# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 5 DHSMEO for UAV Mountain Path-Planning Problem
### Results and Analysis of UAV Mountain Path Planning
Among the results obtained using the comparative algorithms, the standard EO is trapped in a local optimum, DHSMEO generates the shortest planning path, and other comparative algorithms generate different feasible paths within the same feasible corridor. The path-planning results shown in Figure 5 more intuitively highlight the performance differences among the comparative algorithms under the first UAV mountain path-planning case, and DHSMEO exhibits a better ability to address the UAV mountain path-planning problem than other comparison algorithms. Figure 4: Three-dimensional mountain map. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Best** & **Avg** & **Worst** & **Std** \\ \hline EO & 179.1639 & 181.5920 & 188.3981 & 2.504409 \\ DMMAEO & 176.0768 & 179.1847 & 183.0997 & 1.957168 \\ DEEO & 176.2221 & 180.8633 & 185.6625 & 2.120665 \\ ESMA & 176.6373 & 180.6428 & 185.6273 & 2.013366 \\ EDBO & 175.7928 & 180.0901 & 185.5089 & 1.897720 \\ DHSMEO & **174.7972** & **177.2150** & **179.5667** & **1.750398** \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison results of UAV mountain path planning in case 1. Figure 5: UAV mountain path-planning results of compared algorithms in case 1. Unlike the first case with a simple obstacle environment, the second case with a complex obstacle environment requires considering the influence of the mountain terrain obstacle and the dangerous area on the generated path at the same time, which further enhances the difficulty of handling the UAV mountain path-planning issue. Table 16 and Figure 6 showcase the performance comparison of DHSMEO and other algorithms to handle the UAV mountain path-planning issue under this case. The statistical analysis for the comparative algorithms to handle the UAV mountain path-planning issue under this second case is provided in Table 16. Table 16 presents the performance of DHSMEO, with a best value of 176.4555, an average value of 178.8353, a worst value of 182.1692, and a standard deviation of 1.692046. These results remain better than those of the other comparative algorithms across all four performance indicators, and they make DHSMEO still rank first in optimization performance. Additionally, compared with the path-planning results for the compared algorithms in the first case from Table 15, the path-planning results from DHSMEO exhibit the least variation among the path-planning results for comparative algorithms in the second case from Table 16. The above results indicate that DHSMEO maintains its leading optimization performance among the compared algorithms to handle the UAV mountain path-planning issue under the second case with a complex obstacle environment, and it also shows the most stable and competitive overall performance among the comparison algorithms in terms of multiple indicators. Figure 6 further presents the three-dimensional view and the top view for the UAV mountain path-planning results derived from the comparative algorithms under the second scenario. As shown in Figure 6, compared to the paths generated in the first case, all comparative algorithms further adjust the path-planning results for the dangerous area and generate feasible paths to meet the needs of UAV mountain path planning in this case. Although the comparative algorithms adjust their path-planning results for the dangerous area, the standard EO still falls into a local optimum, and DHSMEO still generates the shortest planning path. The path-planning results shown in Figure 5 more intuitively show that DHSMEO still exhibits a better UAV mountain path-planning problem-solving capability among the comparative algorithms under the second case with a complex obstacle environment. In sum, according to the experimental results of UAV mountain path planning presented in Tables 15 and 16 and Figures 5 and 6, the proposed DHSMEO provides practical and competitive optimization results for the UAV mountain path-planning problem across obstacle environments with different levels of complexity.