We compare the ability of single and multi-objective evolutionary algorithms to evolve tunable self-sustained genetic oscillators. Our research is focused on the influence of objective setup on the success rate of evolving self-sustained oscillations and the tunability of the evolved oscillators. We compare temporal and frequency domain fitness functions for single and multi-objective evolution of the parameters in a three-gene genetic regulatory network. We observe that multiobjec-tivization can hinder convergence when decomposing a period specific based single objective setup in to a multi-objective setup that includes a frequency specific objective. We also find that the objective decomposition from a frequency specified single objective setup to a multi-objective setup, which also specifies period, enable the synthesis of oscillatory dynamics. However this does not help to enhance tunability. We reveal that the use of a helper function in the frequency domain improves the tunability of the oscillators, compared to a time domain based single objective, even if no desired frequency is specified.