  A parametric beam lattice model is formulated to analyse the propagation
properties of elastic in-plane waves in an auxetic material based on a
hexachiral topology of the periodic cell, equipped with inertial local
resonators. The Floquet-Bloch boundary conditions are imposed on a reduced
order linear model in the only dynamically active degrees-offreedom. Since the
resonators can be designed to open and shift band gaps, an optimal design,
focused on the largest possible gap in the low-frequency range, is achieved by
solving a maximization problem in the bounded space of the significant
geometrical and mechanical parameters. A local optimized solution, for a the
lowest pair of consecutive dispersion curves, is found by employing the
globally convergent version of the Method of Moving asymptotes, combined with
Monte Carlo and quasi-Monte Carlo multi-start techniques.
