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Microchannel heat sinks are an efficient cooling method for semiconductor packages. However, to properly cool increasingly complex and thermally dense circuits, microchannel designs should be improved and expanded on. In this paper, microchannel designs with secondary channels and with ribs are investigated using computational fluid dynamics and are coupled with a multi-objective optimization algorithm to determine and propose optimal solutions based on observed thermal resistance and pumping power. A workflow that combines Latin hypercube sampling, machine learning-based surrogate modeling and multi-objective optimization is proposed. Random forests, gradient boosting algorithms and neural networks were considered during the search for the best surrogate. We demonstrated that tuned neural networks can make accurate predictions and be used to create an acceptable surrogate model. Optimized solutions show a negligible difference in overall performance when compared to the conventional optimization approach. Additionally, solutions are calculated in one-fifth of the original time. Generated designs attain temperatures that are lower by more than 10% under the same pressure limits as a convectional microchannel design. When limited by temperature, pressure drops are reduced by more than 25%. Finally, the influence of each design variable on the thermal resistance and pumping power was investigated by employing the SHapley Additive exPlanations technique. Overall, we have demonstrated that the proposed framework has merit and can be used as a viable methodology in microchannel heat sink design optimization.