A design space analyzer generates a parametric model associated with a design problem. The design space analyzer then discretizes various parameters associated with the model and generates a plurality of sample designs using different combinations of discretized parameters. The design space analyzer also computes one or more metrics for each sample design. In this fashion, the design space analyzer generates a coarse approximation of the design space associated with the design problem. The design space analyzer then evaluates portions of that approximation, at both global and local scales, to identify portions of the design space that meet certain feasibility criteria. Finally, the design space analyzer modifies the design space to facilitate more efficient exploration during optimization.