## 1 Introduction
Flying Fox Optimization (FFO) is a recently developed MH algorithm that utilizes the techniques used by flying foxes to survive in high temperatures [14]. The Puma Optimizer (PO) is inspired from the natural life of pumas. In PO, powerful mechanisms have been included for exploration and exploitation phases [15]. The classification of the MH algorithms is shown in Figure 1.  
The control of discrete event systems was originally developed as a branch of language theory [16]. Later, various theories such as FSM [17], automata [18], and Petri nets [19] were developed in this field. The foundation of discrete event system control theory is based on the parallel synchronization of Mealy machines, where two Mealy machines can be controlled by a third Mealy machine, namely the controller, to achieve desired system behaviors. However, the theory, known as discrete control synthesis, generally focuses on how this controller can be synthesized according to system behaviors and desired objectives. Pioneering work in this area [20; 21] was carried out on finite systems. Subsequently, refs. [22; 23] developed DCS for infinite systems and addressed the state explosion problem using a symbolic approach. Regarding optimization objectives, Ref. [24] is based on minimizing a cost function. The computational complexity of calculating an SDCS controller is exponential; however, our experimental evaluations indicate that the computation time remains quite reasonable, even with a very high number of states. Additionally, the computation is performed only once to generate the controller. Once the controller is obtained, it operates dynamically and in real-time within the integrated system. One of the primary challenges in real-time implementations is the necessity to model all system behaviors to ensure optimal performance. However, it is worth noting that our approach does not require additional hardware resources. The controller can be embedded within an internal microcontroller, eliminating the need for external hardware requirements. The motivation of this paper is proposing the optimal solutions in both the controller design and path planning sides for the flight of the quadcopters. In the controller design part of this paper, the full control of the quadcopter UAV is considered as a discrete controller synthesis problem. SDCS as an optimal controller is a new approach that aims to minimize a defined objective function to provide a desired system output. The control theory of discrete event systems is framed within a linguistic framework, primarily aimed at synthesizing controllers tailored to specific system dynamics and control objectives. Symbolic modeling entails the representation of systems using labeled input/output automata. Controllability in this context hinges on the premise that achieving desired outputs relies on managing transitions between symbolic states in response to inputs, diverging from event-driven mechanisms. Consequently, employing symbolic modeling and control strategies proves more efficacious in addressing practical challenges encountered in real-world scenarios, particularly in the control of systems governed by manipulable input signals, compared to conventional control algorithms. The originality of this paper is that it is the first in the literature which compare SDCS and FOPID controllers in the control of the quadcopter. In the path planning part of this paper, the optimal solution of the TSP for a single quadcopter and min-max TSP with multiple depots for multi quadcopters are obtained. This is the second motivation of this study, which is related to a research gap in collaborative UAVs. The literature review conducted here provides a comprehensive analysis of the increasing complexity observed in unmanned systems alongside the concurrent development of simulation environments aimed at cost mitigation during installation. The unique challenges encountered by autonomous and collaborative UAVs are underscored as pivotal in this context.