Here we present a framework for the automatic tuning of spiking neural networks (SNNs) that utilizes an evolutionary algorithm featuring indirect encoding to achieve a drastic reduction in the dimensionality of the parameter space, combined with a GPU-accelerated SNN simulator that results in a considerable decrease in the time needed for fitness evaluation, despite the need for both a training and a testing phase. We tuned the parameters governing a learning rule called spiketiming-dependent plasticity (STDP), which was used to alter the synaptic weights of the network. We validated this framework by applying it to a case study in which synthetic neuronal firing rates were matched to electrophysiologically recorded neuronal firing rates in order to evolve network functionality. Our framework was not only able to match their firing rates, but also captured functional and behavioral aspects of the biological neuronal population, in roughly 50 generations.