Sound absorption has recently attracted significant interest due to recent advent of acoustic metamaterials. In contrast to conventional absorbers, metamaterial absorbers can achieve previously attainable subwavelength broadband absorption, which has various application scenarios in industry and daily life to reduce noise, e.g., to control the noise of ventilation ducts. Given the high-dimensional design space of the geometric parameters of metamaterial absorbers, optimization techniques can be applied to enable automatic design and enhance efficiency. In this study, a comprehensive methodology is utilized to design ventilated metamaterial absorbers composed of cylindrical arrays of Helmholtz resonators. An inverse design framework is proposed, with input being the objective absorption band and output being the corresponding geometric parameters. Transfer matrix method is employed to perform analytical calculations considering thermoviscous losses; finite element method is utilized to verify analytical solutions; 3D printed structures and impedance tube measurements are used to exprimentally validate the optimized absorption performance. Different optimization techniques are utilized to find the optimal designs, such as sequential quadratic programming, genetic algorithm, simulated annealing, etc. The effectiveness and efficiency of different optimization methods are compared, resulting in suggestions and best practices on the implementation strategy of optimization in the design of acoustic metamaterial absorbers.