Due to the growing quest for renewable energy, wind turbines grow in size. This means that higher demands are posed on the transporting structures, also called tower grillages, which brings its challenges for their design. The fact that the structures considered in this thesis are placed on a ship makes the design even more complicated. Therefore, a procedure is developed in this thesis that is able to optimize a tower grillage, while keeping the underlying ship intact. This tool is based on a combination of size and shape optimization. The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition. First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint. After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering. From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not. The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering.