Pareto-Front Exploitation in Symbolic Regression

Abstract

Symbolic regression via genetic programming(hereafter, referred to simply as symbolic regression)has proved to be a very important tool for industrialempirical modelling (Kotanchek et al., 2003). Two ofthe primary problems with industrial use of symbolicregression are (1) the relatively large computationaldemands in comparison with other nonlinear empiricalmodeling techniques such as neural networks and (2) thedifficulty in making the trade-off between expressionaccuracy and complexity. The latter issue issignificant since, in general, we prefer parsimonious(simple) expressions with the expectation that they aremore robust with respect to changes over time in theunderlying system or extrapolation outside the range ofthe data used as the reference in evolving the symbolicregression.In this chapter, we present a genetic programmingvariant, Pareto GP, which exploits the Pareto front todramatically speed the symbolic regression solutionevolution as well as explicitly exploit thecomplexity-performance trade-off. In addition to theimprovement in evolution efficiency, the Pareto frontperspective allows the user to choose appropriatemodels for further analysis or deployment. The Paretofront avoids the need to a priori specify a trade-offbetween competing objectives (e.g. complexity andperformance) by identifying the curve (or surface orhyper-surface) which characterises, for example, thebest performance for a given expression complexity.