On solving the 1+1 routing, wavelength and network coding assignment problem with a bi-objective integer linear programming model

Network coding techniques have been viewed as the promising venue to improve the network efficiency and indeed, have been widely explored in the realm of failure recovery in optical networks. The combination of near-instantaneous recovery achieved by dedicated protections and capacity efficiency enabled by network coding brings about new opportunities to challenge the well-established trade-off of trading speed recovery for capacity efficiency and vice versa. In this context, the use of all-optical XOR network coding has reshaped the traditional 1+1 optical path protection in transparent WDM optical networks and established a new problem, called, 1+1 routing, wavelength and network coding assignment (1+1 RWNCA) as the extension of the conventional 1+1 routing and wavelength assignment (1+1 RWA). In this paper, we propose a bi-objective integer linear programming model of the 1+1 RWNCA problem aiming at minimizing the wavelength resources as the primary objective and simultaneously minimizing the wavelength link usage as the secondary objective. Our formulation uses a weighting method to combine two objectives into an integrated one and we provide insights on setting up the weight vectors to capture the priority of individual objectives. The effectiveness of our integrated objective model in comparison with reference designs based on the single-objective model, 1+1 RWA and 1+1 RWNCA, is numerically evaluated on different realistic topologies and traffic sets. Extensive simulation highlights that our proposal uses as efficient as around 60% of the required wavelength link resources of reference designs and simultaneously achieve the highest performance on the primary objective of minimizing the wavelength resources while its computation time is a few time longer than its single objective counterpart model.