Symbolic Regression Using Dynamic Structured Grammatical Evolution with Digit Concatenation and Linear Scaling

Symbolic Regression’s vast search space can lead to computational inefficiencies. However, Grammatical Evolution (GE) narrows down the search by focusing on solutions adhering to specific grammar and guiding the algorithm toward more promising regions. Dynamic Structured Grammatical Evolution (DSGE), a variant of GE, enables the evolution of variable-length structures, addressing the issue of finding concise and interpretable solutions as problem complexity increases. Integrating constants is challenging, as disruption of values may occur. DSGE, by using digit concatenation as a constant creation method, enables better preservation and accurate representation of constant values during the evolutionary process. The evolved equations can overfit in certain cases. The search algorithm mitigates overfitting by incorporating Linear Scaling with error minimization, prioritizing equations with lower errors to promote better generalization and produce more reliable models. Experiments were demonstrated on the Feynman equations, one of the benchmark datasets. The combined methodology results in capturing the exact and symbolically equivalent equations. These findings highlight the potential of the proposed approach for symbolic regression and related problems.