# 3D Global Path Planning Optimization for Cellular-Connected UAVs under Link Reliability Constraint
## 4 Results and Discussions
### Path Planning Optimization  
The positions of the starting point, destination, BSs, obstacles, and no-fly zones were utilized as the inputs, and PSO, GA, and PSO-GA algorithms were employed to solve the problem. Note that the presented figures in this subsection are examples of simulation results selected based on the corresponding mean values, as described earlier in the methodology, Section 3.4. A detail of the statistical results of the simulations is presented in Appendix A Table A1. In addition, to better visualize the results, the path planning results are depicted in a 2D form, a horizontal projection of the 3D path planning on \(xy\) plane, and only an example of 3D simulation results of UAV path planning is presented for Scenario III. Figure 8 presents the path planning optimization simulation results for Scenario I under different algorithms. Obviously, for an obstacle-free path, the shortest path between the starting point and destination is the direct path. However, as seen from the figure, the optimal paths pass through the reliable zones, while making a tradeoff between minimizing the traveling distance and maximizing the link reliability. By comparing the results in Figure 8a, it can be seen that PSO-GA provides a slightly better solution, in which the path is shorter while passing from the reliable zone. Results in Figure 8b show a comparison of the convergence rate of different algorithms. In a small-scale environment, the convergence speeds of all three algorithms are almost the same. Figure 9 shows the statistical results of path length, reliable path length, and reliable path ratio of the considered algorithms for Scenario I. The wider the data distribution (both interquartile range and whiskers), the lower the stability of the algorithms to solve the problem. In addition, a comparison between median values shows that in small-scale environments, PSO and PSO-GA algorithms slightly outperform GA in providing effective solutions for the considered problem. However, due to the simplicity of the problem in Scenario I and the distinctive features of the utilized algorithm, it can be concluded that all considered algorithms offer effective solutions for this problem. Figure 8: Simulation results of different optimization algorithms in Scenario I: (**a**) path planning results and (**b**) cost function value vs. the number of function evaluations. Figure 10 presents the result of the path planning optimization in Scenario II, which corresponds to a long-range BVLOS scenario. The results show better path planning results of the PSO-GA algorithm compared with PSO and GA due to the higher exploration and exploitation capability of the PSO-GA algorithm for searching the entire search space and, consequently, do not trap in the local optimal and better converge to the global optimal. Results also show some of the shortcomings of the PSO and GA algorithms to minimize the cost function and get trapped in local minima. For example, although the designed path by GA provides a shorter path compared with the other two algorithms, for about 4 kilometers, it passes from an area without cellular coverage. In contrast, PSO-GA effectively computes a path with the most reliable coverage while also minimizing the traveling path. The results of Figure 10b show that PSO-GA also surpasses PSO and GA algorithms in terms of convergence speed. Figure 11 compares the statistical results of the path length, reliable path length, and reliable path ratio of 50 simulation experiments on three algorithms in Scenario II. It should be noted that by increasing the environmental scale and enhancing the number of objects, such as BSs and obstacles, the multimodality of the problem will increase, in which the complexity of finding a global optimal for the problem will be increased as well. Based on the interquartile range of presented box plots, the instability of PSO in optimizing a large-scale path planning problem is obvious.