With the development of society, noise pollution has become more and more serious. How prevent and control the noise pollution to get the proper acoustic environment has been the hotspot. Therefore, a broad band sound absorber which is thin, durable, clean and environmentally friendly is highly demanded in modern society. In this paper, a new type of multiple size micro-perforated panel (MPP) absorbers with different cavity depths is proposed and studied. Firstly, a mathematical model for multi-size MPP absorbers with different cavity depths is developed. Thereafter, based on the established model, adaptive genetic algorithm (AGA) is proposed in this study as a tool to solve the optimization problem of finding the best combination of the constitutive parameters of multi-size MPP absorbers with different cavity depths providing the maximum average absorption within a prescribed frequency range. Results show that AGA provides a fast and effective method to solve the structure optimization of multi-size MPP absorbers with different cavity depths.