Designs to be manufactured by Additive Manufacturing (AM) are subject to geometrical restrictions which are necessary to guarantee successful production. This makes it necessary to modify the obtained topology optimized design such that it is manufacturable. By doing this the optimality of the structure can be reduced. To achieve a manufacturable design directly from the topology optimization requires the incorporation of such a geometrical restriction directly into the optimization process. This research has been carried out to develop a method to do so. The manufacturing constraint being implemented is that a structure should be self-supporting. For this to be the case overhanging features in the design must be at an angle of at least 45 degrees with respect to the base plate. Three approaches have been formulated and investigated: (1)a multiple objective, (2)global constraint and (3)a density filter. A global measure has been formulated for the multiple objective and the global constraint and a filtering scheme for the density filter. The three approaches have been implemented into a 2D optimization code written in MATLAB. Three predictable reference models have been used to test the suitability of each method. The results show that the multiple objective and the global constraint remain potential candidates but further investigation is needed to determine proper parameter values. The topologies obtained with these approaches were modified to partially meet the manufacturing constraint but remained with overhanging features. The filtering method produced topologies that had no overhanging features. The design was a compromise between slight alterations and the introduction of support structures. This approach however showed instabilities that are directly linked to the proposed filtering scheme. True convergence was not achieved with any of the approaches. The filtering approach provides a proof of concept for the inclusion of the 45 degree overhang restriction but further development is needed. The other two approaches are also potential candidates for inclusion of the restriction.