This paper proposes a framework for generating design concepts through the loop of comprehensive exploitation and consequent exploration. The former is by any sophisticated optimization such as topology optimization with diversely different. The latter realization is due to the variational deep embedding (VaDE), a deep learning technique with classification capability. In the process of design concept generation first, exploitation through computational optimization generates various possibilities of design entities. Second, VaDE learns them. This learning encodes the clusters of similar entities over the latent space with smaller dimensions. The clustering result reveals some design concepts and identifies voids where as-yet-unrecognized design concepts are prospective. Third, the decoder of the learned VaDE generates some possibilities for new design entities. Forth such new entities are examined, and relevant new conditions will trigger further exploitation by the optimization. In this paper, this framework is implemented for and applied to the conceptual design problem of bridge structures. This application demonstrates that the framework can identify voids over the latent space and explore the possibility of new concepts. This paper brings up some discussion on the promises and possibilities of the proposed framework.