The multivariate microaggregation problem is a key problem in statistical disclosure control, trying to anonymize microdata sets, such that the re-identification of any specific record to be impossible. The paper proposes a new genetic algorithm with problem-specific crossover and mutation operator, where local search is introduced. In addition to the proposed genetic algorithm, hybrid variants are also investigated, where in the initial population results of other algorithms are used. Numerical experiments conducted on three real-world datasets prove the effectiveness and potential of this method.