The multi-local resonance metamaterial is based on the local resonance mechanism of resonators, effectively blocking wave propagation within multiple resonant frequency ranges, a phenomenon known as band gaps. In practical applications for vibration reduction, the goal is to achieve wide-band vibration attenuation at low frequencies. Therefore, this study aims to improve the vibration reduction performance of multi-local resonance metamaterials by lowering the band gap frequency and expanding the band gap width. To achieve this, an objective function was formulated in the optimization problem, considering both the frequency and width of the band gap, with the geometric shapes of the multiple local resonators selected as design variables. The Sequential Quadratic Programming (SQP) technique was employed for optimization. The results confirmed that the band gap was generated at lower frequencies and that the band gap width was expanded.