# A Cluster-Based Hierarchical-Approach for the Path Planning of Swarm
###### Abstract  
This paper addresses the path planning and control of multiple colonies/clusters that have unmanned aerial vehicles (UAV) which make a network in a hazardous environment. To solve the aforementioned issue, we design a new and novel hybrid algorithm. As seen in the mission requirement, to combine the Maximum-Minimum ant colony optimization (ACO) with Vicsek based multi-agent system (MAS) to make an Artificially Intelligent (AI) scheme. In order to control and manage the different colonies, UAVs make a form of a network. The designed method overcomes the deficiencies of existing algorithms related to controlling and synchronizing the information globally. Furthermore, our designed architecture bounds, lemmatizes the pheromone, and finds the best ants which then make the most optimized path. The key contribution of this study is to merge two unique algorithms into a hybrid algorithm that has superior performance than both algorithms operating separately. Another contribution of the designed method is the ability to increase the number of individual agents inside the colony or the number of colonies with a good convergence rate. Lastly, we also compared the simulation results with the non-dominated sorting genetic algorithm II (NSGA-II) in order to prove the designed algorithm has a better convergence rate. bio-inspired algorithm; computer simulations; Max-Min ant colony optimization (MMACO); multi-agent systems (MAS) +
Footnote †: journal: Applied Sciences  
However, in some instances, ACO has a slow convergence rate and falls into the local optimum. To avoid the aforementioned issues, researchers introduced MMACO, a strategy that limits the pheromone on each trail to maximize the chances of getting an optimal result. MMACO differs from ACO in many significant aspects. For instance, MMACO only allows the best ants to add pheromone to the pheromone trail. Multi-Agent System (MAS) contains multiple agents, and every agent determines its state using the state of its neighbor. MAS has numerous applications including in the fields of autonomous vehicles [17] and bio-inspired systems [18]. In most cases of MAS, an outside entity has to drive the agents toward the target. The usual strategy is to designate a few agents as leaders and let the rest of the agents follow the leader. The leader agents function as external entities that can affect the follower states. We can efficiently control a big network of UAVs by selecting fewer leader agents than the followers, which demonstrates the scalability and efficiency of the leader-follower method [19; 20]. [PERSON] et al. [21] introduced a comparable, simpler multi-agent model later known as the Vicsek model. It consists of discrete-time \"N\" autonomous agents having constant absolute velocity. These agents follow the direction of the motion of their neighbors also conjuction with random noises. [PERSON] et al. [21] discovered some exciting results through simulations: all agents will follow the same direction when their density is large and the smaller noise. This phenomenon is called synchronization. Researchers in the field of control theory have tried to rigorously analyze the concept of synchronization. [PERSON] et al. [22] examined the heading angles linearly and presented a series of pointless neighbor grids using the locations of the specific agents. It demonstrated that to ensure the synchronization of the system, the graphs have to be mutually linked in a specific identical manner. Afterward, another study [23] used the headings discretely and examined if the same linear system will synchronize. It demonstrated that we could also achieve synchronization if we connect the union of neighbor graphs infinite times. Contributions: The main offerings of this study are:  
* A multi-colonies-based hierarchical structure is designed which divides the UAVs into three distinct and non-overlapping colonies. In each colony, UAVs form hierarchies with one UAV selected as the colony leader. * This study uses MMACO for the formation of route of a network of UAVs.