Support structure design for Laser Powder Bed Fusion has received little attention in Design for Additive Manufacturing although its importance for a successful and efficient build job. The resulting knowledge insufficiency on support design can lead to in-process failures of the build. Also, parts can crack due to high, unaccounted residual stresses. This, and overestimated support designs, lead to an increased manufacturing time and cost. The presented research contributes to a better understanding of support structure design by developing a workflow for the design of tree-like support structure and its subsequent meta-model based parameter optimisation. The design parameters of resulting support structures for two generic geometries in a cantilever shape with a planar and an arched down-facing surface are compared with each other, showing consistent values for the minimum distance between branches and the branch length. These and other design parameters govern the geometry of the tree-like structure within the design space. An additionally performed sensitivity study revealed high correlations of the stem diameter with the part's displacements. Based on 500 individual support designs and the meta-model evaluation of 9000 parameter sets, a Pareto frontier emerges for the trade-off between the minimum support structure volume and the part's displacements.