A Systematic Evaluation of Evolving Highly Nonlinear Boolean Functions in Odd Sizes
Created by W.Langdon from
gp-bibliography.bib Revision:1.8415
- @InProceedings{carlet:2025:EuroGP,
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author = "Claude Carlet and Marko Durasevic and
Domagoj Jakobovic and Stjepan Picek and Luca Mariot",
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title = "A Systematic Evaluation of Evolving Highly Nonlinear
Boolean Functions in Odd Sizes",
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booktitle = "European Conference on Genetic Programming, EuroGP
2025",
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year = "2025",
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editor = "Bing Xue and Luca Manzoni and Illya Bakurov",
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volume = "15609",
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series = "LNCS",
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pages = "18--34",
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address = "Trieste",
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month = "23-25 " # apr,
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publisher = "Springer Nature",
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keywords = "genetic algorithms, genetic programming, Boolean
functions, nonlinearity, evolutionary algorithms, odd
dimension, encodings",
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isbn13 = "978-3-031-89990-4",
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URL = "
https://www.human-competitive.org/sites/default/files/humies_entry_2025.txt",
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URL = "
https://human-competitive.org/sites/default/files/a_systematic_evaluation_of_evolving_highly_nonlinear_boolean_functions_in_odd_sizes.pdf",
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URL = "
https://rdcu.be/ejgAa",
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DOI = "
doi:10.1007/978-3-031-89991-1_2",
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size = "17 pages",
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abstract = "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 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 GP outperforms other EA in evolving highly
nonlinear functions. Nevertheless, 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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notes = "Entered 2025 HUMIES
also known as
\cite{paper_144_nonlinear_boolean_functions_in_odd_sizes}
Part of \cite{Xue:2025:GP} EuroGP'2025 held in
conjunction with EvoCOP2025, EvoMusArt2025 and
EvoApplications2025",
- }
Genetic Programming entries for
Claude Carlet
Marko Durasevic
Domagoj Jakobovic
Stjepan Picek
Luca Mariot
Citations