Rapid aerodynamic design and optimization is essential for the development of future turbomachinery. The objective of this work is to demonstrate a methodology from 1D mean-line-design to a full 3D aerodynamic optimization of the turbine stage using a parameterization strategy that requires few parameters. The methodology is tested by designing a highly loaded and efficient turbine for the Purdue Experimental Turbine Aerothermal Laboratory. This manuscript describes the entire design process including the 2D/3D parameterization strategy in detail. The objective of the design is to maximize the entropy definition of efficiency while simultaneously maximizing the stage loading. Optimal design trends are highlighted for both the stator and rotor for several turbine characteristics in terms of pitch-to-chord ratio as well as the blades metal and stagger angles. Additionally, a correction term is proposed for the Horlock efficiency equation to maximize the accuracy based on the measured blade kinetic losses. Finally, the design and performance of optimal profiles along the Pareto front are summarized, featuring the highest aerodynamic performance and stage loading.Researchers have used Bezier curves [3] or a combination of splines and b-splines to design airfoil geometries. B-splines have been proven to be a successful tool in reducing turbomachinery loss when coupled to an optimizer. However, they have limitations. Shelton et al. [4] stated that it was difficult to induce large changes to the stagger, trailing edge wedge and leading edge angle using b-splines. They instead used b-splines as a tool to fine-tune the design of the blade. Ghaly and Mengistu [5] used Non-Uniform Rational B-Splines (NURBS) to optimize an existing turbine airfoil design in 2D-NURBS are similar to B-splines except their control points each have a weight. Their parameterization showed that NURBS required fewer points to parameterize a compressor airfoil [6], as opposed to a turbine blade [7] due to the increased curvature of the suction side. Shelton et al.[3] optimized a turbine blade under transonic conditions incorporating a stacking and sweep law. They similarly observed that it was difficult to make large changes to the stagger, wedge angle, and suction side surface angles in their parameterization using b-splines. Hasenjäger et al.[8] adopted b-splines to optimize a low aspect ratio stator blade in 3D and encountered difficulties as well, attempting to limit the number of control points needed to represent the blade surface using spline-like strategies.Bezier curves have been applied in a wide variety of turbomachinery applications because they offer designers the prospect of using less parameters while controlling the curvature by removing the need to parameterize the knot vector [9,10]. Goel et al. [11] used this type of curves to define 2D turbine airfoils using 10 and 8 parameters for the suction and pressure side respectively. Pierret and Van den Braembussche [12] employed a series of Bezier curves to model the suction and pressu...