The optimization of supercritical airfoils is crucial for improving the performance of commercial transonic aircrafts. The formation of shock waves can cause significant aerodynamic drag and limit the lift capabilities of the airfoil, which can lead to decreased fuel efficiency and reduced range. Therefore, optimizing the shape of supercritical airfoils to delay the onset of shock waves is essential to improve the aerodynamic performance of aircraft. Supercritical airfoils have a unique design that includes a flattened upper surface and a curved lower surface with  double camber. This design creates a pressure recovery that reduces the effects of the shock wave, thereby increasing the critical Mach number and allowing the airfoil to operate more efficiently at higher speeds. However, the design of supercritical airfoils is complex, and their performance characteristics depend on several factors, including the shape, size, and location of the camber inflexion point. This research paper aims to study the aerodynamic behavior of supercritical airfoil shapes in an optimization process using a high-fidelity multiblock aerodynamic solver coupled with a hyperbolic structured mesh generator designed to accurately capture the shock wave formation, which is critical for understanding the performance of supercritical airfoils. The class-shape transformation parametrization method was chosen for the airfoil shape representation because of the low number of parameters required for a complex design space that allows a higher probability of finding the optimal solution. This study highlights the importance of selecting an appropriate optimization algorithm for supercritical airfoil design. The use of advanced optimization techniques such as evolutionary algorithms coupled with gradient-based algorithms can significantly improve the optimization process of supercritical airfoils and reduce the computational time required. In conclusion, this research paper provides useful insights into the optimization process of supercritical airfoils.