Designing turbocompressors is a complex and challenging task, as it involves balancing conflicting objectives such as efficiency, stability, and robustness against manufacturing deviations. This paper proposes an integrated design methodology for turbocompressors supported on gas bearings, which utilizes surrogate models and ensemble learning with artificial neural networks. The proposed approach addresses the limitations of nominal and separate optimizations by integrating all relevant design aspects into a single optimization problem. A multi-objective optimization is carried out, considering four objectives and over twenty constraints, including robustness against manufacturing deviations of the radial and axial bearings in terms of stability, load capacity, and efficiency, as well as robustness against performance metric gradients. The proposed methodology maximizes the compressor’s range in speeds and mass flow, while also maximizing the signal-to-noise ratio of the isentropic efficiency over the compressor map. Additionally, the approach maximizes system efficiency, taking into account component losses and isentropic efficiency of the compressor. To enable rapid and automated integrated design, the methodology reduces the compressor representation to a fully cylindrical representation. The study finds that the proposed methodology has the potential to significantly enhance the overall performance of turbocompressors in terms of efficiency, stability, and robustness. The methodology eliminates the need for sequential and iterative design steps, providing an optimal starting point for higher representation of the system with CFD and finite elements study. Furthermore, the proposed methodology has broad applications, including the optimization of other complex and interdependent systems in various fields. This study highlights the crucial role of a comprehensive and integrated approach to turbocompressor design and provides a valuable framework for future research in this area.