In translucent optical networks, the physical layer impairments degrading the optical signal are considered in the network planning. In this paper, we investigate the offline problem of routing and wavelength assignment (RWA) and regenerator placement (RP) in translucent networks, minimizing the lightpath blocking and regenerator equipment cost. We address two variants of the problem, which correspond to two different types of quality of transmission (QoT) estimators, called linear and nonlinear. In a nonlinear QoT, nonlinear impairments like crosstalk or cross-phase modulation, which account for the interferences from neighboring lightpaths in the network are explicitly computed. Then, the QoT estimated for a lightpath depends on the routes of other lightpaths in the network. In the linear QoT, the effects of the nonlinear impairments are overestimated and accumulated to the rest of the impairments in the QoT calculation. As a result, the QoT estimation of a lightpath solely depends on its route.For the linear case, we formulate an optimal integer linear programming model of the problem, to the best of the authors' knowledge, for the first time in the literature. Its simplicity allows us to test it for small- and medium-size networks. Also, we propose two heuristic methods, namely, lightpath segmentation and three-step, and a tight lower bound for the regenerator equipment cost. For the nonlinear QoT case, we propose a new heuristic called iterative RP (IRP). Both the IRP and three-step algorithms are designed to guarantee that no lightpath blocking is produced by signal degradation. This is a relevant difference with respect to earlier proposals. The performance and the scalability of our proposals are then investigated by carrying out extensive tests. Results reveal that the solutions obtained by the heuristic algorithms are optimal or close to optimal, and outperform the earlier proposals in the literature.
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