The incorporation of a Cellular Automata (CA)-like structure into the population of Evolutionary Algorithms (EAs) has been shown to enhance solution quality. However, research on CA-like structures in the context of Genetic Programming (GP) remains limited. This work examines the impact of introducing such structures in Geometric Semantic variants of GP, specifically focusing on the well-established Geometric Semantic GP (GSGP) and the recently proposed SLIM-GSGP, which prioritizes generating smaller and more interpretable individuals. Furthermore, we analyze how cellular structures influence the effectiveness of semantic-based recombination and mutation in both GSGP and SLIM-GSGP. To this end, we conduct a comprehensive evaluation of these genetic operators, examining their effects both individually and in combination. We provide insights into how CA-like structures and semantic genetic operators influence both the quality and size of solutions in GSGP and SLIM-GSGP, offering a clear understanding of the trade-offs associated with these approaches.
