Additive manufacturing processes such as Selective Laser Melting (SLM) facilitate the generation of complex designs for efficient light weight parts. Regular internal lattice structures are state of the art for the stiffening of hollow components with a load-bearing skin. Parametric unit cells are arrayed regularly in the void of the part and undergo a cross section optimization for the adaptation to local loading conditions. A new method for the construction of irregular lattice structures was developed driven by a density based point distribution algorithm. The points were connected via Delaunay triangulation as well as a selective nearest neighbour search. The resulting lattices were optimized for mass with stiffness and strength constraints and compared to regular grids. The irregular lattice structures were optimized by iteratively adapting the point density to the local stresses. The regular grids were edited by a beam topology optimization (BESO) and a cross section optimization. Furthermore, various 3D grid types were optimized and compared with respect to the mass and the heat conduction in a simplified SLM process step. In 2D and 3D the regular lattices feature lower masses and a higher average utilization than the irregular grids. The inhomogeneous lattices require additional construction effort and do not show a well targeted optimization progress. In a linear static load case the 3D model reached the lowest mass without any lattice structures by pure shell thickness optimization. A new method for the calculation of the mechanical loads induced by the SLM process yielded no meaningful results.