Additive manufacturing (AM) is known for its high level of design freedom. Especially for the laser-based powder bed fusion of metals, support structures are often still required for printability reasons or increased process reliability. Currently, there is a lack of knowledge about support structure design, leading to the risk of build failures or increased material consumption. The primary aim of this study was the development of an approach for the design of tree-like support structures to achieve the best mechanical behavior of an AM part. For this, experimental studies on the printability, geometrical accuracy and strength of thin struts were performed and an AM process simulation model was set up for four generic overhang geometries. This model was then used for parameter optimization to determine support structure design parameters, resulting in Pareto optimal support designs regarding the support volume and the parts deformation. Measurements of printed samples were used to verify simulation results and the suitability of tree-like support. In addition, two case studies on the additive manufacturing of discontinued spare parts were used for an initial validation of the approach. This research was the first to consider thermal and structural loads in a parameter optimization for the design of support structures with the objective of an increased mechanical behavior of the part. The potential of the presented approach to achieve a successful print on the first attempt was shown by a case study. Further, the presented approach forms the basis for fully automated support generation tools, which require little to no user input.