  Multi-band transmission is a promising technical direction for spectrum and
capacity expansion of existing optical networks. Due to the increase in the
number of usable wavelengths in multi-band optical networks, the complexity of
resource allocation problems becomes a major concern. Moreover, the
transmission performance, spectrum width, and cost constraint across optical
bands may be heterogeneous. Assuming a worst-case transmission margin in U, L,
and C-bands, this paper investigates the problem of throughput maximization in
multi-band optical networks, including the optimization of route, wavelength,
and band assignment. We propose a low-complexity decomposition approach based
on Column Generation (CG) to address the scalability issue faced by traditional
methodologies. We numerically compare the results obtained by our CG-based
approach to an integer linear programming model, confirming the near-optimal
network throughput. Our results also demonstrate the scalability of the
CG-based approach when the number of wavelengths increases, with the
computation time in the magnitude order of 10 s for cases varying from 75 to
1200 wavelength channels per link in a 14-node network. Code of this
publication is available at github.com/cchen000/CG-Multi-Band.
