Finding an optimal design of a hydrodynamic or aerodynamic surface is costly due to the cost function evaluation (e.g., using computational fluid dynamics) required to determine the performance of the surface-controlled flow. , often impossible. Furthermore, the inherent limitations of the design space itself due to imposed geometric constraints, traditional parameterization methods, and user biases lead to {\it all}Design may be limited. A machine learning design algorithm is used to search the design space. To address these issues, we present a two-pronged attack. (1) We propose a methodology to create design spaces using morphing called {\it Design-by-Morphing} (DbM). (2) an optimization algorithm to search that space using a new Bayesian optimization (BO) strategy called {\it mixed-variable, multi-objective Bayesian optimization} (MixMOBO). Apply this shape optimization strategy to maximize the power output of a hydro-turbine. By applying these two strategies in tandem, we create a novel, geometrically unconstrained design space of draft tube and hub geometries and simultaneously optimize them with the {\it minimum} number of cost function calls. indicates that it can be Our framework is versatile and can be applied to shape optimization for various fluid problems.

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