Improving Genetic Programming for Symbolic Regression of Real-World Design Data

Genetic Programming (GP), especially Geometric Semantic GP (GSGP), has shown great potential in solving numerical benchmarks in Symbolic Regression (SR) domain in recent years. However, its application on real-world problems is still limited due to the large sizes of the resulting expressions, which are prone to over-fitting and are difficult to interpret. In this paper, we suggest a combination of two novel operators for GP that are able to produce accurate expressions while keeping their sizes in check. The first operator utilizes the concept of Semantic Backpropagation, a method to approximate GSGP, to create short expressions which are highly correlated with the outputs. The second operator makes use of Mixed Integer Linear Programming to combine expressions into a final one having extreme accuracy. The proposed approach is tested on one synthetic data set and two real applications, which are the challenging for conventional GP. The experiment results are very promising, with further scope of improvement.