Low-frequency sound wave reduction is hardly feasible for traditional sound absorbers such as porous media. In contrast, locally resonant acoustic metamaterials act as spatial frequency filters, effectively reducing low-frequency noise. However, these materials can have narrow bandgaps, add extra mass to the main system, and function only within a specifically adjusted frequency range. Therefore, this paper proposes a methodology for designing three-dimensional (3D) chiral honeycomb membrane-type acoustic metamaterials (MAM) based on acoustic circular dichroism (ACD), negative effective mass, and local resonance mechanisms (LRM). The paper also uses the genetic algorithm (GA) to maximize sound transmission attenuation and widen bandgaps. The accuracy of the simulations is validated with available experimental data. The key idea of the present study is to automatically design a MAM structure using modern optimization tools. A developed GA aims to maximize the average sound transmission loss (STL) across the desired low-frequency range of 0–850 Hz by optimizing the value of structural parameters associated with the configurations of masses, including rotation and linear offset, as well as their geometrical dimensions, including length and width. COMSOL Livelink with MATLAB is employed as a practical co-simulation tool to find an optimum value for structural parameters. Results indicate a 35% improvement in average STL along with an ultra-wide bandgap with a 507% bandgap coverage factor (BGCF) in the frequency range of interest, verifying the reliability of the developed algorithm. In addition, sound mitigation incidence is justified by exploring the negative effective parameters of the unit cell and displacement vector fields. The proposed designs demonstrate superior performance as both initial and optimized models broke the mass law within the investigated frequency range. Finally, the effect of the selected geometrical parameters on the objective function is observed through sensitivity analysis. This study presents the practical use of optimization algorithms to develop MAMs.