This research discusses the multi-stage security-constrained transmission network expansion planning. In modern power systems, the problem is formulated as a large-scale, mixed-integer, non-linear programming problem, which for a real power systems is very difficult to solve. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. In this paper, a new constructive heuristic approach, based on a local controlled random search (simulated rebounding algorithm) is proposed to choose the decision variables. The model can produce better solutions than other references techniques such as particle swarm optimization, evolutionary particle swarm optimization, genetic algorithms, and simulated annealing algorithm, among other evolutionary methods. The methodology is applied to assess the capabilities of the proposed approach in the Ecuadorian and Chilean Power Systems as an example of application. Simulation results show that the proposed approach is accurate and very efficient, and it has the potential to be applied to real power system planning problems. The algorithm has been presented and applied to the multi-stage security-constrained transmission expansion planning. (c) 2012 Elsevier Ltd. All rights reserved.