## 4 Experiments and Analysis
### Real-World Application of Airfoil Design  
The recent research on airfoil aerodynamic optimization has focused on various methods and technologies to enhance the performance of airfoil designs in different applications. Figure 11: \(D=10\), \(D=20\) [PERSON]’s function comparison chart. Figure 10: \(D=10\), \(D=20\) [PERSON]’s function comparison chart. Researchers have been implementing genetic algorithms to optimize airfoil geometries, focusing on improving aerodynamic efficiency and lift-to-drag ratios. One study detailed the use of a genetic algorithm model to optimize airfoil geometry specifically for low Reynolds number conditions [37]. Artificial neural networks (ANNs): Feed-forward artificial neural networks have been employed as surrogate models to predict the lift and drag coefficients of NACA airfoils. These models help in reducing computational time while maintaining optimization accuracy [38]. Aerodynamic shape optimization: Advances in aerodynamic shape optimization include using physics-informed methods and machine learning to improve the performance of airfoils under various flow conditions. For instance, one study proposed a modified metric-based proper orthogonal decomposition approach for enhancing airfoil designs [39]. In this study, an aerodynamic design optimization problem pertaining to airfoil geometries is employed to critically assess the efficacy of ASAPSO in practical applications. Recognizing that the evaluation of prospective airfoil configurations demands rigorous computational simulations rooted in fluid dynamics, the XFOIL platform is harnessed as an instrumental tool for the analysis and design of subsonic, isolated, single-segment airfoils. The airfoil aerodynamic optimization problem, conceived by Professor [PERSON] of the Massachusetts Institute of Technology, emerges as a quintessential application for the SAEA. This is attributed to the intricate computational fluid dynamics models imperative for prognosticating the performance metrics of potential airfoil configurations. Intrinsically, the optimization challenge revolves around the enhancement of the airfoil's geometry to maximize the lift coefficient-to-drag coefficient ratio. Concurrently, it is paramount to curtail the number of evaluations. Delving into the technical nuances, the airfoil's geometric intricacies are encapsulated by the Hicks-Henne function. Introduced by [PERSON] in the concluding years of the 1970s, this function leverages parametric techniques to modulate airfoil morphologies by characterizing the extent of variances in curvature and thickness. Subsequent to this, the derived variations are meticulously superposed onto the foundal curvature and thickness dimensions of the archetypal airfoil. Intriguingly, the Hicks-Henne typology [32] amalgamates a foundational airfoil with a set of ten decision variables. The NACA0012 airfoil is a commonly used symmetrical airfoil, widely used in aviation fields such as low-speed stunt aircraft main wings and high-performance helicopter rotors. Due to its specific geometric shape and aerodynamic characteristics, precise computational simulations of it require the consideration of multiple factors, including fluid dynamics, pressure distribution on the airfoil surface, and lift and drag under different flight conditions. These calculations not only require accuracy, but also need to consider the effective utilization of computing resources to ensure the efficiency and accuracy of the calculations. Thus, the optimization design of NACA0012 airfoil is quietly difficult to solve.