# A Cluster-Based Hierarchical-Approach for the Path Planning of Swarm
## 6 Simulation Results  
The efficiency and validation of the proposed strategy is defined in this section. By simulating the scenario using MATLAB 2019. The dimensions for the mission area are (\(x\), \(y\), \(z\)) = (30, 30, 2) km. Firstly, in this research, we simulate the scenario by parallel implementing the design hierarchy with the non-dominated sorting genetic algorithm II (NSGA-II) algorithm to check the validity of our scheme. Table 1 presents the constraints used in the algorithm. Now \(\alpha\) and \(\beta\) control the effect of pheromone or heuristics on the outcome. To get a heuristic solution, we select a bigger value of \(\beta\) compared to \(\alpha\). The pheromone evaporation rate is \(\rho\). \(\rho\) controls the speed at which the pheromones evaporate from the path. We want a relatively higher value for \(\rho\) because we need the previous pheromones to evaporate faster and to make way for new pheromones with better information. \(Nc_{max}\) represents the maximum number of iterations, \(m\) is the total ants. \(Nc_{max}\) and \(m\) depend on each other. The higher the number of ants, the lower the iterations. If we decreased the number of ants we need to run more iterations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Constraint** & **Symbol** & **Value** \\ \hline Pheromone constraint & \(\alpha\) & 3 \\ Heuristics constraint & \(\beta\) & 4 \\ Pheromone evaporation rate & \(\rho\) & 0.8 \\ Max iterations & \(Nc_{max}\) & 50 \\ No. of ants & \(m\) & 20 \\ Constant that affects the pheromone rate & \(Q\) & 15 \\ Min pheromone & \(\tau_{min}\) & 0.1 \\ Max pheromone & \(\tau_{max}\) & 1 \\ Min velocity & \(v_{min}\) & 40 ms\({}^{-1}\) \\ Max velocity & \(v_{max}\) & 70 ms\({}^{-1}\) \\ Max turning angle & \(\phi_{max}\) & 105\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Constraints for the Algorithm. \(Q\) is the constant that controls the pheromone rate. We have selected a relatively higher value of \(Q\) because we want more pheromone depositing on the trail. \(\tau_{min}\) and \(\tau_{max}\) are the minimum and maximum pheromones values. The reason we restricted the algorithm within this interval is that it has the best chance of discovering the best solution. The minimum and maximum velocities of the UAV are \(v_{min}\) and \(v_{max}\). These velocities are chosen to best represent the real-life speeds of the UAVs. Lastly, \(\phi_{max}\) is the maximum turning angle. The reason to choose \(105^{\circ}\) is that at higher angles, chances of collision among UAVs increase. First, we compare our proposed method with the NSGA-II algorithm to prove the effectiveness of our method. NSGA-II is a multi-objective evolutionary algorithm. It is an efficient algorithm and works on a non-dominated sorting method. It uses an elitist strategy and has an effective parameter handling approach. Figure 5 presents the comparison between the two methods. As it is clear from the plot, our proposed method finds a shorter path than the NSGA-II while also avoiding the hilly peaks and tornadoes. This is because our proposed method is computationally faster than the NSGA-II and hence, can plot the path quicker than NSGA-II while avoiding the obstacles. Meanwhile, the NSGA-II also takes more turns than our proposed method. Frequent turns can introduce instability and inconsistency in the flight. Table 2 presents the flight details of the comparison between the proposed method and the NSGA-II algorithm. Confirming the previous simulation given in Figure 5, we can see that the path planned by the proposed method is over 2 km shorter than the NSGA-II. This proves the superiority of the designed strategy over NSGA-II. Case Study I: In this scenario, to test the efficiency of the designed strategy, we consider three ant colonies that launch from three different positions and arrive at the destination concurrently. The environment is hazardous and contains hilly peaks. First, each colony uses MMACO to find its best ant.