  Over the past decade, evolutionary algorithms, data mining, and other methods
showed great success in solving the main problem of theoretical
crystallography: finding the stable structure for a given chemical composition.
Here we develop a method that addresses the central problem of computational
materials science: the prediction of material(s), among all possible
combinations of all elements, that possess the best combination of target
properties. This nonempirical method combines our new coevolutionary approach
with the carefully restructured "Mendelevian" chemical space, energy filtering,
and Pareto optimization to ensure that the predicted materials have optimal
properties and a high chance to be synthesizable. The first calculations,
presented here, illustrate the power of this approach. In particular, we find
that diamond (and its polytypes, including lonsdaleite) are the hardest
possible materials and that bcc-Fe has the highest zero-temperature
magnetization among all possible compounds.
