In this study, laminar single-phase fluid flow and conjugate heat transfer for three different shapes of microchannel heat sinks (MCHS) were numerically investigated using Computational Fluid Dynamics (CFD) and optimized with Non-dominated Sorting Genetic Algorithm II (NSGA-II) to reveal geometric design variables for optimum solutions. A clear comparison of different shapes of MCHS under the same design constraints is necessary to establish an understanding of efficient MCHS designs. The hydraulic diameters of rectangular, triangular and trapezoidal microchannels were kept constant at 150 mu m for a fair comparison. Minimization of power consumption and enhancing heat transfer were determined as objective functions of the optimization represented by pumping power and averaged Nusselt number (Nu). The objective functions were expressed in terms of the design variables consisting of Reynolds number (Re), aspect ratio of rectangular channel, apex angle of triangular channel and junction angle of trapezoidal channel. For each configuration, parametric CFD analyzes were performed to establish correlations between design variables and objective functions to be used in the optimization process. For the rectangular MCHS configuration, low aspect ratio was shown to increase heat transfer with a power consumption penalty. For triangular and trapezoidal microchannels, 50 of apex angle and 60 of junction angle were suggested as optimum geometric parameters, respectively. Pareto frontal comparison of the three configurations revealed that rectangular microchannel was the most effective configuration in terms of thermal and hydrodynamic performance. For the same amount of heat transfer, the rectangular microchannel configuration required 17% and 40% less pumping power than the trapezoidal and triangular microchannels, respectively.