Research performed under this grant will develop methods to rapidly assess early engineering designs. To assess many designs using conventional approaches requires a significant and often economically infeasible amount of computation. The approach to rapid assessment of early designs to be researched under this grant utilizes set-based representations of early design descriptions thereby permitting approximate assessment of the performance of regions or sets of the design space. This work will extend initial results to efficient mapping of sets in high dimensional design spaces, and to design problems with realistic mappings (nonmonotonic performance evaluation functions). The results of this research will permit engineering designers to rapidly and inexpensively determine the approximate region of performance that a candidate set of designs will exhibit. Set-based design can increase concurrency by permitting information to be passed to downstream or parallel groups as sets of possible designs. These results will permit designers to exchange imprecise, partially complete, design information to accelerate the design process and shorten the engineering design cycle.