We have applied the genetic algorithm (GA) technique, a nonlinear globaloptimization method, to determine the radial viscosity structure of the mantle from regional geoidal patterns. From numerical simulations of 2-D mantle convection, we examine the horizontal spectra of the vertical mass flux at 660 km depth and find that for long wavelengths there are minor differences between partially layered convection induced by the phase transitions and mantle convection without any phase transition. The differences in the spectra of the vertical mass flux become more prominent at shorter wavelengths. This result has led us to study mantle viscosity for the intermediate wavelength geoid from the whole-mantle and blocked-flow situations, in which the appropriate boundary condition is imposed on the radial velocity at 660 km depth. In order to confirm the robustness of this study, two different density models have been used, which were constructed from three tomographic models and appropriate velocity-to-density scaling relations based on recent results from mineral physics. We have analyzed only oceanic geoid spanning between spherical harmonic degree el = 12-25. The correlation of the predicted geoid with the observations over the Atlantic, Indian, and Pacific Oceans have been employed as the fitting function in our GA approach, which has been modified from the common algorithm. In constructing the families of suitable viscosity profiles we have used 100 parents, which have been iterated for 100 generations, and have been started with 10 different sets of initial parents. Convergence to acceptable viscosity solutions is obtained for all the three oceans and for both the whole-mantle and layered models. In some cases multiple viscosity solutions are found acceptable by using the correlation criteria. The outstanding feature of these models is the nearly ubiquitous presence of two low viscosity zones, one lying under the lithosphere, the other right under the bottom of the spinel to perovskite phase change. The solutions for the whole-mantle model can fit better and are preferred over the solutions with the layered boundary condition, which generally result in unrealistic viscosity profiles. Our results would suggest a more complex mantle viscosity structure, which has not been detected previously from geoid signals with longer wavelengths, and also reveal the potential difficulties in treating the dynamical boundary condition at the 660 km discontinuity.