Transcription factors (TFs) affect the production of mRNAs. In essence, the TFs form a large computational network that controls many aspects of cellular function. This article introduces a computational method to optimize TF networks. The method extends recent advances in artificial neural network optimization. In a simple example, computational optimization discovers a four-dimensional TF network that maintains a circadian rhythm over many days, successfully buffering strong stochastic perturbations in molecular dynamics and entraining to an external day-night signal that randomly turns on and off at intervals of several days. This work highlights the similar challenges in understanding how computational TF and neural networks gain information and improve performance.