A structural optimization framework integrating the receptance method (RM) is developed to enhance the dynamic stability of a plane-grating monochromator (PGM). Three vertical geometric dimensions are selected as physically interpretable design variables. The plane-mirror angular vibration under ambient ground excitation is minimized directly in the geometric design space, so resonance and antiresonance features are modified implicitly, without prescribing modal targets. The meta-model of optimal prognosis (MOP) surrogates, selected using the coefficient of prognosis (CoP), enables global sensitivity analysis (SA) and surrogate-assisted multi-objective evolutionary optimization with a limited number of finite element (FE) evaluations. The SA identifies D₂ as the dominant driver of the mirror angular response, with D₃ providing secondary tuning and D₁ remaining nearly neutral within the investigated range. In the FE simulations, the optimized geometry reduces the peak angular vibration by 19.8% and the root mean square (RMS) angular vibration by 37.5%. Under identical ground microvibration excitations, laser Doppler vibrometer (LDV) measurements show a 22.8% reduction in the RMS. Receptance comparisons further confirm suppressed resonance peaks and a lower high-frequency response envelope after optimization. These results provide a practical and physically transparent method for improving the dynamic stability of complex optical systems.