Modular Multi-Tree Genetic Programming for Evolutionary Feature Construction for Regression

Evolutionary feature construction is a key technique in evolutionary machine learning, with the aim of constructing high-level features that enhance performance of a learning algorithm. In real-world applications, engineers typically construct complex features based on a combination of basic features, re-using those features as modules. However, modularity in evolutionary feature construction is still an open research topic. This paper tries to fill that gap by proposing a modular and hierarchical multitree genetic programming (GP) algorithm that allows trees to use the output values of other trees, thereby representing expressive features in a compact form. Based on this new representation, we propose a macro parent-repair strategy to reduce redundant and irrelevant features, a macro crossover operator to preserve interactive features, and an adaptive control strategy for crossover and mutation rates to dynamically balance the trade-off between exploration and exploitation. A comparison with seven bloat control methods on 98 regression datasets shows that the proposed modular representation achieves significantly better results in terms of test performance and smaller model size. Experimental results on the state-of-the-art symbolic regression benchmark demonstrate that the proposed symbolic regression method outperforms 22 existing symbolic regression and machine learning algorithms, providing empirical evidence for the superiority of the modularized evolutionary feature construction method.