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The design of metamaterials is nowadays an intense field of research. However, most of the metamaterials described in the literature arise from physical intuition, often, assuming infinite periodicity. There is therefore a need for a tool capable of providing patterns and designs involving two materials, combined cleverly in a pixel by pixel finite way, such that we wind up obtaining some effective metamaterial properties. All in all, binary programming techniques need to be considered, in contrast to classic gradient optimization algorithms, which often provide continuous solutions. Nevertheless, the computational complexity of discrete optimization problems is usually NP and thus intractable. In this document, we will present a reduced basis optimization approach involving a generalized binary gradient. Solutions will thus be always binary and, although they might not be global optima, they will be obtained efficiently.

metamaterial design; binary optimization; HDG