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Inspired by the Theory of Neuronal Group Selection (TNGS), we have carried out synthesis of frequency generator via spiking neurons network through genetic algorithm. The TNGS sets that a neuronal group is the most basic unit in the cortical area and are generated by synapses of localized neural cells in the cortical area of the brain firing and oscillating in synchrony at a predefined frequency. Each one of these clusters (Neuronal Groups) is a set of localized, tightly coupled neurons developed in the embryo. According to this proposal, this paper describes a method of tuning the parameters of the Izhikevich spiking neuron model. Computational experiments consisting of a network with all neurons of the same type and a network with different neurons were conducted. A genetic algorithm was used to tune the parameters in these two different cases. The results were compared in order to find the best way to create a frequency generator of spiking neurons network.