Prioritized grammar enumeration: Symbolic regression by dynamic programming

We introduce Prioritized Grammar Enumeration (PGE), a deterministic Symbolic Regression (SR) algorithm using dynamic programming techniques. PGE maintains the tree-based representation and Pareto non-dominated sorting from Genetic Programming (GP), but replaces genetic operators and random number use with grammar production rules and systematic choices. PGE uses non-linear regression and abstract parameters to fit the coefficients of an equation, effectively separating the exploration for form, from the optimization of a form. Memoization enables PGE to evaluate each point of the search space only once, and a Pareto Priority Queue provides direction to the search. Sorting and simplification algorithms are used to transform candidate expressions into a canonical form, reducing the size of the search space. Our results show that PGE performs well on 22 benchmarks from the SR literature, returning exact formulas in many cases. As a deterministic algorithm, PGE offers reliability and reproducibility of results, a key aspect to any system used by scientists at large. We believe PGE is a capable SR implementation, following an alternative perspective we hope leads the community to new ideas.