This work describes my activity carried out within the Von Karman Institute in the Department of Turbomachinery and Propulsion on the Metamodel-Assisted Multidisciplinary Optimization applied to the Ported Shroud Centrifugal Compressor inside a Turbocharger in which a Cost Model will be added to the optimizer. The project is born from a collaboration between VKI and General Motors and we want to obtain a design of a ported shroud compressor that presents a recirculation channel with an innovative U-Bend shape. The current manufacturing techniques employed to obtain the Ported Shroud configuration, especially to ensure a low cost for high volume productions, do not provide an optimal shape for the ported shroud recirculation channel and, for this reason, it is not possible to exploit its full potential in terms of reducing aerodynamic losses.