# A Cluster-Based Hierarchical-Approach for the Path Planning of Swarm
## 6 Simulation Results
MMACO achieves this by continuously modeling a journey of a colony of ants from the initial point to the destination. Whenever an ant finds an obstacle, it changes its direction and leaves a pheromone for other ants so they can avoid \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Initial Position** & **Destination** & **Distance** \\ \hline Proposed Algorithm & (0,0,0) & (25,25,1.8) & 34.321 \\ NSGA-II & (0,0,0) & (24.8,24.8,1.81) & 36.393 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Flight Details of proposed algorithm and NSGA-II. Figure 5: Comparison of the proposed algorithm with NSGA-II algorithm. the obstacle as well. This process is repeated a fixed number of times until the best ant with the shortest distance is discovered. Afterward, Vicsek MAS designates the best ant as the leader and the rest of the ants follow the leader as agents. Figure 6 illustrates the proposed strategy in action and shows that our strategy will easily fulfill the mission requirement. Figure 5(a) presents the 3D simulation from one view while Figure 5(b) presents it from another angle. Figure 7 demonstrates the optimization costs of finding the best path. It is clear from Figure 7 that we find no significant decline in the cost after the 5 th iteration. There is a slight variation in the costs of colonies 2 and 3 but is negligible. The reason for this decline is that the algorithm has discovered the best route around the 5 th iteration. Afterward, the ants just travel on the best path and hence almost the same cost for the subsequent iterations. Figure 6: Simulation Results with Hilly Peaks; (**a**) 3D simulation seen from one point of view (**b**) 3D simulation from another point of view. Table 3 shows the flight details of the best ant of each colony. Table 3 also shows the complete flight distance from the initial position to the target. Case Study II: In this scenario, to test the efficiency of the designed strategy, we consider three ant colonies (UAVs) that launch from three different positions and arrive at the destination concurrently. The environment is dynamic and contains not only hilly peaks but also tornadoes. First, each colony uses MMACO to find its best ant. The process of finding the ant is similar to the one explained in _Case Study I_. Afterward, Vicsek MAS designates the best ant as the leader and the rest of the ants follow the leader as agents. Figure 8 illustrates the proposed strategy in action and shows that our strategy will easily fulfill the mission requirement. Figure 8a shows the mission area from one point of view while Figure 8b presents it with another view to clearly show the peaks and tornadoes. Figure 8: _Cont._  
Figure 7: Optimization Costs for Case Study I. To solve the predefined mission scenario, the paper combined Max-Min ant colony optimization (ACO) with Vicsek based multi-agent system (MAS) to make a meta-heuristic algorithm. Moreover, in our designed control structure, Max-Min (ACO) is used to bound, lemmatize the pheromone, and gives the best ants to every colony, which makes the most optimized path. Lastly, we tested the proposed method in two different dynamic environments, and the simulation results demonstrated that the proposed method is robust and efficient. The designed strategy finds the best path quickly with minimum cost. The simulation results also compared the proposed method with the NSGA-II algorithm, to prove the designed algorithm has a better convergence rate and optimal path. Future work includes increasing the number of UAVs in each colony and also increasing the number of colonies. This conceptualization and methodology of this research was done by [PERSON], [PERSON] and [PERSON] confirms the validation, revised the article and writing. The final proof read was done by [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.