Multi-objective Genetic Programming with the Adaptive Weighted Splines Representation for Symbolic Regression

Christian Raymond, Qi Chen, Bing Xue, Mengjie Zhang

Abstract: Genetic Programming (GP) based symbolic regression is prone to generating complex models which often overfit the training data and generalise poorly onto unseen data. To address this issue, many pieces of research have been devoted to controlling the model complexity of GP. One recent work aims to control model complexity using a new representation called Adaptive Weighted Splines. With its semi-structured characteristic, the Adaptive Weighted Splines representation can control the model complexity explicitly, which was demonstrated to be significantly better than its tree-based counterpart at generalising to unseen data. This work seeks to significantly extend the previous work by proposing a multi-objective GP algorithm with the Adaptive Weighted Splines representation, which utilises parsimony pressure to further control the model complexity, as well as improve the interpretability of the learnt models. Experimental results show that, compared with single-objective GP with the Adaptive Weighted Splines and multi-objective tree-based GP with parsimony pressure, the new multi-objective GP method generally obtains superior fronts and produces better generalising models. These models are also significantly smaller and more interpretable.