Multi-junction solar cells allow to utilize sunlight more effectively than single junction solar cells. In this work, we present optical simulations of III-V-on-silicon solar cells with a metal grating at the back, which experimentally have reached more than 33% power conversion efficiency. First, we perform simulations with the finite element method and compare them with experimental data to validate our model. We find that accurately modeling the investigated geometrical structure is necessary for best agreement between simulation and experimental measurements. Then, we optimize the grating for maximized light trapping using a computationally efficient Bayesian optimization algorithm. The photo current density of the limiting silicon bottom cell is improved from 13.48 mA/cm² for the experimental grating to 13.85 mA/cm² for the optimized metal grating. Investigation of all geometrical optimization parameters of the grating (period, height,…) shows that the structure is most sensitive towards the period, a parameter highly controllable in manufacturing by inference lithography. The results show a pathway to exceed the current world record efficiency of the III-V-on-silicon solar cell technology.