## 5 Numerical Experiments and Analysis of Results
### Solving the TOP with Obstacles and Environmental Factors  
In this section, we extend our analysis to evaluate the robustness of our approach under more realistic operational conditions. We examine how environmental factors such as obstacles, wind conditions, and payload weight affect route optimization in Scenario 1 (the one with 21 nodes).  
We first analyze the effect of obstacles on route planning. Figure 11 illustrates the optimal routes generated by our algorithm for Scenario 1 with obstacles, UAV speed of 1.1 km/min, payload of 1.0 kg, and wind speed of 0.2 km/min at 0\({}^{\circ}\) direction (easerly wind). The presence of obstacles (represented by black rectangles) significantly impacts the routes, forcing UAVs to take detours that increase travel times and distances. Our algorithm successfully generated feasible routes that avoid all obstacles while maximizing reward collection.  
Our best solution (OBD) for this variant with obstacles is as follows: route 1 = [1, 11, 19, 9, 15, 13, 21], with reward = 145.0, and travel time = 49.54 min; and route 2 = [1, 8, 4, 2, 12, 10, 5, 21], with reward = 140.0, and travel time = 49.82 min. The total reward was 285.0.  
To investigate the impact of wind conditions on route optimization, we conducted experiments with constant drone speed (1.1 km/min), payload (1.0 kg), and wind speed (0.2 km/min) while varying the wind direction. This analysis reveals how our algorithm adapts routes based on prevailing wind conditions. As can be seen in Figure 12, with a northerly wind our algorithm generated more conservative routes: route 1 = [1, 19, 11, 13, 21], with reward 90.0, and travel time 48.88 min; and route 2 = [1, 8, 16, 5, 21], with reward = 50.0, and travel time 49.55 min. The total deterministic reward decreased to 140.0.  
Several key observations emerge from this analysis: (i) wind direction substantially impacts achievable rewards due to the specific geographic distribution of nodes; (ii) the neural network demonstrates remarkable adaptability across different wind directions; and (iii) the algorithm maintains consistent computational performance across all wind directions, with average computation times ranging from 64.15 to 64.63 s per iteration.  
Figure 11: Route optimization under obstacle constraints.  
We also examined the impact of travel time stochasticity on solution reliability. Using a constant variance level parameter \(\lambda=0.3\), we conducted multiple simulation runs to evaluate how solutions optimized for deterministic conditions performed under uncertainty. This moderate level of variability typically resulted in simulation-based reward estimates (OBS) that were approximately 10-15% lower than their deterministic counterparts (OBD), highlighting the importance of accounting for uncertainty during the optimization process. The consistent gap between deterministic and stochastic solution quality demonstrates the value of our simheuristic approach, which explicitly accounts for uncertainty when evaluating and selecting solutions. Without this consideration, planners might overestimate the achievable rewards in real-world deployments, leading to suboptimal resource allocation and mission planning. The combined effect of obstacles, payload weight, and wind conditions creates a complex optimization scenario that traditional exact solvers would not be able to address efficiently. Our neural network-based approach demonstrates robust performance across these varying conditions, providing solutions that balance reward maximization with route feasibility and reliability.