Metastructures are known to provide considerable vibration attenuation for mechanical systems. With the optimization of the internal geometry of metastructures, the suppression performance of the host structure increases. While the zigzag inserts have been shown to be efficient for vibration attenuation, the geometric properties of the inserts affect the suppression performance in a complex manner when attached to the host structure. This paper presents a genetic algorithm based optimization study conducted to come up with the most efficient geometric properties of the zigzag inserts. The inserts studied in this paper are simply cantilever zigzag structures with a mass attached to the unsupported tips. Numerical simulations are run to show the efficiency of the optimization process.