a global analysis

Geometric Semantic Genetic Programming (GSGP) is a powerful variant of Genetic Programming (GP) that defines genetic operators inducing unimodal fitness landscapes. 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. The core idea of GSM-LS is to incorporate a linear regression step during mutation, thereby accelerating convergence toward high-quality solutions. While GSM-LS helps the convergence of the evolutionary search, it is prone to overfitting. Thus, it was suggested to apply GSM-LS only for a limited number of generations and then revert 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 investigate several strategies to mitigate overfitting in GSM-LS and GSGP-reg, ranging from simple regularized regression techniques to adaptive methods that estimate overfitting risk at each mutation. The latter approaches partition the training set into two subsets: one used to perform the mutation, and the other to evaluate the risk of overfitting based on the mutation's impact on held-out data. Experimental evaluations across seven real-world regression benchmarks show that, while plain GSGP underperforms on all datasets, methods incorporating local search often achieve significantly better test performance. For example, on the Airfoil dataset, the GSM-LS variant achieves a median RMSE below 10 compared to 30 with standard GSGP. On the LD50 and Bioavailability datasets, the proposed gen and ridge-regularized variants effectively mitigate overfitting, reducing test RMSE by up to 40% relative to baseline GSGP. We conclude that local search, when used with regularization strategies, enhances GSGP's performance and generalization capability across a diverse range of tasks.