ing is used and MPLS layer and optical layer have separated survivability mechanisms, it is exact. Unfortunately, this is not the generic situ- ation and in real networks excluding grooming brings to a suboptimal design. Naturally smaller the W, more difficult an effective grooming, more performing the method of disjoined design. Another important simplification is possible when the network is divided into zones and only a few LSRs are routed through different zones. In this case, the Telecommunication Networks problem can be divided into a different problem for each zone and a global prob- lem only for the interzone LSRs. The single-zone problem can be solved exactly being relative to a network with much less nodes, while if the interzone GLSPs are really a small quantity of the traffic, they can routed through a suboptimum algorithm without affecting greatly the final network cost. If W is small (that is, the LSR are high speed and a small number of that fit into a wavelength) and the network is poorly connected, further simplification can be achieved assuming that all the paths having the same extremes are routed through the same route. In this case, the routing matrix loses the last dimension, since all the LSRs are routed together. This decreases the number of elements of the routing matrix by a factor M, SO simplifying the resulting computation. If W is great and a large number of GLSPs are routed toward each couple of nodes (that is, the traffic matrix elements are large), the problem can be simplified by creating sets of GLSPs and routing them together. 8.4.2.3.2 Mathematical Approximations of the ILP problem Since it is well known that an ILP problem can be very hard to solve, several mathemati- cal studies have been developed to analyze possible approximations of the problem that reduces its complexity [19,20]. A simple method to obtain an upper-bound and a lower-bound to the solution of the ILP problem is to use the so-called relaxation method. This method simply consists in eliminating the condition t