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 %connection between the geometry of the fitness
landscape measure of the nonlinear behavior of a solution %and generalization
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.

通过利用两种简单的方法来利用程序树的输入和输出进行扰动，适应性最小化（SAM）被用于树形遗传编程（TGP）来估计锋利度并用作进化过程中的第二个优化标准。实验结果表明，在 TGP 中使用任何两种提议的 SAM 改进方法都能显著减少种群中的树大小，并减少树中的冗余。在真实世界的基准测试中，精英解的泛化能力不会下降。