Preserving Population Diversity Based on Transformed Semantics in Genetic Programming for Symbolic Regression

Population diversity plays an important role in avoiding premature convergence in evolutionary techniques including genetic programming (GP). Obtaining an adequate level of diversity during the evolutionary process has became a concern of many previous researches in GP. This work proposes a new novelty metric for entropy-based diversity measure for GP. The new novelty metric is based on the transformed semantics of models in GP, where the semantics are the set of outputs of a model on the training data and principal component analysis is used for a transformation of the semantics. Based on the new novelty metric, a new diversity preserving framework, which incorporates a new fitness function and a new selection operator, is proposed to help GP achieve a good balance between the exploration and the exploitation, thus enhancing its learning and generalization performance. Compared with two stat-of-the-art diversity preserving methods, the new method can generalize better and reduce the overfitting trend more effectively in most cases. Further examinations on the properties of the search process confirm that the new framework notably enhances the evolvability and locality of GP.