Large-scale emergency or off-grid power generation is typically achieved through diesel or natural gas generators. To meet governmental emission requirements, emission control systems (ECS) are required. In operation, effective control over the generator’s acoustic emission is also necessary, and can be accomplished within the ECS system. Plug flow mufflers are commonly used, as they provide a sufficient level of noise attenuation in a compact structure. The key design parameter is the transmission loss of the muffler, as this dictates the level of attenuation at a given frequency. This work implements an analytically decoupled solution, using multiple perforate impedance models, through the transfer matrix method (TMM) to predict the transmission loss based on the muffler geometry. An equivalent finite element model is implemented for numerical simulation. The analytical results and numerical results are then evaluated against experimental data from literature. The transmission loss required in each application of the ECS system will vary depending on the noise profile of the generator in question; therefore, it is necessary to have an effective method of redesigning the muffler to meet the design requirements. Prior work on TMM-based muffler shape optimization utilized complex algorithms such as neural networks and simulated annealing. The present study simplifies the process by using the bounded, limited-memory implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm in a multi-start framework for shape optimization to achieve the desired transmission loss. By constraining the multi-start method with appropriate design limits, the algorithm is initialized at multiple random points within the design space, ensuring that the solution approaches the global optimum when using a sufficiently large number of initializations.