A recent Boolean model of the tryptophan operon in Escherichia coli has been developed, aiming to capture the operon’s on/off states through a set of fixed points. However, when updated synchronously, the model also reveals the presence of unwanted spurious limit cycles, that have a larger basin of attraction. This study introduces an evolutionary computation framework to search for threshold network models that accurately portray the desired fixed points while eliminating occurrences of limit cycles. Employing both differential evolution and particle swarm optimization within the proposed framework, the latter emerges as the most efficient and effective method based on simulation results. Notably, networks were successfully identified for both continuous weight matrix values within the real interval [−1,1] and discrete values limited to {−1,0,1}. The results confirm that the proposed evolutionary computation framework is capable of identifying threshold networks that accurately model the asymptotic behavior of the tryptophan operon in Escherichia coli .