We propose a genetic algorithm (GA) to search for plateaued boolean functions, which represent suitable candidates for the design of stream ciphers due to their good cryptographic properties. Using the spectral inversion technique introduced by Clark, Jacob, Maitra and Stanica, our GA encodes the chromosome of a candidate solution as a permutation of a three-valued Walsh spectrum. Additionally, we design specialized crossover and mutation operators so that the swapped positions in the offspring chromosomes correspond to different values in the resulting Walsh spectra. Some tests performed on the set of pseudoboolean functions of $n=6$ and $n=7$ variables show that in the former case our GA outperforms Clark et al.’s simulated annealing algorithm with respect to the ratio of generated plateaued boolean functions per number of optimization runs.