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This article deals with the design of optimum microchannel heat sinks through Unified Particle Swarm Optimisation (UPSO) and Harmony Search (HS). These heat sinks are used for the thermal management of electronic devices, and we analyse the performance of UPSO and HS in their design, both, systematically and thoroughly. The objective function was created using the entropy generation minimisation criterion. In this study, we fixed the geometry of the microchannel, the amount of heat to be removed, and the properties of the cooling fluid. Moreover, we calculated the entropy generation rate, the volume flow rate of air, the channel width, the channel height, and the Knudsen number. The results of several simulation optimizations indicate that both global optimisation strategies yielded similar results, about 0.032 W/K, and that HS required five times more iterations than UPSO, but only about a nineteenth of its computation time. In addition, HS revealed a greater chance (about three times) of finding a better solution than UPSO, but with a higher dispersion rate (about five times). Nonetheless, both algorithms successfully optimised the design for different scenarios, even when varying the material of the heat sink, and for different heat transfer rates.