Hybrid Symbolic Regression with the Bison Seeker Algorithm

Abstract

This paper focuses on the use of the Bison Seeker Algorithm (BSA) in a hybrid genetic programming approach for the supervised machine learning method called symbolic regression. While the basic version of symbolic regression optimizes both the model structure and its parameters, the hybrid version can use genetic programming to find the model structure. Consequently, local learning is used to tune model parameters. Such tuning of parameters represents the lifetime adaptation of individuals. This paper aims to compare the basic version of symbolic regression and hybrid version with the lifetime adaptation of individuals via the Bison Seeker Algorithm. Author also investigates the influence of the Bison Seeker Algorithm on the rate of evolution in the search for function, which fits the given input-output data. The results of the current study support the fact that the local algorithm accelerates evolution, even with a few iterations of a Bison Seeker Algorithm with small populations.

Two-layer genetic programming

“…Raidl and Gunther in [11] introduced HGP (hybrid genetic programming), added weights to the top-level tree members and optimized them using a robust least squares method. For example, gradient descent [12,13], simulated annealing combined with the simplex method [14], particle swarm optimization (PSO) [15], multiple regression in the STROGANOFF method [16,17], evolutionary strategies [13,18,19], genetic algorithms [13], self-organizing migrating algorithm (SOMA) [13,20], the Bison Seeker algorithm [21], and non-linear optimization using the Levenberg-Marquardt algorithm [22,23] can be used to optimize the constants. There are many modern approaches for GP optimization.…”