  Boolean functions are mathematical objects with numerous applications in
domains like coding theory, cryptography, and telecommunications. Finding
Boolean functions with specific properties is a complex combinatorial
optimization problem where the search space grows super-exponentially with the
number of input variables. One common property of interest is the nonlinearity
of Boolean functions. Constructing highly nonlinear Boolean functions is
difficult as it is not always known what nonlinearity values can be reached in
practice. In this paper, we investigate the effects of the genetic operators
for bit-string encoding in optimizing nonlinearity. While several mutation and
crossover operators have commonly been used, the link between the genotype they
operate on and the resulting phenotype changes is mostly obscure. By observing
the range of possible changes an operator can provide, as well as relative
probabilities of specific transitions in the objective space, one can use this
information to design a more effective combination of genetic operators. The
analysis reveals interesting insights into operator effectiveness and indicates
how algorithm design may improve convergence compared to an operator-agnostic
genetic algorithm.
