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We tackle the design problem of the logical overlay network used by the reliable label switched paths (ILSPs) in Internet protocol (IP) networks. The design problem consists to find the minimum capacity on each link and the routing metrics that ensure the successful rerouting of the reliable LSPs for all failure scenarios of interest to the network planner. The objective is to minimize the cost of the network overlay. A mixed nonlinear bi-level mathematical programming model is proposed for the problem and a tabu-search heuristic algorithm is designed to find "good" solutions of the model. Numerical results show that quasi-optimal solutions can be found with the proposed algorithm.