Systematic modeling of architecture design spaces is needed when architecting complex systems, to support experts in making less biased decisions, and to formulate the optimization problem needed to explore the large combinatorial design space. Existing methods do not offer enough compatibility with the Model-Based Systems Engineering (MBSE) approaches, cannot model all needed design scenarios, or are not flexible enough when it comes to architecture evaluation. A new method is presented that provides a semantic representation of the architecture design space, modeled as the Architecture Design Space Graph (ADSG). The ADSG represents three types of architectural decisions: function-component mapping, component characterization, and component connection. The ADSG is constructed from a design space definition, and discrete architectural decisions are automatically inserted according to specified rules. Once decisions and metrics have been defined, the hierarchical, mixed-integer, multi-objective optimization problem can be formulated: decisions are mapped to design variables, and performance metrics are mapped to objectives or constraints. An application of the method to the Apollo mission architecting problem is presented. Nomenclature