Evaluation of Population Initialization Methods for Genetic Programming-based Symbolic Regression

2026-06-30

AI Summary

This study investigates the impact of population initialization methods on the performance of genetic programming for symbolic regression. Within the NSGA-II multi-objective evolutionary framework, it systematically compares three random initialization strategies against an initialization based on small-scale optimized solutions from Exhaustive Symbolic Regression (ESR) across multiple synthetic and real-world datasets. The findings reveal that although ESR-based initialization offers a modest advantage in early evolutionary stages, the choice of initialization strategy does not significantly affect the accuracy or complexity of the final Pareto front; differences between strategies vanish within a few generations. These results challenge the common assumption that sophisticated initialization substantially enhances symbolic regression performance, suggesting instead that the structure of the initial population has limited influence on long-term evolutionary outcomes.

Abstract

We analyze the effect of optimizing the initial population of genetic programming (GP) for symbolic regression (SR) on the accuracy and complexity of solutions. We compare three well-established random initialization methods as well as initialization with small optimized solutions from exhaustive symbolic regression (ESR) using a GP/SR implementation which is based on the multi-objective evolutionary algorithm NSGA-II. We compare the final Pareto fronts found with each initialization method on twelve synthetic problems of varying complexity and one real-world dataset. We find no significant differences in accuracy or model complexity among the initialization methods. The initial advantage of initialization with ESR disappears after only a few generations. Our results show that, given similar diversity in the initial population, the effect of the initialization method in GP-based symbolic regression on the final Pareto front is negligible.

Problem

• genetic programming
• symbolic regression
• population initialization
• NSGA-II
• Pareto front

Innovation

• genetic programming
• symbolic regression
• population initialization
• NSGA-II
• Pareto front