PurposeThis study aims to satisfy the thermal management of gallium nitride (GaN) high-electron mobility transistor (HEMT) devices, microchannel-cooling is designed and optimized in this work.Design/methodology/approachA numerical simulation is performed to analyze the thermal and flow characteristics of microchannels in combination with computational fluid dynamics (CFD) and multi-objective evolutionary algorithm (MOEA) is used to optimize the microchannels parameters. The design variables include width and number of microchannels, and the optimization objectives are to minimize total thermal resistance and pressure drop under constant volumetric flow rate.FindingsIn optimization process, a decrease in pressure drop contributes to increase of thermal resistance leading to high junction temperature and vice versa. And the Pareto-optimal front, which is a trade-off curve between optimization objectives, is obtained by MOEA method. Finally, K-means clustering algorithm is carried out on Pareto-optimal front, and three representative points are proposed to verify the accuracy of the model.Originality/valueEach design variable on the effect of two objectives and distribution of temperature is researched. The relationship between minimum thermal resistance and pressure drop is provided which can give some fundamental direction for microchannels design in GaN HEMT devices cooling.