  The advanced data structure of the zero-suppressed binary decision diagram
(ZDD) enables us to efficiently enumerate nonequivalent substitutional
structures. Not only can the ZDD store a vast number of structures in a
compressed manner, but also can a set of structures satisfying given
constraints be extracted from the ZDD efficiently. Here, we present a ZDD-based
efficient algorithm for exhaustively searching for special quasirandom
structures (SQSs) that mimic the perfectly random substitutional structure. We
demonstrate that the current approach can extract only a tiny number of SQSs
from a ZDD composed of many substitutional structures (>$10^{12}$). As a
result, we find SQSs that are optimized better than those proposed in the
literature. A series of SQSs should be helpful for estimating the properties of
substitutional solid solutions. Furthermore, the present ZDD-based algorithm
should be useful for applying the ZDD to the other structure enumeration
problems.
