A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems
This work addresses a specific bottleneck in genetic programming for symbolic regression, offering an incremental improvement over existing methods.
The authors tackled the problem of inefficient search in Linear Genetic Programming (LGP) for symbolic regression by proposing a probabilistic method using Stochastic Context-Free Grammar (SCFG) to guide genetic operators, resulting in statistically better performance on benchmark problems compared to traditional LGP.
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.