Geometric Semantic Genetic Programming with Perpendicular Crossover and Random Segment Mutation for Symbolic Regression

Geometric semantic operators have been a rising topic in genetic programming (GP). For the sake of a more effective evolutionary process, various geometric search operators have been developed to utilise the knowledge acquired from inspecting the behaviours of GP individuals. While the current exact geometric operators lead to over-grown offsprings in GP, existing approximate geometric operators never consider the theoretical framework of geometric semantic GP explicitly. This work proposes two new geometric search operators, i.e. perpendicular crossover and random segment mutation, to fulfil precise semantic requirements for symbolic regression under the theoretical framework of geometric semantic GP. The two operators approximate the target semantics gradually and effectively. The results show that the new geometric operators bring a notable benefit to both the learning performance and the generalisation ability of GP. In addition, they also have significant advantages over Random Desired Operator, which is a state-of-the-art geometric semantic operator.