Research on new techniques of perforated silencers has been addressed; however, the research work in shape optimization for a volume-constrained silencer requested upon the demands of operation and maintenance inside a constrained machine room is rare. Therefore, the main purpose of this paper is not only to analyze the sound transmission loss of a one-chamber perforated muffler but also to optimize the best design shape under space-constrained conditions. In this paper, both the generalized decoupling technique and plane wave theory are used. The four-pole system matrix used to evaluate acoustic performance is also deduced in conjunction with a genetic algorithm (GA); moreover, numerical cases of sound elimination with respect to pure tones (150, 550, 950 Hz) are fully discussed. Before GA operation can be carried out, the accuracy of the mathematical model has to be checked using Crocker’s experimental data. The results reveal that the maximum value of sound transmission loss (STL) can be optimally and precisely achieved at the desired frequencies. Consequently, the approach used for the optimal design of the one-chamber perforated mufflers is indeed easy and quite effective.