Nowadays, PID controls add techniques such as neural networks and evolutionary algorithms, resulting in high accuracy and dynamic performance for different engineering control problems. Systems are becoming adaptive to external disturbances. For example, in [7], an adaptive PID tuning method is reported, which is pre-trained by a genetic algorithm to tune the weights of a neural network and auto-tunes online the proportional, integral, and derivative units of a PID. The design and implementation of control laws in QUAVs consider multiple variants that are tuned for each control in a constrained-based optimization manner, similar to the path planning problem [8; 9]. Those limitations motivate solutions of stochastic nature. There are different stochastic algorithms, the most popular are metaheuristics, both evolutive and population-based, with high effectiveness and easy implementation. Evolutionary metaheuristic algorithms are based on the laws of biological evolution, which do not share information with another generation. However, the best-qualified individuals composing the new group and better quality individuals will remain up to the end. Some of the most popular are genetic algorithm (GA) [10; 11; 12] and differential evolution (DE) [13] with many variants, refinements, and hybridization. Population-based metaheuristics are motivated by collaboration capabilities, social interaction and sharing knowledge, present in many groups in nature. This type of metaheuristic is one of the most popular techniques to solve multiobjective optimization problems, thanks to their ability to compute multiple solutions in a single repetition [14]. The problem of tuning a PD or PID for a QUAV dynamic system results in a complex underactuated system, highly coupled in its variables, and many parameters to adjust, nonlinear, where it is not easy to apply conventional control techniques. Using these techniques, the dynamic model must meet convexity, differentiability, continuity, and linearity properties, leading to an excessive simplification of the model to obtain a global optimum, but failing to represent all the relevant features of the real system [15]. By using metaheuristic algorithms to solve this type of problem, it is impossible to show that the global optimum is reached; for this reason, a series of repetitions of the runs are carried out to verify the robustness and accuracy of the solutions obtained. Nevertheless, it generates satisfactory solutions in a reasonable time [16]. Previous studies have addressed the problem of tuning controllers applied to UAVs. In [17], a comparison between proportional (P), PD and PID controllers relating to time to tune and stability is done, applying a particle swarm optimization algorithm (PSO) for choosing the parameters to control attitude and altitude of QUAV (4 of 6 possible dynamics). Similarly, the authors in [18] have proposed the artificial bee colony (ABC) algorithm, PSO and GA to optimize PID parameters and add a comparison with Ziegler-Nichols method applied to QUAV attitude dynamics. In the same way, the optimization of a PID controller using GA, Crow Search Algorithm (CSA) and PSO only for orientation and altitude was performed in [19]. In this paper, we report the development of a dynamic model for a QUAV using the Newton-Euler formulation taking into account all the six dynamics for a QUAV. We compare eight optimization algorithms for PD and four for the PID controller. All algorithms were applied to the dynamic model. Initially, the parameters were obtained using different population-based metaheuristic algorithms, including PSO, Gray Wolf Optimization (GWO), Hunger Games Search (HGS), extended and improved SHADE (LSHADE, LSPACMA), Marine Predators Algorithm (MPA), Slime Mould Algorithm (SMA), and Whale Optimization Algorithm (WOA) [20; 21; 22; 23; 24; 25; 26; 27; 28]. Usually, a set of benchmark functions is used to demonstrate the performance of optimization algorithms by evaluating the accuracy, precision, and robustness.