## 1 Introduction  
The increase in global energy consumption and the decrease in fossil fuels forces governments to spend more on alternative energy resources. Wind energy is alternative renewable energy that is clean, economical, and available in abundant quantity [1, 2]. The fast-growing trend of wind energy worldwide has increased the demand for efficient and optimized performance of airfoil, which further paved the way for energy harvesting systems. To harvest maximum energy from the wind, a properly designed airfoil is required for wind turbine blades to maximize lift and minimize drag. Therefore overall researches need to be improved to meet essential needs for the aerodynamic performance of wind turbines. Airfoil design is important to increase the aerodynamic performance of a wind turbine rotor. The selection of an optimum aerodynamic design that effectively fits a specified range of flow conditions is very important. Nowadays, the optimization of aerodynamic shape has become crucial with the rapid development of aerospace and mechanical engineering. As [PERSON] et al. [3] explained, the idea to control devices and aerodynamic shapes that locally change the aerodynamic performance of the airfoil on the wind turbine blade. The parametric method in aerodynamic shape plays a crucial role in the optimized process of airfoil optimization. A good parameterization method with fewer design parameters can handle larger shape changes of the wing in the design space [4]. Due to the industrial revolution and new computational fluid dynamics and technological changes, some numerical tools for optimizing airfoils have been developedinstead of using plate theory to design airfoils [5]. Two main approaches for the design of aerodynamic shapes are (a) Inverse design (ID) and (b) Direct Numerical Optimization (DNO) [6; 7]. The first method solves the geometry and searches for different airfoils that can meet the demand of fluid dynamic structure and as a result, it produces pressure distribution. The second method (DNO) combines with geometric definition and analysis is done for aerodynamic shape in an iterative process to generate the best concerning different goals and constraints. The above methods indicate that it is necessary to modify the present airfoil design or to achieve a new and better design through partial airfoil modification by applying even different parameterization methods. These local airfoil shape modifications can be achieved through analytical function by smooth perturbations of original airfoil coordinates, for instance, Bernstein polynomials [8]. ASO is a combination of parameterization and optimization process as well as design analysis of aerodynamic shape. The parameterization method has a great impact on the optimization output which can accommodate a large number of potential airfoils with smaller design variables in design space [9]. In a recent study, [PERSON] et al. developed and employed an inverse design method and linked it with Ball Spine Algorithm (BSA), which showed promising results to solve complex geometries for various flow regimes [10; 11]. Different parameterization techniques have been developed to parameterize the aerodynamic shape [12]. A variety of parametric methods which are implemented to ASO are the PARSEC method, B-spline, Bezier curves which are used to fit aerodynamic shapes by interpolation methods [13; 14]. [PERSON]'s [15] function was explained earlier in their work about airfoil families which can be represented by deriving analytical functions. The result of these above methods cannot be used to design new concepts but the methods are robust enough to illustrate different airfoils. Due to the larger number of parameters used in the airfoil, the search for optimized design results is more feasible [15; 16; 17; 18]. However, due to an increase in design variable which leads to increase inevitably, the search problem of optimization algorithms are not beneficial to search-optimized design results.