Geometric Semantic Geometric Programming (GSGP) is one of the most prominent Genetic Programming (GP) variants, thanks to its solid theoretical background, the excellent performance achieved, and the execution time significantly smaller than standard syntax-based GP. In recent years, a new mutation operator, Geometric Semantic Mutation with Local Search (GSM-LS), has been proposed to include a local search step in the mutation process based on the idea that performing a linear regression during the mutation can allow for a faster convergence to good-quality solutions. While GSM-LS helps the convergence of the evolutionary search, it is prone to overfitting. Thus, it was suggested to use GSM-LS only for a limited number of generations and, subsequently, to switch back to standard geometric semantic mutation. A more recently defined variant of GSGP (called GSGP-reg) also includes a local search step but shares similar strengths and weaknesses with GSM-LS. Here we explore multiple possibilities to limit the overfitting of GSM-LS and GSGP-reg, ranging from adaptive methods to estimate the risk of overfitting at each mutation to a simple regularized regression. The results show that the method used to limit overfitting is not that important: providing that a technique to control overfitting is used, it is possible to consistently outperform standard GSGP on both training and unseen data. The obtained results allow practitioners to better understand the role of local search in GSGP and demonstrate that simple regularization strategies are effective in controlling overfitting.

翻译：几何语义遗传编程（GSGP）是最突出的遗传编程（GP）变体之一，这得益于其坚实的理论基础、优异的性能表现以及显著小于基于标准语法的遗传编程的执行时间。近年来，一种新型变异算子——带局部搜索的几何语义变异（GSM-LS）被提出，该算子在变异过程中引入局部搜索步骤，其核心思想是在变异期间执行线性回归可更快地收敛至高质量解。尽管GSM-LS有助于进化搜索的收敛，但它容易陷入过拟合。因此，建议仅在有限代数内使用GSM-LS，随后切换回标准几何语义变异。近期定义的GSGP变体（称为GSGP-reg）同样包含局部搜索步骤，但与GSM-LS具有相似的优缺点。本文探索了多种限制GSM-LS和GSGP-reg过拟合的方法，范围从自适应评估每次变异过拟合风险的策略到简单的正则化回归。结果表明，限制过拟合的具体方法并非关键：只要采用控制过拟合的技术，就能够在训练数据和未见数据上持续优于标准GSGP。所得结果使实践者更深入理解局部搜索在GSGP中的作用，并证明简单的正则化策略能有效控制过拟合。