During the development process of complex embedded systems there typically is a large number of architectural decisions that engineers are facing. Each of them can influence the properties of the end result (i.e.: cost, performance, etc.). A systematic process that supports this decision making is often referred to as Design Space Exploration (DSE). The need for computer-aided DSE methods was recognized by the research community which resulted in a large number of publications in this area. The contribution of this PhD project is two-fold: First contribution is a classification of typical DSE problems that arise during the development process of embedded systems. Due their high popularity in this area the focus of this work lies on the model-based approaches. The second contribution is two provide a decomposition approach for complex DSE problems. The decomposition strategy is thereby based on the previously identified DSE problem classes.