Evolvability Degeneration in Multi-Objective Genetic Programming for Symbolic Regression

TL;DR

This paper identifies that low-complexity models in multi-objective genetic programming for symbolic regression over-replicate due to lack of evolvability, and proposes evoNSGA-II, an improved algorithm that tracks and limits models based on evolvability to enhance diversity and performance.

Contribution

The paper introduces evoNSGA-II, a novel extension of NSGA-II that incorporates evolvability tracking to improve diversity and effectiveness in multi-objective genetic programming.

Findings

evoNSGA-II outperforms or matches existing approaches in most tests

Models with higher evolvability dominate the population

Evolvability tracking reduces over-replication of low-complexity models

Abstract

Genetic programming (GP) is one of the best approaches today to discover symbolic regression models. To find models that trade off accuracy and complexity, the non-dominated sorting genetic algorithm II (NSGA-II) is widely used. Unfortunately, it has been shown that NSGA-II can be inefficient: in early generations, low-complexity models over-replicate and take over most of the population. Consequently, studies have proposed different approaches to promote diversity. Here, we study the root of this problem, in order to design a superior approach. We find that the over-replication of low complexity-models is due to a lack of evolvability, i.e., the inability to produce offspring with improved accuracy. We therefore extend NSGA-II to track, over time, the evolvability of models of different levels of complexity. With this information, we limit how many models of each complexity level are allowed to survive the generation. We compare this new version of NSGA-II, evoNSGA-II, with the use of seven existing multi-objective GP approaches on ten widely-used data sets, and find that evoNSGA-II is equal or superior to using these approaches in almost all comparisons. Furthermore, our results confirm that evoNSGA-II behaves as intended: models that are more evolvable form the majority of the population.