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Existing Design Space Exploration (DSE) frameworks are tailored specifically to a particular problem domain and cannot be easily re-used between domains. Typically these frameworks translate the DSE problem to a single formulation of the problem (e.g. ILP or CSP) and then solve it to retrieve satisfying alternatives. In order to compare the efficiency of different formulations/techniques on a given problem, the domain-expert has to manually reformulate the problem in another constraint language, which is time-consuming. In order to overcome this lack of reusability and flexibility in the current frameworks, we present here the Generic Design Space Exploration (GDSE) framework that allows the designer to solve DSE problems from different domains. Rather than using one strict formulation of the design problem, the framework supports a higher level formulation that can be mapped to different low level encodings. The main contributions of this framework are: 1) a generic representation which can be used to express any DSE problem, and 2) a flexible exploration technique which supports several exploration techniques.