Phoxonic crystal (PXC) is a promising artificial periodic material for optomechanical systems and acousto-optical devices. The multi-objective topology optimization of dual phononic and photonic max relative bandgaps in a kind of two-dimensional (2D) PXC is investigated to find the regular pattern of topological configurations. In order to improve the efficiency, a multi-level substructure scheme is proposed to analyze phononic and photonic band structures, which is stable, efficient and less memory-consuming. The efficient and reliable numerical algorithm provides a powerful tool to optimize and design crystal devices. The results show that with the reduction of the relative phononic bandgap (PTBG), the central dielectric scatterer becomes smaller and the dielectric veins of cross-connections between different dielectric scatterers turn into the horizontal and vertical shape gradually. These characteristics can be of great value to the design and synthesis of new materials with different topological configurations for applications of the PXC.
