A Better Multi-Objective GP-GOMEA -- But do we Need it?

TL;DR

This paper compares single-objective and multi-objective variants of modular GP-GOMEA for symbolic regression, finding the single-objective approach often yields better hypervolume, and explores re-use incentives in multi-objective optimization.

Contribution

It provides a detailed analysis of when single-objective GP-GOMEA outperforms multi-objective versions and introduces an objective to promote re-use in modular GP-GOMEA.

Findings

Single-objective GP-GOMEA achieves higher hypervolume on average.

Multi-objective approach benefits from an archive used only for logging.

Re-use incentives can influence the evolution process.

Abstract

In Symbolic Regression (SR), achieving a proper balance between accuracy and interpretability remains a key challenge. The Genetic Programming variant of the Gene-pool Optimal Mixing Evolutionary Algorithm (GP-GOMEA) is of particular interest as it achieves state-of-the-art performance using a template that limits the size of expressions. A recently introduced expansion, modular GP-GOMEA, is capable of decomposing expressions using multiple subexpressions, further increasing chances of interpretability. However, modular GP-GOMEA may create larger expressions, increasing the need to balance size and accuracy. A multi-objective variant of GP-GOMEA exists, which can be used, for instance, to optimize for size and accuracy simultaneously, discovering their trade-off. However, even with enhancements that we propose in this paper to improve the performance of multi-objective modular GP-GOMEA, when optimizing for size and accuracy, the single-objective version in which a multi-objective archive is used only for logging, still consistently finds a better average hypervolume. We consequently analyze when a single-objective approach should be preferred. Additionally, we explore an objective that stimulates re-use in multi-objective modular GP-GOMEA.