This study investigates the optimization of the acoustic performance of a double-wall structure featuring a porous material of polyurethane foam (PU). The main idea is to optimize the microstructure dimensions of polyurethane foams, which are closely linked to their acoustic parameters (resistivity, viscous length, thermal length, porosity and tortuosity). The aim is to determine the optimum morphology of foam cells to achieve good acoustic insulation performance in the double-wall system. The Transfer Matrix Method (TMM) serves as a tool to estimate the sound transmission loss of the double-wall systems with porous materials. A genetic algorithm (GA) is used to optimize the foam’s microstructural properties. A case study was conducted to evaluate the optimization process for two types of PU foam with different reticulation rates: highly reticulated and less reticulated. The results demonstrated that the proposed optimization methodology yielded significant improvements in the sound transmission loss for the two foam types. However, the enhancement was more pronounced for the foam with a lower reticulation rate, characterized by fewer open cells and higher airflow resistivity, particularly in high-frequency ranges.