Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship hull, thus decreasing resistance. To attain efficient hydrofoils, the geometries can be obtained from an automated optimization process, based on simulations. However, hydrofoil high-fidelity simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil. Simulation-based optimization can therefore be very expensive. Automated surrogate models, trained by a limited number of simulations, can reduce the required computational demand for the optimization by performing simulations where these are more informative. Furthermore, if an efficient low-fidelity hydrofoil performance prediction tool (with a low computational cost) is available, using surrogates in a multi-fidelity framework can provide a further reduction in required simulations, by combining the accuracy of a few high-fidelity with an exploration process based on a larger number of low-fidelity computations. In this study, we propose a hydrofoil optimization procedure based on two simulation codes, a dedicated hydrofoil potential flow solver for low-fidelity simulations and a RANS solver for both medium-and high-fidelity simulations. The RANS solver uses adaptive grid refinement to attain high accuracy with a limited computational budget. Two different multi-fidelity frameworks are compared for a parameterized geometric model of a realistic hydrofoil: only RANS based and potential-RANS based. The effect of different combinations of fidelity levels on the efficiency of the optimization and the performance of the kitefoil-type hydrofoil is investigated and discussed.