This paper describes the computational fluid dynamics (CFD) approach coupled with an automated grid generation technique utilized for the numerical optimization of a modern centrifugal compressor with an inducer vaned shroud for increased operability margin. The grid generation process was automated to permit rapid optimization of the impeller and vaned shroud geometry. A three-dimensional, viscous, steady flow, mixing-plane approach was utilized to numerically analyze the impeller and vaned shroud in a coupled fashion to capture the interaction effects. The numerical technique verifies the ability of the vane shroud to extend compressor surge margin at the part-speed operating condition, while maintaining acceptable high-speed performance. CFD analyses confirm that the aerodynamics of the vaned shroud match expectation, and are consistent with the mass-averaged compressor speedline characteristics generated from the CFD results.