This article delves into the optimization process of centrifugal compressors, to improve their performance and efficiency in industrial applications. The study focuses on the use of the One-Dimensional Code for the Calculation of Centrifugal Compressors (ODC4) as a valuable tool for evaluating various geometries and selecting optimal alternatives. The reliability of ODC4 is validated by comparisons with experimental data and computational fluid dynamics (CFD) simulations. The optimization process aims to maximize the isentropic efficiency and minimize the Mach number in the rotor discharge, which involves two phases: evaluation and refinement. The ratio of radii (r1/r2) significantly influences the isentropic efficiency, with a ratio of 0.6 yielding the highest efficiency and 0.5 resulting in the lowest Mach numbers. Inconsistent designs occur when specific radius ratios are combined with high relative flow angles. In addition, higher Mach numbers generally correlate with higher isentropic efficiency. These results provide valuable information on the relationship between control variables, such as radius ratio and flow angles, and performance indicators, aiding in the optimization of centrifugal compressors.