Sound absorption by microperforated panels (MPP) has received increasing attention the past years as an alternative to conventional porous absorbers in applications with special cleanliness and health requirements. The absorption curve of an MPP depends on four parameters: the holes diameter, the panel thickness, the perforation ratio, and the thickness of the air cavity between the panel and an impervious wall. It is possible to find a proper combination of these parameters that provides an MPP absorbing in one octave band or two, within the frequency range of interest for noise control applications. However, when a wider absorption frequency band is required, it is necessary to design multiple-layer MPP (ML-MPP). The design of an N-layers MPP depends on 4N parameters. Consequently, the tuning of an optimal ML-MPP by exhaustive search within a prescribed frequency band becomes impractical. Therefore, simulated annealing is proposed in this paper as a tool to solve the optimization problem of finding the best combination of the constitutive parameters of an ML-MPP providing the maximum average absorption within a prescribed frequency band.