Metamaterials (MMs) are composites that are artificially engineered to have unconventional mechanical properties that stem from their microstructural geometry rather than from their chemical composition. Several studies have shown the effectiveness of viscoelastic MMs in vibration attenuation due to their inherent vibration dissipation properties and the Bragg scattering effect. This study presents a multiobjective optimization based on genetic algorithms (GA) that aims to find a viscoelastic MM crystal with the highest vibration attenuation in a chosen low-frequency range. A multiobjective optimization allows considering the attenuation due to the MM inertia versus the Bragg scattering effect resulting from the periodicity of the MM. The investigated parameters that influence wave transmission in a one-dimensional (1D) MM crystal included the lattice constant, the number of cells and the layers' thickness. Experimental testing and finite element analysis were used to support the optimization procedure. An electrodynamic shaker was used to measure the vibration transmission of the three control specimens and the optimal specimen in the frequency range 1-1200 Hz. The test results demonstrated that the optimized specimen provides better vibration attenuation than the control specimens by both having a band-gap starting at a lower frequency and having less transmission at its passband.