The prediction of the hemodynamics (blood flow) in larger arteries using numerical simulation can help in several clinically relevant situations. One field of application are implants such as stent, stent-grafts and bypass-grafts. Further, cardiovascular assistant devices and external pumps for hemoydialysis can be targeted. In all such application, a flow in a moving domain must be considered to obtain accurate predictions and if soft vessel walls (biological or artificial) are involved, the elastic deformation must be considered as well. Beyond the prediction of hemodynamic quantities for a given implant or device, numerical simulations can also be used to optimize their design with respect to certain risk factors based on, e.g, wall-shear stress related quantities. To this end, the risk factor is considered as an objective function that is minimized using gradient based steepest descent methods. A derivative of the objective function is derived using the continuous adjoint method, which yields discretization independent expressions for the derivative. In each optimization iteration, the primal problem and the adjoint problem are solved, before the derivative is evaluated and the solution of an auxiliary problem yields the desired gradient. In the presentation we will elaborate on the algorithmic design of the sketched optimization method for fluid-structure interaction problem and explore the possibility to employ reduced models for a more efficient computation of the derivative. As an exemplary application we consider the shape optimization of the connection region between a bypass-graft and an artery, which known as an anastomosis. Anastomoses are prone to abnormal growth of the vessel wall due to irregular wall-shear stresses and their optimization constitutes an active and clinically relevant field of research.