The design of a turbocharger compressor must meet aerodynamic performance requirements, operate within specified stress and vibration limits, and respond quickly to changes in operating conditions. Design optimization must therefore include static, thermal and modal analysis (including weight and polar moment of inertia calculations) along with aerodynamic analysis (CFD). In some cases, a design optimized for aerodynamic performance only can be optimized separately to meet structural goals, using impeller backface geometry, bore radius and fillet radius inputs, which generally do not impact aerodynamic performance. If, however, impeller geometry inputs such as R1t-R1h, R2, B2 influence both aerodynamic and structural analysis, a coupled optimization is required, and each design must have both CFD and FEA analyses. In this study, a radial compressor with a vaneless diffuser at a single operating point is considered. The aerodynamic parameters for the impeller (BETA1H, BETA1S, BETA2S, main blade count, B2, R2, R1t) and diffuser (Pinch, R3/R2, Rex/R2) comprise in total 10 independent aerodynamic inputs. The aerodynamic objectives are to meet the operating point pressure ratio target and to maximize efficiency. The structural parameters for the backface (shoulder position, shoulder radius, web thickness at outer diameter (OD), OD angle, shoulder angle), bore radius and fillet radius comprise in total 7 independent structural inputs. The main structural objectives are to minimize the polar moment of inertia, and satisfy constraints on allowable maximum stress, deflection and the frequencies of blade vibration (flapping) modes. Successful multi-disciplinary optimization requires both CFD and FEA analysis to complete successfully for each trial design. Initial test runs of the optimization resulted in many geometries for which a valid CFD grid or FEA grid could not be generated. The high percentage of failed runs in the initial DOE impeded the construction of a viable surrogate model. A comprehensive investigation of all failure modes led to pre-screening of both CFD and FEA geometry generation, using input constraints. The failure rate was greatly reduced as a result, leading to an improved search. Prior to the geometry screening, the optimizer found a large Pareto frontier between the efficiency and polar moment of inertia objectives. Following the screening, the efficiency and IP objectives became more cooperative. The optimization was carried out using Concepts NREC tools AxCent (R) and TurboOPT IIT, NUMECA Fine/Turbo, and ESTECO modeFRONTIER (R).