Our discussion in this article centers on the application of a Lagrangean relaxation and a subgradient optimization technique to the problem of primary route assignment (PRA) in survivable connection-oriented networks. The PRA problem consists in a static optimization of primary routes minimizing the Lost Flow in Node (LFN) function. The major contribution of this work is a combination of the Lagrangean relaxation with other heuristic algorithms. We evaluate the performance of the proposed Lagrangean-based heuristic by making a comparison with their counterparts including evolutionary algorithm and GRASP using various network topologies and demand patterns. The results of simulation tests show that the new algorithm provides sub-optimal results, which are better than other heuristics.