<p>  </p> <p>In this thesis, two optimizations of squealer tip geometries are completed for first stage turbine blades for use in a supercritical carbon dioxide turbine. First, an optimization is performed on a baseline trapezoidal turbine blade and a set of solution geometries is chosen from along the Pareto front. Next, a second optimization is completed on an advanced blade design and the geometries are grouped by performance characteristics and geometric features. The success of similar geometries across these two optimizations is also analyzed and demonstrates consistency of performance increases from tip geometries over the baseline geometry. An analysis of a flat tip geometry in a stationary condition is also performed to begin validation of annular cascades as a method for testing squealer tip geometries. </p>