Structures whose thickness is tapered according to a power law exhibit the acoustic black hole (ABH) effect and can provide effective vibration absorption with a net reduction in mass. However, it remains unclear what constitutes the best design of ABH vibration absorbers, including how the power-law taper is implemented in practice. This talk will present a formal optimization study of three styles of one-dimensional ABH vibration absorbers. Each ABH is embedded in a simply supported beam, which is excited by a harmonic force at one end. A multi-objective approach is used to identify the set of ABH designs that optimally minimize the structure’s vibration response and its overall mass. Results show that each style has a similar tradeoff between the two objectives but that the choice of how the power-law taper is implemented can be significant. Finally, the optimal designs will be evaluated on other criteria that may be of importance in the practical implementation of such ABH vibration absorbers, including buckling load and sound radiation.