Table 1 SR methods overview

GP

[15] (1994)

Application of GP to SR

APF-FE

[25, 26] (2009, 2011)

Age-fitness Pareto optimization approach using co-evolved fitness estimation

APF

[16] (2010)

Age-fitness Pareto optimization approach

FFX

[33] (2011)

The fast function extraction algorithm – non-evolutionary technique based on a machine learning technique called path-wise regularized learning

ABCP

[17] (2012)

Artificial bee colony programming approach

EPLEX

[32] (2016)

A parent selection method called \(\epsilon\)-lexicase selection

MRGP

[34] (2014)

It decouples and linearly combines a program’s subexpressions via multiple regression on the target variable

Local optimization NLS

[18] (2018)

Constants optimization in GP by nonlinear least squares

FEAT

[35] (2018)

Features are represented as networks of multi-type expression trees comprised of activation functions; differentiable features are trained via gradient descent

SBP-GP

[24] (2019)

The idea of semantic back-propagation utilized in GP

BSR

[27] (2019)

ML-based approach; Bayesian symbolic regression

DSR

[28] (2019)

Deep symbolic regression based on a RNN approach further utilizing the policy gradient search

Operon

[22] (2020)

Utilizing nonlinear least squares for parameter identification of SR models with LS

OccamNet

[30] (2020)

A fast neural network approach; the model defines a probability distribution over a non-differentiable function space; it samples functions and updates the weights with back-propagation based on cross-entropy matching in an EA strategy

AI-Feynman

[3] (2020)

A physics-inspired divide-and-conquer method; it also uses neural network fitting

GOMEA

[19] (2021)

A model-based EA framework called gene-pool optimal mixing evolutionary algorithm

ITEA

[20] (2021)

EA based approach called the interaction-transformation EA

SA

[21] (2021)

Simulated annealing approach