  Bent Boolean functions are important objects in cryptography and coding
theory, and there are several general approaches for constructing such
functions. Metaheuristics proved to be a strong choice as they can provide many
bent functions, even when the size of the Boolean function is large (e.g., more
than 20 inputs). While bent Boolean functions represent only a small part of
all Boolean functions, there are several subclasses of bent functions providing
specific properties and challenges. One of the most interesting subclasses
comprises (anti-)self-dual bent Boolean functions. This paper provides a
detailed experimentation with evolutionary algorithms with the goal of evolving
(anti-)self-dual bent Boolean functions. We experiment with two encodings and
two fitness functions to directly evolve self-dual bent Boolean functions. Our
experiments consider Boolean functions with sizes of up to 16 inputs, and we
successfully construct self-dual bent functions for each dimension. Moreover,
when comparing with the evolution of bent Boolean functions, we notice that the
difficulty for evolutionary algorithms is rather similar. Finally, we also
tried evolving secondary constructions for self-dual bent functions, but this
direction provided no successful results.
