In embedded system development, specifically in Platform-Based Design (PBD), current Design Space Exploration (DSE) methodologies are challenged by the increasing number of design decisions at multiple abstraction levels, which leads to an explosion of combination of alternatives. However, only a reduced number of these alternatives leads to feasible designs, which fulfill non-functional requirements. Moreover, each design decision influences subsequent decisions and system properties, hence there are inter-dependencies between design decisions, so that the order decisions are made matters to the final system implementation. Furthermore, there is a trade-off between heuristics for specific DSE, which improves the optimization results, and global optimizers, which improve the flexibility to be applied in different DSE scenarios.In order to overcome the identified challenges an MDE methodology for DSE is proposed. For this methodology a DSE Domain metamodel is proposed to represent relevant DSE concepts such as design space, design alternatives, evaluation method, constraints and others. Moreover, this metamodel represents different DSE problems, improving the flexibility of the proposed framework. Model transformations are used to implement DSE rules, which are used to constrain, guide, and generate design candidates. Focusing on the mapping between layers in a PBD approach, a novel design space abstraction is provided to represent multiple design decisions involved in the mapping as a single DSE problem. This abstraction is based on Categorical Graph Product, decoupling the exploration algorithm from the design space and being well suited to be implemented in automatic exploration tools. Upon this abstraction, the DSE method can benefit from the MDE methodology, opening new optimization opportunities, and improving the DSE integration into the development process and specification of DSE scenarios.