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This study presents a simple and efficient genetic algorithm-assisted approach for joint quantised precoding and transmit antenna selection based on the criterion of maximum capacity. The objective is to alleviate the effect of multi-user interference and to reduce hardware costs, such as the cost of radio frequency chains associated with antennas in the downlink of multi-input multi-output systems with limited feedback. To avoid the enormous search effort required by existing approaches, the authors propose a novel variant of the conventional genetic algorithm, called the hybrid genetic algorithm, in which each chromosome is divided into a bit string for precoding vector selection and an integer string for transmit antenna selection. In addition, new crossover and mutation operations are employed to accommodate these new chromosomes. The results of simulations show that the performance of the proposed approach is close to that of the exhaustive search method, but its computational complexity is substantially lower.