Synthetic biology is highly valued in the recent decade. In a previous study, Elowitz and Leibler have made a biological oscillator in consisting of three genes, and found out its mathematical expressions. In which, design of an oscillator is regarded as a tracking design problem. Designing the optimal transcription rates of mRNA and the decaying rate of protein concentration to track desired sinusoidal signal and achieve the best oscillation have becoming a challenge. Genetic algorithm (GA) bears the feature of searching the global optimal for the optimization problem. However, directly applying that kind of algorithms usually leads to premature convergence of the solution and cannot result in solution with the cheapest structure. In this paper, we introduce the real structure genetic algorithm (RSGA) to solve for the design problem of synthetic biological oscillators. The design approach is shown to be capable of yielding genetic oscillators with a cheapest structure.