Abstract: Much deformation of the large aperture mirror by deadweight leads to large PV (peak-to-valley) value of its aperture surface, and it is hard to ensure the point accuracy on laser beams of optical facility. Finite element model is built up to calculate the PV value of the mirror surface in this paper. Moreover, parameters including position and size of erection column as well as the mirror thickness are optimized in order to minimize the PV value of the aperture surface. Both the direct optimization based on finite element model and the optimization based on surrogate model are adopted herein, and the PV value is reduced by 74% of its initial value as a result. In contrast to direct optimization, optimization based on surrogate model conveniently provides the objective variation with design variables and sensitivity analysis as well, which brings much benefit for structure design. In case of numerous and wide-range design variables, it is suggested to firstly decrease the design range according to prior knowledge or low-fidelity surrogate model and then optimize the parameters based on high-fidelity surrogate model within the shrunk range in order to avoid large amount of calculation. Furthermore, a scheme of four-cylinder support is recommended to replace the three-cylinder support for smaller PV value according to the optimization result.