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

This study investigates whether seeding the initial population of a Genetic Programming (GP) system for Symbolic Regression (SR) with high-quality, pre-optimized models improves the final outcome. The authors compare three standard random initialization methods (Grow, PTC-2, and Balanced Tree Creator) against an approach using Exhaustive Symbolic Regression (ESR) to seed the population with the most accurate, algebraically unique models within a specific complexity limit. The researchers evaluated these methods across twelve synthetic problems and one real-world dataset (the Nikuradse friction dataset) using the NSGA-II multi-objective evolutionary algorithm.

The researchers found that while ESR-initialized populations start with a clear advantage in accuracy, this benefit is transient. In almost all cases, the performance gap between the seeded and randomly initialized populations vanishes within a few generations. The evolutionary process, driven by selection, crossover, and mutation, quickly erases the initial bias, leading to final Pareto fronts that are statistically indistinguishable across all tested initialization methods. The only exception was a simple synthetic problem where the ground truth was extremely close to the best ESR-found model, allowing for rapid convergence.

These results suggest that for standard GP-based symbolic regression, the computational overhead of complex population seeding is not justified. Because the evolutionary process is highly effective at exploring the search space and refining models, the specific starting point—provided it maintains sufficient diversity—has a negligible impact on the final results. The authors recommend using computationally inexpensive, balanced initialization methods like BTC or PTC-2, as they provide equivalent performance to more intensive seeding strategies.