In the design of filters for real time applications, designers have found different inconveniences trying to get better relations between computational cost and mean square error (MSE). This article presents a solution using evolutionary Algorithm (GA) theory, SPEA algorithm has been chosen to find the Pareto optimal for this problem and different kinds of IIR filters (Chebyshev, Butterworth and Elliptical) have been designed by traditional methods. Additive White Gaussian Noise (AWGN) has been added to a sinusoidal signal and the noisy signal is used as the input of every filter. MSE only depends of the input and output signals of each filter, meanwhile computational cost is related with the number of operations.