Conductance-based models of biological neurons can accurately reproduce the waveform of the membrane voltage, as well as the spike timing in response to injected currents. Nevertheless, finding the good model parameter set to fit membrane voltage recordings is often a very time-consuming and complex task, difficult to achieve manually. We present a new variant of an optimization algorithm, the differential evolution. We specifically designed this technique for the automated tuning of neuro-mimetic analog integrated circuits based on an Hodgkin-Huxley formalism for a point-neuron model. It indeed enables us to estimate all the parameters of the model, while avoiding local minima. The method is first tested on three types of neuron models (fast spiking, regular spiking, and intrinsically bursting), and then applied to the automated tuning of a neuro-mimetic circuit from the reference membrane voltage of a fast spiking neuron model.