## 1 Introduction
Optimization of an airfoil plays another important role where aerodynamic performance is optimized to obtain benefits in drag minimization or high endurance if the L/D ratio is maximized. The shape of the airfoil changes by optimization process to achieve the objective function, but it is too compact to use all of the design variable sets during the optimization process. Therefore, the variables used for design should be reduced from almost infinite to a limited set, and a parametric method should be used to illustrate a new airfoil or initial airfoil. [PERSON] [19] has surveyed parameterization techniques and confirmed that the method has a great impact on the optimization process in aerodynamic shape design. [PERSON] and [PERSON] [20] believe that polynomial methods based on parameterization will strongly influence the design variables generated through an optimization process. Some physically tried and tested methods allowed us to use the parameters of the airfoil to define its shapes, such as angle of the trailing edge, wing thickness, and radius of the leading-edge. [PERSON] and [PERSON] [21; 22; 23] introduced a new parametrization technique which is also called Kulfan parameters, or CST method. This CST parameterization is a powerful method because of its simplicity and robustness. [PERSON] [24] presented a new methodology for parameterization called PARSEC. A total of 11 parameters are used to define the shape of the airfoil. It has designed a variety of aerodynamic shapes with smooth geometric shapes, with fewer parameters and equations [25]. With a lower order polynomial, preliminary design and optimization of the airfoil can be easy since only a few numbers of parameters are required to control the shape of an airfoil. Since the CST equation is an addition operation of the Bezier curve with a class function term so CST is considered to be very similar to the Bezier curve. Different aerodynamic shapes are derived from the class function which is classified as basic functions. These aerodynamic shapes are biconvex, Sears-Haack body, round nose, and pointed aft end airfoil which is similar to NACA airfoil, oval airfoil, wedge airfoil, and some other different airfoils. These types of airfoils can be converted into axisymmetric bodies, can also be modified by shape function to obtain a new airfoil shape. The shape function in the same class is indicated by the class function has its geometric shape. Compared with the Bezier curve, the advantage of CST is that it can fit the curve to specific shapes with a smaller coefficient. Related to the previous literature, in this study the CST parametrization in combination with a genetic algorithm has been employed to bring forward a unified solution for aerodynamic shape optimization. The prime motive is carrying out the optimized shapes in a simplified manner by considering airfoil shapes as under-investigated profiles. The subsonic NREL S-821 airfoil and transonic RAE-2822 airfoil are selected for this purpose, which is the most commonly used for aerospace and wind energy applications. The panel method technique is used to calculate the drag coefficient of the airfoil. The resulting lift to drag ratio of the optimized and baseline airfoil are correlated with the NREL experimental data to verify the proposed optimization method. Besides, numerical validation and CFD analysis were implemented for the S-821 airfoil to check the applicability of the airfoil constraint inside the structured mesh in the numerical simulation and compared it with the experimental results. Findings are described in detail and shown with indicators like pressure coefficient, convergence graph, and grid independence study. Finally, the coefficient of drag (Cd), lift coefficient (Cl) and lift to drag (L/D) ratio for baseline and optimized airfoil at 3\({}^{\circ}\) angle of attack (AOA) is discussed and reported in the paper. The shape optimization of the baseline airfoil used in the paper has a great impact on the energy harvesting system of the wind turbine blades.