With the advent of intelligent multilayer networks, like GMPLS, connections can be protected against failures effectively; however, to capitalize the advantages, novel sophisticated routing methods are needed. This paper addresses the task of finding path-pairs in a survivable multilayer network in order to ensure high availability for each connection. Known methods (like running a shortest path algorithm twice) either do not guarantee physical disjointness (SRLG constraints) or may not find solution even if it exists. Besides the Integer Linear Program based approach that yields a solution with minimal total cost, we propose a heuristic method to solve the problem, and extend it to (1) minimize the number of spans used by both working and protection paths, (2) to find the weighted working path while ensuring the existence of a protection path, and (3) to find more than one backup paths for high priority traffic. It is shown with numerous simulations that our proposed method finds solution for significantly (up to 35%) more node pairs than traditional methods, while the running time is only slightly increased. Furthermore, it yields connection availabilities close to the optimum.