In laser-based powder bed fusion of metals (PBF-LB/M), the laser beam shape significantly influences the temperature distribution and melt pool dimensions. Recent advances in beam shaping technology allow for more flexibility in changing the laser beam profile in time and space. For example, ring-shaped and top-hat beam profiles can improve the process efficiency and product quality compared to common Gaussian beam profiles, as they distribute the heat input over a larger area. Non-rotationally symmetric beam shapes are more interesting for homogeneous temperature fields to reduce effects such as spatter formation due to Marangoni flow. Developing new beam profiles by iterative adjustments and repeated experiments is costly, time-consuming, and often not feasible. The presented contribution automates this process using numerical optimization, complementing the experiments with computer simulations that are based on a thermal model with nonlinear material parameters. The optimization uses a gradient-based approach combined with the adjoint state method to compute the sensitivities. The presented inversion framework is verified by choosing the temperature field resulting from a Gaussian beam shape as an optimization target and it is demonstrated that it recovers the original Gaussian shape after only a few iterations. Then, an application of the method is demonstrated by computing an axisymmetric beam shape that corresponds to a melt pool in conduction mode. The model is validated by comparing the computed melt pool shapes to experimentally evaluated melt track cross-sections, where a good agreement is obtained. Finally, the flexibility of the optimization framework is demonstrated by showing optimized laser beam shapes without the axisymmetric constraint of the previous example.