Over the years, the installed capacity of offshore wind turbines is increasing rapidly. However, the Levelized Costs Of Energy (LCOE) is still higher than the LCOE of traditional energy production methods like nuclear power or energy from coals or gas. This research focuses on a further decrease of the LCOE, by minimizing the mass of a monopile support structure of a wind turbine. This is done in a so called integrated way: Optimizing the tower and the foundation together. The design variables used in this research are the wall thickness and the diameter of every +-3 meter section. These can even be cylindrical or conical. To simplify the problem, a parametrization of the designs is used, which reduces the design variables from around 180 to 28. This is checked with existing designs. Due to the interaction between mostly the first eigenfrequency and eigenmode, the diameter and the waves, it is expected that several local optima exist. Therefore, the proposed optimization strategy is a Particle Swarm Optimization which can be used for a global search for an initial position for a gradient based optimization to find a local optimum, which is possibly the global optimum. In this research the focus is on the Particle Swarm Optimization. The constraints of the optimization are Fatigue, Buckling, the maximum deflection of the monopile, the angle of the conical parts and the D/t-ratio of the monopile. These are used in the initial design of support structures, so that the optimized designs are realistic. To take the constraints into account, the objective is taken as the mass extended by the penalized constraints. To reduce the optimization time, the evaluations of the objective function are done by using load estimations instead of extensive load calculations. Several methods are compared on a theoretical basis: Response Surface Methodology, Radial Basis Functions, Kriging, Support Vector Regression, Multi-adaptive Regression Splines and Non-Uniform Regression B-Splines. The performance of a selection of methods is checked on the problem, to come up with reliable estimation methods. To improve the accuracy of the estimations, interaction of Particle Swarm Optimization and the estimators is proposed via estimator updating. During this research, an optimization tool for monopile support structures is developed. This tool is able to use calculations or estimations of the loads. In order to study the behaviour of the proposed optimization approach and to compare it with the traditional design approach, several case studies are formulated based on a realistic design problem. These are optimized with the optimization tool. Using a constant tower diameter, the optimization tool is able to reduce the mass of the support structure with 13\%. Using the tower diameter also as design variable in the optimization gives a further reduction of the mass with 4\%. Several test runs are done, to check whether a global optimum is found or not.