Pareto-Front Exploitation in Symbolic Regression

Abstract

Symbolic regression via genetic programming (hereafter, referred to simply as symbolic regression) has proven to be a very important tool for industrial empirical modeling (Kotanchek et al., 2003). Two of the primary problems with industrial use of symbolic regression are (1) the relatively large computational demands in comparison with other nonlinear empirical modeling techniques such as neural networks and (2) the difficulty in making the trade-off between expression accuracy and complexity. The latter issue is significant since, in general, we prefer parsimonious (simple) expressions with the expectation that they are more robust with respect to changes over time in the underlying system or extrapolation outside the range of the data used as the reference in evolving the symbolic regression.

In this chapter, we present a genetic programming variant, ParetoGP, which exploits the Pareto front to dramatically speed the symbolic regression solution evolution as well as explicitly exploit the complexity-performance trade-off. In addition to the improvement in evolution efficiency, the Pareto front perspective allows the user to choose appropriate models for further analysis or deployment. The Pareto front avoids the need to a priori specify a trade-off between competing objectives (e.g. complexity and performance) by identifying the curve (or surface or hyper-surface) which characterizes, for example, the best performance for a given expression complexity.