# Enhanced Path Planning by Repositioning the Starting Point +
## 4 Experimental Evaluation
### Computational Efficiency Analysis
#### 4.2.5 Scaled-Up Experimental Analysis  
Building upon the comprehensive evaluation presented in Section 4.2.4, the significant computational advantages of the geometric median approach enabled us to undertake a more ambitious experimental investigation. While the original 65,000-scenario dataset provided robust statistical validation, the growing complexity of operational requirements in real-world drone applications demanded evaluation across broader parameter ranges, particularly for large-scale missions involving extensive station networks and substantial drone fleets. Given the substantial computational time requirements for processing larger scenario sets--with complete test cycles extending to multiple days--we implemented a strategic adjustment to maintain experimental feasibility while expanding coverage. The iteration  
Figure 17: Geometric median vs. brute force: time efficiency for finding the optimal center. count was reduced from 1000 to 500 scenarios per configuration, allowing for a significant expansion in the parameter space without compromising statistical reliability. The scaled experimental framework encompassed station configurations ranging from 5 to 800 stations (specifically 5, 10, 15, 20, 25, 45, 60, 100, 200, 400, and 800 stations) and drone fleet sizes extending from 2 to 60 drones (2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, and 60 drones). This expanded configuration resulted in another set of 58,500 randomly generated scenarios, representing a completely new, independently generated dataset that enables analysis of optimization performance across industrially relevant scales, including large infrastructure monitoring operations, extensive agricultural surveys, and comprehensive environmental assessment missions. The scaled experimental results, presented in Figures 18 and 19, reveal several critical insights regarding optimization performance at increased operational scales, building upon the patterns initially observed in Figures 15 and 16. Figure 18 illustrates performance patterns for larger drone fleet configurations, extending the insights originally presented in Figure 15.  
The extended drone fleet analysis, as illustrated in Figure 18, encompasses operational scenarios relevant to major commercial and research applications, extending well beyond the original 2-10 drone range examined in Figure 15. Notably, the extended drone analysis reveals that performance improvements actually increase with larger fleet sizes, contrary to the declining pattern observed with increased station counts. This behavior aligns with theoretical expectations, as each additional drone introduces two new starting point connections (departure and return paths), providing additional optimization opportunities while maintaining the same fundamental operational constraints. Similarly, Figure 19 demonstrates the behavior of the geometric median approach across the extended station range, providing direct comparison with the original station-based analysis from Figure 16.  
The extended station analysis confirms and extends the declining performance trend clearly established in the original experimental range shown in Figure 16. While the original findings demonstrated the predictable declining trend as station counts increase from 5 to 100 stations, the extended range in Figure 19 reveals the continuation of this pattern at much larger scales and identifies specific performance transition zones. Beyond 200 stations, improvements stabilize at lower but still meaningful levels, indicating that even for very large missions, geometric median optimization provides consistent benefits. _Comparative Analysis: Original vs. Scaled Results_  
Direct comparison between the original results (Figures 15 and 16) and scaled experimental results (Figures 18 and 19) provides valuable insights into the robustness and scalability of the optimization approach. The overlapping parameter ranges involving 5 to 100 stations and 2 to 10 drones demonstrate remarkable consistency between datasets.