Improving Genetic Programming for Symbolic Regression with Equality Graphs

TL;DR

This paper introduces eggp, a novel method using equality graphs to efficiently avoid revisiting equivalent expressions in genetic programming for symbolic regression, leading to improved performance and more accurate models.

Contribution

The paper presents eggp, an innovative adaptation that leverages equality graphs to enhance genetic programming by reducing redundant evaluations and improving model quality.

Findings

eggP improves performance on small expressions

eggP produces accurate models for benchmarks and real-world data

Efficiently filters out revisited expressions without extra computational cost

Abstract

The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets.