A geometric semantic macro-crossover operator for evolutionary feature construction in regression

Evolutionary feature construction has been successfully applied to various scenarios. In particular, multi-tree genetic programming-based feature construction methods have demonstrated promising results. However, existing crossover operators in multi-tree genetic programming mainly focus on exchanging genetic materials between two trees, neglecting the interaction between multi-trees within an individual. To increase search effectiveness, we take inspiration from the geometric semantic crossover operator used in single-tree genetic programming and propose a macro geometric semantic crossover operator for multi-tree genetic programming. This operator is designed for feature construction, with the goal of generating offspring containing informative and complementary features. Our experiments on 98 regression datasets show that the proposed geometric semantic macro-crossover operator significantly improves the predictive performance of the constructed features. Moreover, experiments conducted on a state-of-the-art regression benchmark demonstrate that multi-tree genetic programming with the geometric semantic macro-crossover operator can significantly outperform all 22 machine learning algorithms on the benchmark.