Modern synchrotron light source storage rings, such as the Swiss Light Source upgrade (SLS 2.0), use multibend achromats in their arc segments to achieve unprecedented brilliance. This performance comes at the cost of increased focusing requirements, which in turn require stronger sextupole and higher-order multipole fields for compensation of their effects on particles with energy deviation and lead to a considerable decrease in the dynamic aperture and/or energy acceptance. In this paper, to increase these two quantities, a multiobjective genetic algorithm (MOGA) is combined with a modified version of the well-known tracking code _TRACY. As a first approach, a massively parallel implementation of a MOGA is used. Compared to a manually obtained solution this approach yields very good results. However, it requires a long computation time. As a second approach, a surrogate model based on artificial neural networks is used in the optimization. This improves the computation time, but the quality of the results deteriorates beyond that of the manually obtained solution. As a third approach, the surrogate model is retrained during the optimization. This ensures a solution quality comparable to the one obtained with the first approach while also providing an order of magnitude speedup. Finally, good candidate solutions for SLS 2.0 are shown and further analyzed.