The survivable logical topology routing problem for a given IP-over-WDM network is to map each logical link into a lightpath in the physical network which guarantees connectivity of the IP network after any physical link failure. Such a survivable routing is said to protect the logical network against all single physical link failures. But, it is possible that a logical topology may not admit a survivable routing. In view of this, we define a logical topology routing to be optimum if this routing maximizes the number of single physical link failures that do not disconnect the logical topology. First, we give a mixed integer linear programming formulation to determine an optimum logical topology routing. The failure localization problem is to localize the single physical link failures which disconnect the logical network under a given optimum routing. Given a set of monitoring trails and the lightpath routings in an optimum routing, we give a mixed integer linear programming formulation to determine an optimum routing and the corresponding failure localization. We also propose a heuristic approach for these problems to handle large scale IP-over-WDM networks.