This paper proposes geometry parameterization of a complete single centrifugal compressor stage and applies CFDdriven optimization using artificial neural networks and a Kriging surrogate model. Kinematic velocity triangle analysis is used to arrive at an initial design, which is then improved by using automated optimization algorithms and fundamental flow physics using CFD simulation. By allowing the design to evolve, guided by CFD, new and untested optimum designs are possible. This work deals specifically with design and optimization of the flow path. Design for structural aspects such as vibration, rotor dynamics and other mechanical aspects is outside the scope of this work. The CAD parameterization enables robust specification of the flow path geometry while maintaining a sufficiently small set of parameters for practical design space exploration. The parameterization includes an impeller with optional splitter blades, a vaneless diffuser and volute. Steady-state, RANS-based CFD is employed in the analysis of both the rotationally-periodic components and the volute geometry. Direct optimization and response surface optimization are demonstrated for rotationally periodic components to maximize design-point efficiency of the flow path using a multi-objective genetic algorithm (MOGA). Improvements in total-total isentropic efficiency of between 4 and 5 percent are achieved. Optimization of the flow path of the volute is likewise demonstrated. In the case of the volute, a Kriging responsesurface model is used and a 1.4 percentage point improvement is shown. Further research in the utilization various implementations of Artificial Intelligence (AI) machine learning techniques in conjunction with parameterized turbomachinery flow paths to enable enhanced designs to be generated effectively is proposed.