  Sharpness-Aware Minimization (SAM) was recently introduced as a
regularization procedure for training deep neural networks. It simultaneously
minimizes the fitness (or loss) function and the so-called fitness sharpness.
The latter serves as a measure of the nonlinear behavior of a solution and does
so by finding solutions that lie in neighborhoods having uniformly similar loss
values across all fitness cases. In this contribution, we adapt SAM for tree
Genetic Programming (TGP) by exploring the semantic neighborhoods of solutions
using two simple approaches. By capitalizing upon perturbing input and output
of program trees, sharpness can be estimated and used as a second optimization
criterion during the evolution. To better understand the impact of this variant
of SAM on TGP, we collect numerous indicators of the evolutionary process,
including generalization ability, complexity, diversity, and a recently
proposed genotype-phenotype mapping to study the amount of redundancy in trees.
The experimental results demonstrate that using any of the two proposed SAM
adaptations in TGP allows (i) a significant reduction of tree sizes in the
population and (ii) a decrease in redundancy of the trees. When assessed on
real-world benchmarks, the generalization ability of the elite solutions does
not deteriorate.
