A Systematic Evaluation of Evolving Highly Nonlinear Boolean Functions in Odd Sizes
CoRR(2024)
摘要
Boolean functions are mathematical objects used in diverse applications.
Different applications also have different requirements, making the research on
Boolean functions very active. In the last 30 years, evolutionary algorithms
have been shown to be a strong option for evolving Boolean functions in
different sizes and with different properties. Still, most of those works
consider similar settings and provide results that are mostly interesting from
the evolutionary algorithm's perspective. This work considers the problem of
evolving highly nonlinear Boolean functions in odd sizes. While the problem
formulation sounds simple, the problem is remarkably difficult, and the related
work is extremely scarce. We consider three solutions encodings and four
Boolean function sizes and run a detailed experimental analysis. Our results
show that the problem is challenging, and finding optimal solutions is
impossible except for the smallest tested size. However, once we added local
search to the evolutionary algorithm, we managed to find a Boolean function in
nine inputs with nonlinearity 241, which, to our knowledge, had never been
accomplished before with evolutionary algorithms.
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