Diauxie, or the sequential consumption of carbohydrates in bacteria such as Escherichia coli, has been hypothesized to be an evolutionary strategy which allows the organism to maximize its instantaneous specific growth-giving the bacterium a competitive advantage. Currently, the computational techniques used in industrial biotechnology fall short of explaining the intracellular dynamics underlying diauxic behavior. In particular, the understanding of the proteome dynamics in diauxie can be improved. We developed a robust iterative dynamic method based on expression- and thermodynamically enabled flux models to simulate the kinetic evolution of carbohydrate consumption and cellular growth. With minimal modeling assumptions, we couple kinetic uptakes, gene expression, and metabolic networks, at the genome scale, to produce dynamic simulations of cell cultures. The method successfully predicts the preferential uptake of glucose over lactose in E. coli cultures grown on a mixture of carbohydrates, a manifestation of diauxie. The simulated cellular states also show the reprogramming in the content of the proteome in response to fluctuations in the availability of carbon sources, and it captures the associated time lag during the diauxie phenotype. Our models suggest that the diauxic behavior of cells is the result of the evolutionary objective of maximization of the specific growth of the cell. We propose that genetic regulatory networks, such as the lac operon in E. coli, are the biological implementation of a robust control system to ensure optimal growth.