Based on the Theory of Neuronal Group Selection (TNGS), we have investigated the emergence of synchronicity in a network composed of spiking neurons via genetic algorithm. The TNGS establishes that a neuronal group is the most basic unit in the cortical area of the brain and, as a rule, it is not formed by a single neuron, but by a cluster of tightly coupled neural cells which fire and oscillate in synchrony at a predefined frequency. Thus, this paper describes a method of tuning the parameters of the Izhikevich spiking neuron model through genetic algorithm in order to enable the self-organization of the neural network. Computational experiments were performed considering a network composed of neurons of the same type and another composed of neurons of different types.