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There are many methodologies that, using the frequency response of a grounding system impedance, permit to get the coefficients of a transfer function or the electrical parameters of a specific circuit, that behave as equivalents of that system. In this paper in the first part, the coefficients of the transfer function and the parameters of the circuit were obtained using the simplex method to optimize the values and minimize the square error between the objective function and the frequency response of the software Gtierras. The results of the methodologies depend on the selection of the initial values (which change for every case evaluated) to start the process. This happens because the simplex method can get local values. In the second part it is proposed a genetic algorithm (global values) to get the initial values of the simplex method and solve the problem. The result of mixing both methods is compared with the vector fitting method, showing that it is possible to obtain a circuit or a transfer function that reproduce successfully the impedance of the grounding systems in the frequency domain.