Genetic algorithms (GAs) are considered to be one of the main types of evolutionary algorithms (EAs) and are being increasingly used in various engineering design applications. To a large extent, plate-fin heatsinks are used in the thermal management of compact electronic equipment and data centers. The shape optimization of the heatsinks is not rigorously investigated during the design process of high power electronics. Any improvements in the effectiveness of the heatsinks impact the energy consumed by large-scale information communication technology (ICT) facilities including data centers and telecommunication systems and promote a more sustainable use of raw materials. This paper investigates the optimization of plate-fin heatsinks by modifying the fin layout in a forced crossflow using a multi-objective genetic algorithm (MOGA) combined with computational fluid dynamics (CFD) simulations. The main objective is to improve the heat dissipation rate by modifying geometric parameters, i.e., the number, arrangement, and orientation of fins. For a generic heatsink test case, the optimized performance is examined in terms of thermal resistance, turbulence intensity, pumping power, coefficient of performance, and Chilton–Colburn j-factors. Among all of the cases investigated, the input parameter optimization configurations which coupled and rotated fins in groups of ten proved to be the most successful. For one case, an 18% increase in the effectiveness of heat dissipation is reported. However, when weight reduction was considered by dividing by the unit mass, the designs in one of the investigated families which remove a number of fins from the heatsink outperformed the rest, achieving improvements of 65% over the baseline.