Position of the optimization variable.

To enhance the aerodynamic performance of centrifugal impellers, this study presents an advanced optimization design methodology. This methodology addresses the challenges associated with numerous design variables, inflexible configurations, and low optimization efficiency. We propose two distinct spline function parameterization techniques: a global mapping model for Bezier surfaces and a local mapping model for Free-Form Deformation (FFD) control bodies. We investigate the impact of these parameterization methods on blade geometry configuration and aerodynamic performance. By integrating these two parameterization approaches with multi-objective evolutionary algorithms and Computational Fluid Dynamics (CFD) techniques, we enable global and local optimization of centrifugal compressor blades. The optimization results demonstrate a 1.77% enhancement in isentropic efficiency under rated operating conditions, a 7.8% increase in surge margin, a 1.6% improvement in isentropic efficiency under normal operating conditions, and an 11.8% enhancement in surge margin. Through two optimization stages, the optimization space for blade geometry is thoroughly explored, enhancing solution quality and contributing to the advancement of impeller mechanical optimization design theory.