Boundary Layer Ingesting (BLI) refers to the ingesting of the aircraft wake by the propulsors and has been associated with reduced fuel burn. Although, this can potentially be offset by the reduced efficiency and stability experienced by the propulsor in the presence of distorted inflow. Therefore, engine intakes must be optimized in order to mitigate the effects of BLI on the propulsion system. In this work, the shape optimization of a BLI intake is investigated using a free form deformation technique in combination with a multi-objective genetic algorithm, in order to minimize pressure losses and distortion at the engine inlet. The general trend of the optimal designs shows that to reduce the distortion the optimizer accelerates the flow to increase the dynamic pressure at the engine inlet. In contrast, the pressure losses were reduced by decreasing the velocity as well as shifting the region of maximum velocity to the outlet.