Adaptive signal decomposition is an important signal processing method. The chirp-based signal representation, for example, the Gaussian chirplet decomposition, has been an active research topic in the field of signal processing. A main challenge of the Gaussian chirplet decomposition is the numerical implementation of the matching pursuit, which is an adaptive signal decomposition scheme, and the challenge remains an open research topic. In this paper, a new optimal time-frequency atom search method based on the adaptive genetic algorithm is proposed, aiming to the low precision problem of the traditional methods. Firstly, a discrete formula of finite length time-frequency atom sequence is derived. Secondly, an algorithm based on the adaptive genetic algorithm is described in detail. Finally, a simulation is carried out, and the result displays its validity and stability.