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Performances of a centrifugal turbocharger compressor are investigated and validated in this paper. Based on the validation results, numerical optimizations are performed using ANN and CFD methods. Different impeller geometry with free parameters controlling stacking laws, end-wall, blade sectional camber curves and corresponding performances are used as input layer of ANN in the optimization, while adiabatic total-to-total efficiency and total pressure ratio are used as output layer of the optimization cycle. With this method, the performances of the compressor investigated in this paper are improved notably.