## 4 Experimental Evaluation
The second focus of this study is to calculate the optimum path that has the minimum length to be followed by the quadcopter. The path planning problem was constructed within the scope of traveling salesman problem (TSP). The TSP is based on calculating the shortest path starting from and ending at the same waypoint by visiting all the other predefined waypoints. SDCS was also implemented to obtain the optimal path for a single quadcopter. Various population sizes of the MH algorithms and various waypoint numbers and were used in the tests. The results obtained with the tested MH algorithms and the SDCS method is shown in Table 9.  
The optimal solution of min-max TSP with multiple depots for multi quadcopters was investigated using the tested MH algorithms and SDCS method. To obtain the optimal solution, the generation of quadcopter trajectories must be performed in a well-balanced manner. The existing literature discusses the generation of balanced trajectories with two main objective functions: MinSum and MinMax. MinMax is utilized for minimizing the longest UAV trajectory, while MinSum provides a reduction in the total length of all trajectories. In this research, a single objective function that combines these two objective functions was utilized and is presented in Equation (12). \[Total\ cost\ =\ n\ x\ lng_{trj}+sum_{trj} \tag{12}\]  
In Equation (12), total cost represents the objective function, \(\mathrm{lng_{trj}}\) is the longest trajectory, \(\mathrm{sum_{trj}}\) is the total length of the trajectories, and \(\mathrm{n}\) is the number of quadcopters. Tables 10 and 11 show the performances of the tested methods in obtaining the optimal paths for two and three quadcopters, respectively. Figure 14: Graph of controller performances on Psi angle. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Waypoint** & **Population** & **FFO (m)** & **FHO (m)** & **PO (m)** & **SDCS (m)** \\ \hline
20 & 50 & 345 & 324 & 324 & 324 \\
20 & 100 & 324 & 324 & 324 & 324 \\
40 & 50 & 756 & 772 & 731 & 722 \\
40 & 100 & 756 & 756 & 722 & 722 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance of the tested methods in obtaining the optimal path. As the number of waypoints increases, the possible solutions increase, making it difficult to find the optimal solution. For this reason, as the number of waypoints increases, the difference between the solutions found by MH algorithms increases. Since the SDCS method provides an exact solution, it provides the optimal solution regardless of the number of waypoints. In tables related to path planning, it is seen that, as the population size increases, results closer to the optimal solution are obtained. Another test with a set including 100 randomly selected waypoints was performed. Figures 15 and 16 show the generated quadcopter trajectories by the PO algorithm when the population size is defined as 50 and 100, respectively. Total length of the trajectories are 549 m and 498 m for Figures 15 and 16, respectively. When the trajectory lengths and figures are examined, it is seen that the change in population size in the MH algorithms will cause significantly different results not only numerically but also geometrically. Figure 17 shows the trajectories generated by the SDCS method for three quadcopters. The square waypoints are the starting and ending points of the balanced quadcopter trajectories, which are formed within the scope of the TSP. Generated trajectories start and end on same waypoints. The SDCS method reduced both the total path length and the longest path length together, considering Equation (12). In the path planning part of this study, firstly, performances of the FFO, FHO, and PO algorithms and SDCS were compared within the scope of TSP defined for single quadcopter trajectory. Considering the Table 9, the PO algorithm provided the optimal solution among the MH algorithms.