Complexity Measures for Multi-objective Symbolic Regression

TL;DR

This paper investigates various complexity measures for multi-objective symbolic regression using NSGA-II, introducing a novel semantic-based measure and analyzing its impact on model accuracy and complexity trade-offs.

Contribution

It presents a new semantic complexity measure for symbolic regression and evaluates its effectiveness compared to existing measures.

Findings

Semantic complexity measure influences search direction.

New measure improves trade-off between accuracy and simplicity.

Benchmark results show varying effects of different complexity measures.

Abstract

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity. In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.