Recently, an innovative heat dissipation technique of fractal-tree structures has attracted attention due to its excellent high heat transfer efficiency and low pumping power. Though the impact of geometrical parameters such as branching level and dimension ratios of successive branches on the heat transfer efficiency and pumping power are considered to be critical, the impact mechanisms are still not well studied and formulated. Hence, there is still no clear method to optimally arrange the fractal-tree microchannels (FTMCs) in a rectangular heat sink to achieve better thermal and hydraulic performance. Therefore, we developed a multi-objective optimization algorithm (distributed-adaptive genetic algorithm, DAGA) to optimize the different types of novel FTMCs concerning achieving an optimal COP (coefficient of performance, heat transfer/ pumping power). The developed DAGA can improve the computational efficiency and the quality of optimum by around 87.63% and 12.48%, respectively in the present work. Then, taking conventional rectangular parallel microchannels (RPMCs) as a reference, the COP of the optimized FTMCs in the same heat sink shows an enhancement of around 0.09 ∼ 0.57. The highest COP is achieved by the three-level branching FTMC. Furthermore, the optimized results reveal that branching level, bifurcation number, and microchannel width at the first branching level are sensible, while dimension ratio factors and microchannel length at the first branching level show low sensibility to the COP of FTMCs.