We describe an architecture for exploring very large design spaces, for example, spaces that arise when design candidates are generated by combining components systematically from component libraries. A very large number of candidates are methodically considered and evaluated. This architecture is especially appropriate during the stage of conceptual design when high-level design decisions are under consideration, multiple evaluation criteria apply, and a designer seeks assurance that good design possibilities have not been overlooked. We present a filtering technique based on a dominance criterion that can be used to select, from millions of design candidates, a relatively small number of promising candidates for further analysis. The dominance criterion is lossless in that it insures that each candidate not selected is inferior to at least one of the selected candidates. We also describe an interactive interface in which the selected designs are presented to the designer for analysis of tradeoffs and further exploration. In our current implementation, the computational load is distributed among a large number of workstations in a client-server computing environment. We describe the results of experiments using the architecture to explore designs for hybrid electric vehicles. In a recent experiment more than two million distinct designs were evaluated.