Nanostructured front surface is an important method to improve the photovoltaic performances. Different nanostructure characteristics, which include the reflectance of nanostructure at a wavelength of 0.35-1.1 mu m (R-a,R-0.35-1.1), the polarization sensitivity, the reflectance of nanostructure at a wavelength of 1.1-2.5 mu m (R-a,R-1.1-2.5), and the surface area enhancement ratio (A(r)), have different effects on photovoltaic performances. Therefore, the investigation of the coupling effects of the nanostructure characteristics on photovoltaic performances is an important way to optimize nanostructures. However, there is multi-physics coupling problem in this investigation. Hence, a multi-physics mathematical model is developed and applied in the physical model of an all-back-contact silicon solar cell with nanostructured front surface. Three types of nanostructures are chosen in this study. The grating with rectangle section and moth-eye nanostructures have their own advantages (easy processing and excellent anti-reflection). By combining the advantages of the two types of nanostructures, the grating with parabola section is proposed. The dimensions of the three nanostructures are determined by the height H, the bottom width (diameter), and the spacing L between the two adjacent nanostructures. Through analyzing nanostructure characteristics of each type of nanostructure with 22,386 different dimensions, it is found the grating with parabola section nanostructure not only has relatively lower R-a,R-0.35-1.1, but also has an advantage in the variation trend of the R-a,R-0.35-1.1 due to the polarization sensitivity. In addition, its A(r) is the lowest, and it is also not sensitive to the variation of the dimension as same as its R-a,R-1.1-2.5. In this case, comparing to moth-eye with excellent anti-reflection, the grating with parabola section nanostructure not only has an absolute advantage in open circuit voltage and fill factor due to temperature, but also has comprehensive advantage in short circuit current, which make it have best performance in maximum output power density. Based on the analyses, a clear optimization proposal for nanostructures is proposed, and in the end, its effectiveness is verified in the actual environment through dynamic analysis.