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In this paper, a novel phoxonic crystal (PxC) structure composed of silicon, with optimal dual phononic band gap (PNBG) and photonic band gap (PTBG), is presented. Using the finite element analysis method, both the transmission characteristics and dispersion relation of PNBG and PTBG are calculated, and the existence of dual BGs is demonstrated by the means of the analysis of transmission for the PxC structure. The influences of structural parameters on the dual forbidden band characteristics are further explored, the sensitive structure parameters can be determined: the width of elastic beams, the length of square silicon, and the length of square hole. Using the orthogonal test, 25 experimental runs based on 3-factor and 5-level experiment are performed to finish the numerical experimental design and analysis. Four functional relationships can be acquired between the three sensitive parameters and dual BGs. Finally, the unified objective function method is employed to perform the construction of the single objective optimization model for the purpose of obtaining the optimal dual BGs and the corresponding optimal parameter combinations of the PxC structure. Such scheme can be used as the potential optimization way, which may find wide application in the development and design of PxCs. [ABSTRACT FROM AUTHOR]