Semantic Forward Propagation for Symbolic Regression

Abstract

In recent years, a number of methods have been proposed that attempt to improve the performance of genetic programming by exploiting information about program semantics. One of the most important developments in this area is semantic backpropagation. The key idea of this method is to decompose a program into two parts—a subprogram and a context—and calculate the desired semantics of the subprogram that would make the entire program correct, assuming that the context remains unchanged. In this paper we introduce Forward Propagation Mutation, a novel operator that relies on the opposite assumption—instead of preserving the context, it retains the subprogram and attempts to place it in the semantically right context. We empirically compare the performance of semantic backpropagation and forward propagation operators on a set of symbolic regression benchmarks. The experimental results demonstrate that semantic forward propagation produces smaller programs that achieve significantly higher generalization performance.