On affine symbolic regression trees for the solution of functional problems

Symbolic regression has emerged from the more general method of Genetic Programming (GP) as a means of solving functional problems in physics and engineering, where a functional problem is interpreted here as a search problem in a function space. A good example of a functional problem in structural dynamics would be to find an exact solution of a nonlinear equation of motion. Symbolic regression is usually implemented in terms of a tree representation of the functions of interest; however, this is known to produce search spaces of high dimension and complexity. The aim of this chapter is to introduce a new representation—the affine symbolic regression tree. The search space size for the new representation is derived, and the results are compared to those for a standard regression tree. The results are illustrated by the search for an exact solution to several benchmark problems.