Research on new techniques of perforated plug silencers has been well addressed. Most researchers have explored noise reduction effects based on a pure plane wave theory. However, the maximum noise reduction of a silencer under a space constraint, which frequently occurs in engineering problems, is rarely addressed. Therefore, the optimum design of mufflers becomes an essential issue. In this paper, to save the design time during the flexible optimum process, a simplified mathematical model of a muffler is constructed with a neural network with a series of real data - input design data (muffle dimensions) and output data (theoretical sound transmission loss (STL)) were approximated by a theoretical mathematical model (TMM) in advance. To assess the optimal mufflers, the neural network model (NNM) is used as an objective function in conjunction with a genetic algorithm (GA). Moreover, the numerical cases of sound elimination with respect to various parameter sets and pure tones (500, 1000, and 2000 Hz) are exemplified and discussed. Before the GA operation is carried out, the approximation between TMM and real data is checked. In addition, both the TMM and NNM are compared. It is found that the TMM and the experimental data are in agreement. Moreover, the TMM and NNM conform. Optimal results reveal that the maximum amount of the STL can be optimally obtained at the desired frequencies. Consequently, the optimum algorithm proposed in this study can provide an efficient method to develop optimal silencers in industry.
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