## 4 Analysis of Experimental Results
### GTSP-Based Algorithm Performance Evaluation
#### 4.1.2 Performance Comparison and Analysis  
The GA, IWOA and ABC Algorithm are implemented on four GTSP benchmark instances in this section. The analysis will consider the algorithms' best solution cost, worst solution cost, average solution cost, and the difference between known best and worst solutions. Each method was executed 20 times for every instance, yielding the best, worst, and average solutions. In these tables, best indicates the lowest cost. Worst indicates the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **GA** & **IWOA** & **ABC** & **WSHA** \\ \hline Population size & 50 & 50 & 50 & 50 \\ Crossover rate & 0.2 & N/A & N/A & N/A \\ Mutation rate & 0.8 & N/A & N/A & N/A \\ \(w_{IWOA}\) & N/A & N/A & N/A & 0.5 \\ \(w_{ABC}\) & N/A & N/A & N/A & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameterization of the algorithm.  
Figure 7: LSCDHead structure and internal modules. (**a**) LSCDHead structure; (**b**) Internal structure of GnConv and ShConv.  
shortest path length on four different datasets. Both on the smaller dataset City (17,11) and the larger dataset City (39,25), the can converge to the shorter path length faster, and its performance is relatively stable throughout the iterations. This further demonstrates the efficiency and stability of the WSHA in dealing with such problems.  
Secondly, this paper also visualized the paths that pass through the city, as shown in Figure 9. From Figure 9, one can visualize the path-planning graphs generated by the WSHA on different datasets. These path planners show the entire route from the starting point to each target city, and back to the starting point. For the smaller dataset City (17,11), the paths generated by the WSHA are relatively simple but can effectively cover all the necessary city nodes. For the larger dataset City (39,25), the WSHA generates more complex but equally efficient paths, demonstrating the algorithm's scalability and robustness in dealing with large-scale problems.  
Figure 8: Comparison of the variation of the shortest path lengths of the four datasets. (**a**) City (17,11); (**b**) City (24,15); (**c**) City (31,16); (**d**) City (39,25).  
Finally, in this paper, the shortest path planning of City (39,25) is mapped in detail and simulated with multiple rounds of simulation with the actual space located in Texas, USA. The results obtained are shown in Figure 10. By comparing Figure 10, the close correspondence between the shortest path planning of the City (39,25) and the actual space layout in Texas can be seen. This precise mapping relationship not only helps to visualize the significant advantages of the WSHA in path planning but also reinforces the applicability and effectiveness of the algorithm in real spatial applications. Each city in the figure is represented as a point, while the paths are represented by line segments connecting these points. The result not only visualizes the effect of the algorithm, but also provides a solid theoretical and practical foundation for the promotion and application of the WSHA in actual spatial planning.  
Figure 9: Four dataset path-planning diagrams. (**a**) City (17,11); (**b**) City (24,15); (**c**) City (31,16); (**d**) City (39,25).