| Different from optimization study of the single performance of turbocharger impeller, this paper takes the compressor isentropic efficiency, the impeller maximum stress, and the impeller maximum deformation as the optimization objective. Based on ANSYS Workbench, the turbocharger compressor flow thermal solid multi physics coupling simulation model was established. Using the orthogonal matrix method and the 2k method, the key design parameters of the compressor were studied. The radial basis function and non dominated sorting genetic algorithm II were applied to solve the global optimization problem. Finally, the optimal scheme of impeller structure design were obtained. The results show that the most significant decrease is the impeller maximum deformation of 28.09%, the impeller maximum stress is decreased by 16.34%, and the compressor isentropic efficiency is increased by 2.83%.