This article reports the numerical geometric optimization of three-dimensional microchannel heat sinks with rectangular, elliptic, and isosceles triangular cross sections. The cross-sectional areas of the mentioned microchannels can change according to the degrees of freedom, that is, the aspect ratio and the solid volume fraction. Actually, the purpose of geometric optimization is to determine the optimal values of these parameters in such a way that the peak temperature of the wall is minimized. The effects of solid volume fraction and pressure drop upon the aspect ratio, hydraulic diameter, and peak temperature of the microchannels are investigated. Moreover, these microchannel heat sinks are compared with each other at their optimal conditions. Considering the constraints and geometric parameters for the optimization of the present study, it is revealed that microchannel heat sinks with rectangular and elliptic cross sections have similar performances, while microchannels with isosceles triangular cross sections show weaker performances. The optimal shapes of all three kinds of channels are achieved numerically and compared with the approximate results obtained from scale analysis, for which good agreements are observed.