  In this paper we present a comprehensive study on the multi-objective
optimization of two-dimensional porous phononic crystals (PnCs) in both square
and triangular lattices with the reduced topology symmetry of the unit-cell.
The fast non-dominated sorting-based genetic algorithm II is used to perform
the optimization, and the Pareto-optimal solutions are obtained. The results
demonstrate that the symmetry reduction significantly influences the optimized
structures. The physical mechanism of the optimized structures is analyzed.
Topology optimization combined with the symmetry reduction can discover new
structures and offer new degrees of freedom to design PnC-based devices.
Especially, the rotationally symmetrical structures presented here can be
utilized to explore and design new chiral metamaterials.
