## 1 Introduction
The finding shows that the proposed method could find the optimal solutions for all cutting strategies. [PERSON] and [PERSON] [67] used GWO to estimate the permanent magnet's unknown parameters for the DC coreless motor. A comparative study with GA was conducted, and the result showed that the GWO can provide outstanding results in estimating the average prediction error of the unknown motor parameters. [PERSON], [PERSON] [68] used GWO to optimize the fractional order controller's parameter and the integer-order controller. The result showed that the controller'sparameters tuned by GWO are much better since they can minimize the setting time and maintains the desired phases of classical problems. [PERSON], [PERSON] [69] examined the optimal solution for surface wave dispersion in an inversion scheme. The result showed that the GWO could balance the exploitation and exploration phase for local optima with fast convergence time. A comparative study with GA and hybrid PSO-GSA was conducted. The finding showed that the performance of the GWO was superior to others. [PERSON] proposed an Improved GWO (IGWO) for optimum trajectories planning of multi-unmanned aerial vehicles (UAV) for target tracking in an urban environment. MPC was employed in the IGWO for searching ability, stability, and computation efficiency. The IGWO solved the target tracking problem at the end. In summary, this section has provided an extensive review of the controller and especially the GWO algorithm's applications. From this literature, it can be noted that most of the authors concluded that the GWO algorithm was capable of solving the problem given in the respective application effectively. Apart from that, it was also found that the GWO can provide better performance compared to other algorithms. Nevertheless, based on these reviews, the application of the GWO in the area of quadrotor stabilization and control was compared to the other applications. Therefore, for this particular reason, we propose a hybrid proportional double derivative and linear quadratic regulator controller (PD2-LQR) optimized by an improved Grey Wolf Optimization (IGWO) algorithm for quadrotor stabilization and control application. This study's main objective is to realize the contribution of the nature-inspired optimization algorithm, specifically GWO, to enhance the controller's performance by optimally obtaining the controller's parameters' best solution. From this point of view, a comparative study with the conventional controller, namely PD, PID, LQR, P-LQR, PD-LQR, PD2-LQR controller, and the original GWO based PD2-LQR controller was undertaken. Four PD2-LQR controllers were designed for altitude (z) and attitude (roll, pitch, and yaw) motion. The conventional controllers' parameters were manually optimized using the trial and error method, while the parameters of the PD2-LQR controller were optimized by using the traditional GWO and IGWO algorithms. The rest of this paper is arranged as follows; in Section 2, the quadrotor's mathematical model based on the Newton-Euler approach and its associated parameters are presented. The development of the control structure is presented in Section 3, and in Section 4, the GWO and IGWO algorithms are described. In Section 5, the simulation result is discussed. Lastly, a conclusion based on the proposed controller presented.