The use of nanofluids as coolant fluid in the microchannel heat sink (MCHS) is an effective technique for the improvement of thermal performance in electronic devices. A comparative study is performed with the help of a multi-objective genetic algorithm (MOGA) to find the optimal geometric variables of the MCHS and choose the appropriate nanofluid and its optimal characteristics. For that purpose, four practical nanofluids, including Al2O3-water, Cu-water, SiO2-water, and carbon nanotube (CNT)-water, are thoroughly investigated. Simultaneously minimization of the total thermal resistance and pumping power consumption are taken into account as the optimization goal, and the MOGA is employed to achieve the optimal solution. To check the accuracy of the thermal resistance modeling and assessing the optimization algorithm, several case studies with a different number of optimization variables are defined to investigate the capability of the algorithm in finding the optimal microchannel design variables and choosing the suitable nanofluid. The optimization variables consist of the channel aspect and wall ratios, base thickness, volume nanoparticle concentration, diameter, and volume flow rate. Compared to other nanofluids, CNT provides better thermal performance. Increasing the concentration of nanoparticles enhances thermal performance, which can also be achieved through the reduction of nanoparticle diameter. Results of the considered case studies also show that considering more design variables through the optimization procedure, better thermal performance is achievable.