In this paper, the authors address a railway network design problem (RNDP) and its robust version. The RNDP under consideration is characterized by the existence of a competing mode, and the goal is to design a network covering as many passengers as possible.

The authors describe a novel integer programming (IP) formulation for the problem with several constraints: budget, alignment location, routing demand conservation, location-allocation, splitting demand, and binary.

Due to the complexity of the problem, and the fact that the CPLEX optimizer failed to provide solutions for realistic instances, the authors propose a greedy randomized adaptive search procedure (GRASP) algorithm for solving the RNDP using local search as an intensifying phase.

The paper describes this algorithm, and includes a probabilistic version of the RNDP in which link failures may occur, an IP formulation in this case, and an adaptation of the GRASP algorithm for this variant of the RNDP.

The computational results show that the proposed GRASP approach is an attractive and appropriate method to explore the solution space of this complex problem, and that it can lead to good solutions within reasonable computational times.