Geometric Semantic Crossover with an Angle-Aware Mating Scheme in Genetic Programming for Symbolic Regression

Recent research shows that incorporating semantic knowledge into the genetic programming (GP) evolutionary process can improve its performance. This work proposes an angle-aware mating scheme for geometric semantic crossover in GP for symbolic regression. The angle-awareness guides the crossover operating on parents which have a large angle between their relative semantics to the target semantics. The proposed idea of angle-awareness has been incorporated into one state-of-the-art geometric crossover, the locally geometric semantic crossover. The experimental results show that, compared with locally geometric semantic crossover and the regular GP crossover, the locally geometric crossover with angle-awareness not only has a significantly better learning performance but also has a notable generalisation gain on unseen test data. Further analysis has been conducted to see the difference between the angle distribution of crossovers with and without angle-awareness, which confirms that the angle-awareness changes the original distribution of angles by decreasing the number of parents with zero degree while increasing their counterparts with large angles, leading to better performance.