# Online Diversity Control in Symbolic Regression via a Fast Hash-based Tree Similarity Measure

## TL;DR

This paper introduces a fast hash-based tree similarity measure to efficiently maintain diversity in symbolic regression genetic algorithms, significantly improving search performance.

## Contribution

It presents a novel hash-based tree distance measure that accelerates diversity calculation and integrates it with standard genetic algorithms for better search outcomes.

## Key findings

- Our method outperforms standard GA in benchmark problems.
- The hash-based measure significantly reduces computation time.
- Enhanced diversity leads to improved symbolic regression results.

## Abstract

Diversity represents an important aspect of genetic programming, being directly correlated with search performance. When considered at the genotype level, diversity often requires expensive tree distance measures which have a negative impact on the algorithm's runtime performance. In this work we introduce a fast, hash-based tree distance measure to massively speed-up the calculation of population diversity during the algorithmic run. We combine this measure with the standard GA and the NSGA-II genetic algorithms to steer the search towards higher diversity. We validate the approach on a collection of benchmark problems for symbolic regression where our method consistently outperforms the standard GA as well as NSGA-II configurations with different secondary objectives.