In this paper, we present a generative design optimization (GDO) approach for additive manufacturing (AM) by using topology optimization, support vector machines, cellular lattice structures (CLS), design of experiments, morphing and metamodel-based design optimization. By starting from appropriate design domains, a trade-off curve of design concepts is generated by SIMP-based topology optimization (TO). Then, a smooth implicit representation of the TO-solution is established by classifying the discrete density values using soft non-linear support vector machines (SVM). Instead of using the standard soft non-linear SVM of Cortez and Vapnik, we classify the TO solutions by using the 1-norm SVM of Mangasarian. In such manner, the classification is obtained by linear programming instead ofquadratic programming. The implicit SVM-model is further modified by incorporating cellular lattice structures, such as e.g. Gyroid lattice structures, by applying boolean operators. Design of experiments using finite element analysis are then set up by morphing the CLS-modified SVM models for different volume fractions. Finally, metamodel-based design optimization is performed by using optimal ensembles of polynomial regression models, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression. The steps presented above constitute our proposed generative design optimization approach for additive manufacturing and are presented in more detail in the paper.