# A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems

## TL;DR

This paper introduces a probabilistic linear genetic programming approach using stochastic context-free grammar, which adaptively guides the search process for symbolic regression, outperforming traditional LGP methods.

## Contribution

It proposes integrating a stochastic context-free grammar into linear genetic programming, with an adaptive probability model that improves search efficiency and solution quality.

## Key findings

- Statistically better results than traditional LGP.
- Effective adaptation of grammar to linear representations.
- Improved performance on symbolic regression benchmarks.

## Abstract

Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP) methods were proposed to overcome this issue through a probability model that captures the structure of the fit individuals and use it to sample new individuals. This work proposes the use of LGP with a Stochastic Context-Free Grammar (SCFG), that has a probability distribution that is updated according to selected individuals. We proposed a method for adapting the grammar into the linear representation of LGP. Tests performed with the proposed probabilistic method, and with two hybrid approaches, on several symbolic regression benchmark problems show that the results are statistically better than the obtained by the traditional LGP.