Turbomachines are prevalent within the aerospace industry and vital for both power production and flight systems. To achieve better performance and higher efficiency, a numerical optimization technique is used to optimize designs. Previous work has primarily focused on performing steady-state optimization of turboma- chinery using Reynolds Averaged Navier Stokes simulations. In efforts for further performance increases, the next step of turbomachinery optimization is to incorporate time-accurate solvers. These time-accurate solvers are computationally more expensive than steady solvers, which hinders usage in optimization. The harmonic balance method was developed to reduce computational requirements compared to a time-accurate solver while maintaining unsteady flow characteristics in the simulation results. Optimization using the harmonic balance method has shown better performance in 2D cases, but there has not been work reporting on a 3D case. Fur- ther analysis of how optimization changes flow irreversibility in a design has not been shown between harmonic balance and mixing plane based optimization. This work’s novel contribution is to perform a comparative study of harmonic balance and mixing plane based optimization of a 3D multistage turbine and perform a loss quantification comparison of the optimized designs. In this work, the flow around a 3D 1.5 stage axial turbine in the subsonic to transonic flow regime was simulated and optimized using the mixing plane and harmonic balance methods. The turbine blade shapes are parameterized using a CAD-based NURBS parameterization and optimized using a gradient-based adjoint algorithm. Flow features, entropy trends, and computational costs between harmonic balance and mixing plane simulation and optimization were compared. This study shows that most entropy creation differences between harmonic balance and mixing plane methods occur in the rotating domain. A turbine design optimized using the harmonic balance method has better fluid-dynamic performance than a design optimized using the mixing plane method. Turbine designs combining blades from both harmonic balance and mixing plane based optimization show better performance than a design using a single flow simulation method for optimization. Results also indicate that a grid converged mesh may not be necessary for entropy generation minimization of turbomachinery designs for transonic flow.