A recent Boolean model of the tryptophan operon in Escherichia coli has been introduced, which exhibits a desired set of fixed points modeling the operon state being on or off. Nevertheless, when updated synchronously, the model also reveals spurious limit cycles with a larger basin of attraction than the desired fixed points. This paper presents the search via evolutionary computation for threshold network models that exhibit the desired fixed points without any limit cycles. The proposed framework was applied using differential evolution and particle swarm optimization, the latter being the most efficient and effective method based on the results obtained by the simulations. Particle swarm optimization found two correct threshold networks, one of which has only weight values -1,0,1, making the model more interpretable.