# 3D Global Path Planning Optimization for Cellular-Connected UAVs under Link Reliability Constraint
## 4 Results and Discussions
### Path Planning Optimization
The generated paths vary from straight lines to curvy paths, such as the designed paths by GA and PSO-GA in Figure 10a, respectively. One of the reasons for this behavior is the feature of information flow in the PSO algorithm, which helps the algorithm to explore the search space better. Meanwhile, during the optimization procedure, due to the inertia, cognitive, and social acceleration  
Figure 10: Simulation results of different optimization algorithms in Scenario II: (**a**) path planning results and (**b**) cost function value vs. the number of function evaluations. Figure 9: Statistical results of Scenario I: (**a**) optimal path, (**b**) reliable path, and (**c**) ratio of the reliable path. coefficient adjustments, the exploration rate gradually decreases, and the exploitation rate gradually increases. This sometimes results in premature convergence, and the algorithm gets trapped in local minima. On the other hand, although GA provides concentrated results, which look stable, it should be noted that in most simulation experiments, the algorithms converge to a local minimum and is not capable of effectively making a tradeoff between objectives, minimizing the traveling distance and maximizing the link reliability. Among all algorithms, PSO-GA provides stable solutions with a slightly better reliable path length and reliable path ratio. Scenario III was developed based on a set of real-world constraints, such as the locations of BSs (in this case, the cellular network design in suburban environments), obstacles, and a no-fly zone. The added constraints considerably enhanced the complexity of the problem as well as its multimodality. Simulation results in Figure 12 show that all three algorithms are capable of computing acceptable paths for the considered problem. However, with the same justification as Scenario II, the PSO-GA algorithm still surpasses the other two algorithms in terms of generating a smoother path and faster convergence speed. Figure 13 depicts a 3D map of the UAV path planning with the PSO-GA algorithm for Scenario III, and Figure 14 depicts an overlay of the horizontal projection of the 3D path planning on the Google map of the considered environment. As can be seen from the figures, PSO finds a valid path while effectively avoiding obstacles and the no-fly zone and maximizing the reliable path length. Figure 11: Statistical results of Scenario II: (**a**) optimal path, (**b**) reliable path, and (**c**) ratio of the reliable path. Figure 12: Simulation results of different optimization algorithms in Scenario III: (**a**) path planning results and (**b**) cost function value vs. the number of function evaluations. Figure 15 compares the statistical results of the path length, reliable path length, and reliable path ratio of the three algorithms in Scenario III. By comparing the results of Figure 15a, it can be seen that the median values of all three algorithms are almost the same. However, PSO-GA surpasses the other two algorithms due to the shorter uppers and lower whiskers, as well as the closeness of the median value to the minimum computed path length. The results comparison also reveals the lower stability of PSO compared with GA and PSO-GA. By comparing the results of Scenarios II and III, it can be seen that in Scenario III, the performance of the algorithms is more similar compared with Scenario II. Figure 14: Overlaying a horizontal projection of the 3D path planning on the Google map of the considered environment. Figure 13: An example of a 3D representation of UAV path planning. That is because by adding more constraints to the problem, the search space becomes more restricted, which limits algorithms' instability in generating more diverse solutions. As previously mentioned, enlarging the scale of the problem and increasing the number of objects in a problem will increase the complexity of the problem. Figure 16 presents the results of the average execution time of three algorithms in different scenarios.