final deployment location. (**c**) Convergence curve. Figure 10c shows the objective function value obtained for different deployment strategies. Our objective is to minimize this function value, and as the figure illustrates, the IBGA method achieves the lowest overall objective value compared to the other algorithms, with IBGA performing the best and GA ranking second. This is due to the ability of the GA algorithm to search multiple regions of the solution space and to search faster for the optimal deployment location. The improved IBGA algorithm demonstrates superior convergence due to its approach of replacing random searches with targeted searches for candidate positions, thus avoiding redundant searches for the same node pairs. Additionally, by employing two populations that evolve simultaneously, the algorithm reduces the time required to find the optimal solution. To simulate real-world conditions more accurately, we increased the number of devices to better reflect the complexity of a natural mining area. This increase allowed us to replicate the actual workload encountered in such environments. We then evaluated the algorithm's performance under different task density conditions, assessing how it adapts to the increased workload and varying demands. Figure 11 illustrates the impact of four node deployment solutions as the number of terminal devices increases, with a fixed count of nine edge nodes. As shown in Figure 11a, the response time for each strategy increases parallel with the increase in terminal devices. Notably, it is evident that IBGA exhibits the shortest service time, while the randomized algorithm yields the longest service time across varying numbers of end devices. When compared with the randomized and k-means algorithms, the IBGA algorithm demonstrates notable reductions in service delays, with savings of 1012.5 ms and 539.8 ms, respectively. This improvement is due to the increase in task generation as more terminals are introduced, leading to higher computational demands on the edge nodes. Consequently, these nodes must provide enhanced computing services, resulting in a general increase in response times for all strategies. Figure 11: Performance comparison of fixed device edge node deployment algorithms. (**a**) Tasks latency. (**b**) Node deployment costs. Figure 10: Performance comparison of fixed device edge node deployment algorithms. (**a**) Tasks latency. (**b**) Node deployment costs. (**c**) Node deployment location.