# Exploration and Exploitation in Symbolic Regression using Quality-Diversity and Evolutionary Strategies Algorithms

## TL;DR

This paper presents a hybrid approach combining Genetic Programming, MAP-Elites, and Covariance Matrix Adaptation Evolution Strategy to improve exploration and success rates in symbolic regression, effectively solving multiple benchmark problems.

## Contribution

The paper introduces a novel combination of algorithms that enhances exploration and diversity in symbolic regression, achieving high success rates on standard benchmarks.

## Key findings

- High success rates in symbolic regression benchmarks
- Effective exploration and diversity preservation
- Successful evaluation of multiple targets from literature

## Abstract

By combining Genetic Programming, MAP-Elites and Covariance Matrix Adaptation Evolution Strategy, we demonstrate very high success rates in Symbolic Regression problems. MAP-Elites is used to improve exploration while preserving diversity and avoiding premature convergence and bloat. Then, a Covariance Matrix Adaptation-Evolution Strategy is used to evaluate free scalars through a non-gradient-based black-box optimizer. Although this evaluation approach is not computationally scalable to high dimensional problems, our algorithm is able to find exactly most of the $31$ targets extracted from the literature on which we evaluate it.