Within the past decades, numerous optimization methods have been developed to maximize the aerodynamic characteristics of various turbomachinery components. Lately, more attention is being paid to methods able to enhance their aeroacoustic performance due to the increasing demand for quiet propulsion systems for the aircraft industry. In the framework of the present work, a multi-disciplinary, multi-objective, gradient-based shape optimization is performed to minimize the shockassociated tonal noise of NASA Rotor37, while maximizing its isentropic efficiency. The rotor's flow field is obtained through three-dimensional Reynolds averaged Navier Stokes simulations with the Spalart-Allmaras turbulence model, while the corresponding sound power level is obtained using a simple noise calculation tool based on the flow perturbations at the rotor's inlet. An adjoint approach is used for computing the gradients of the objective functions with respect to the 41 design variables, which parametrize the geometry of the blade. A Sequential Quadratic Programming optimization algorithm is used to identify several trade-off points of the noise-efficiency Pareto front. Constraints are added to the optimization problem to keep the mass flow within a given range. Results show a substantial improvement in the overall performance of the rotor, with 2.75dB of sound power level reduction and a 1.4% increase in isentropic efficiency. Compared to a similar study that was conducted with a gradient-free algorithm, these results are obtained at a limited computational effort thanks to the adjoint-based methodology. The flow fields of the baseline and optimized designs are analyzed to understand the mechanisms behind the performance improvements.