This paper presents three different multi-objective optimization strategies for a high specific speed centrifugal volute pump design. The objectives of the optimization consist of maximizing the efficiency and minimizing the cavitation while maintaining the Euler head. The first two optimization strategies use a 3D inverse design method to parametrize the blade geometry. Both meridional shape and 3D blade geometry is changed during the optimization. In the first approach Design of Experiment method is used and the efficiency computed from CFD computations, while cavitation is evaluated by using minimum pressure on blade surface predicted by 3D inverse design method. The design matrix is then used to create a surrogate model where optimization is run to find the best tradeoff between cavitation and efficiency. This optimized geometry is manufactured and tested and is found to be 3.9% more efficient than the baseline with little cavitation at high flow. In the second approach the 3D inverse design method output is used to compute the efficiency and cavitation parameters and this leads to considerable reduction to the computational time. The resulting optimized geometry is found to be similar to the more computationally expensive solution based on 3D CFD results. In order to compare the inverse design based optimization to the conventional optimization an equivalent optimization is carried out by parametrizing the blade angle and meridional shape. Two different approaches are used for conventional optimization one in which the blade angle at TE is not constrained and one in which blade angles are constrained. In both cases larger variation in head is obtained when compared with the inverse design approach. This makes it impossible to create an accurate surrogate model. Furthermore, the efficiency levels in the conventional optimization is generally lower than the inverse design based optimization.