Multi-Disciplinary Optimization (MDO) is widely used to handle the advanced design in several engineering applications. Such applications are commonly simulation-based, in order to capture the physics of the phenomena under study. This framework demands fast optimization algorithms as well as trustworthy numerical analyses, and a synergic integration between the two is required to obtain an efficient design process. In order to meet these needs, an adaptive Computational Fluid Dynamics (CFD) solver and a fast optimization algorithm have been developed and combined by the authors. The CFD solver is based on a high-order discontinuous Galerkin discretization while the optimization algorithm is a high-performance version of the Artificial Bee Colony method. In this work, they are used to address a typical aero-mechanical problem encountered in turbomachinery design. Interesting achievements in the considered test case are illustrated, highlighting the potential applicability of the proposed approach to other engineering problems.