# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 5 DHSMEO for UAV Mountain Path-Planning Problem
### Results and Analysis of UAV Mountain Path Planning  
To evaluate the practicality of DHSMEO, this section applies DHSMEO in addressing the UAV mountain path-planning problem. Additionally, the UAV mountain path-planning problem is also addressed by integrating other algorithms (EO [13], DMMAEO [21], DEEO [32], ESMA [34], and EDBO [39]) with the quasi-uniform cubic B-spline method in comparative performance analysis. The optimization performance of these algorithms is assessed through the best value (Best), average value (Avg), worst value (Worst), and standard deviation (Std). Among the comparative algorithms, EO serves as the original algorithm. D MMAEO, DEEO, and ESMA are the top three algorithms derived from the comparative experimental results of the previous section. And EDBO is a recently proposed algorithm for solving the UAV path-planning problem. The parameter configurations in the algorithms for the comparative analysis are derived from their original works. According to different influencing factors in the UAV mountain path-planning environment, this subsection constructs two cases of three-dimensional mountain maps, which are shown in Figure 4. In the first case, a simple obstacle environment formed solely by the mountain terrain obstacle is considered. In the second case, a complex obstacle environment formed by a combination of the mountain terrain obstacle and the dangerous area is further considered. In these two cases of maps, the blue gradient area represents the infeasible mountain obstacle, the red cylindrical area indicates the threatening dangerous area, and the yellow square and green pentagram denote the starting position and the ending position of the UAV path-planning mission. To ensure a fair evaluation of the performance of comparative algorithms in UAV mountain path planning, the comparative algorithms involved in this UAV mountain path-planning experiment adopt the same experimental configuration. Each algorithm is independently tested 30 times on the UAV mountain path-planning problem, and the results of the comparative algorithms are presented in Tables 15 and 16. In the comparative experimental results shown in Tables 15 and 16, the top-performing results of the compared algorithms within the UAV mountain path-planning experiments are marked in bold. Figures 5 and 6 further visualize the path-planning results of the comparative algorithms in the three-dimensional mountain map through black curves, which more intuitively reflect the capability of comparative algorithms to handle the UAV mountain path-planning issue. In the first case with a simple obstacle environment, the UAV mountain path-planning issue needs to generate the shortest path connecting the starting position and the ending position in the fluctuating infeasible mountain terrain. Table 15 and Figure 5 illustrate the UAV mountain path-planning results of DHSMEO and other comparative algorithms under this case. The performance statistics of the comparative algorithms in handling the UAV mountain path-planning issue under the first case are summarized in Table 15. In accordance with the results from Table 15, the best value, average value, worst value, and standard deviation of DHSMEO are 175.3896, 178.1529, 179.9603, and 1.883847, respectively. These results of DHSMEO exhibit superior performance across all four evaluation indicators compared to other algorithms, and its optimization performance ranks first. The above analysis reveals that DHSMEO provides the most efficient optimization capability among the compared algorithms in the first UAV mountain path-planning case and shows the most competitive overall capability in terms of several indicators. Figure 5 further presents the three-dimensional view and the top view of the UAV mountain path-planning results obtained using the comparative algorithms in the first case. The comparison results in Figure 5 reveal that all the algorithms generate feasible paths in the fluctuating infeasible mountain terrain. However, the UAV path-planning results differ across the algorithms.