Single and multi-objective optimizations based on genetic algorithms are performed to find optimized designs of heat sinks with Y-shaped fractal network, and 3D fluid-solid conjugate heat transfer models are developed to revel the differences among heat sinks under different optimization objectives. The accuracy of GA and simulation results are validated by experimental results. Two single-objective optimizations are implemented, and hydraulically optimal model with only 13 mW pumping power and thermally optimal model with 0.121 K/W thermal resistance are obtained, showing the excellent heat and mass transfer characteristics of fractal network. Results indicate that hydraulically optimal model has higher energy economy and requires less pumping powers, about 54.5-67.2% of thermally optimal model with coolant flow rate ranging from 200 to 400 ml/min. However, it performs poorly in heat removal. Thermally optimal model shows excellent cooling performance, and the thermal resistance is about 1/2 of the hydraulically optimal model, but it requires much more energy input in comparison to the hydraulically optimal model. A multi-objective optimal model is obtained by joint optimizations of the thermal resistance and pumping power. It's found that multi-objective optimal model exhibits similar cooling performance to the thermally optimal model, T-max and Delta T of multi-objective model are about 3 K and 2 K higher than thermally optimal model with heat flux of 100 W/cm(2). Furthermore, the multi objective optimal model shows higher energy economy which is comparable to the hydraulically optimal model, and requires less pumping power compared with thermally optimal model, about 25% lower at 400 ml/min. The multi-objective optimal model offers excellent thermal management within high power density ICs while reducing energy consumption effectively. Therefore, the multi-objective optimization based on genetic algorithms is an effective method for the design of MCHSs. (C) 2018 Elsevier Ltd. All rights reserved.