In the present article, it shows the evaluation of two heuristic optimization methods, called genetic algorithms AG and simulated tempering AS (Simulated Annealing), applied to find the best solution with the lowest cost in planning the expansion of a network transmission system, which, in addition to meeting the expected demand, considers a list of candidate alternatives with known cost and transport capacity. With the development of the AG and AS algorithms, it is possible to guarantee the best optimization solution, measuring the computational cost of the algorithms. It was verified that the Genetic Algorithm optimization method can find the best optimal solution at a lower computational cost, compared to the Simulated Annealing algorithm. All results obtained in this work for the expansion of the system in an optimalway are satisfactory as they also meet all restrictions.