In the present paper we study genetic algorithms for the codebook generation problem in vector quantization. There are two different approaches to the problem: a codebook-based and a partition-based. From these, the codebook-based approach is clearly superior to the partition-based approach. The experiments show that a pure genetic algorithm does not give comparable results to the existing methods, but the inclusion of GLA iterations is vital. Even in this case, the time-distortion performance of the algorithm is still inferior to simulated annealing. In the case of binary images, the hybrid combination of GA and GLA gives the best results. The greatest deficiency of the algorithm is still its high running time.