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Boolean functions are mathematical objects with numerous applications indomains like coding theory, cryptography, and telecommunications. FindingBoolean functions with specific properties is a complex combinatorialoptimization problem where the search space grows super-exponentially with thenumber of input variables. One common property of interest is the nonlinearityof Boolean functions. Constructing highly nonlinear Boolean functions isdifficult as it is not always known what nonlinearity values can be reached inpractice. In this paper, we investigate the effects of the genetic operatorsfor bit-string encoding in optimizing nonlinearity. While several mutation andcrossover operators have commonly been used, the link between the genotype theyoperate on and the resulting phenotype changes is mostly obscure. By observingthe range of possible changes an operator can provide, as well as relativeprobabilities of specific transitions in the objective space, one can use thisinformation to design a more effective combination of genetic operators. Theanalysis reveals interesting insights into operator effectiveness and indicateshow algorithm design may improve convergence compared to an operator-agnosticgenetic algorithm.

Digging Deeper: Operator Analysis for Optimizing Nonlinearity of Boolean Functions