The Effects of Population Size on the Performance of BEAGLE GPU-Based Genetic Programming Runs

2026-04-27

AI Summary

This study systematically investigates the impact of population size on the performance of symbolic regression in GPU-accelerated genetic programming. Leveraging the BEAGLE framework, it presents the first comprehensive evaluation of training efficacy across an unprecedented range of population sizes—from as small as 1,000 to as large as 10,000,000—within a GPU computing environment. The authors introduce a staged population strategy that dynamically adjusts population size during evolution to balance exploration breadth and exploitation depth. Experimental results demonstrate that different symbolic regression problems benefit variably from either broad-and-shallow or narrow-and-deep search regimes. The proposed adaptive strategy effectively reconciles these opposing requirements, significantly enhancing both optimization success rates and algorithmic robustness across diverse problem instances.

Abstract

The Beagle framework, through GPU-based Genetic Programming, enables population dynamics previously unattainable (within practical time frames) by CPU-constrained Genetic Programming systems. This work explores how GPU-enabled population sizes impact the success of training for symbolic regression problems. Specifically, when using constant population sizes, we see benefits of using very narrow and deep searches (as narrow as 1000 individuals) for some problems, while other problems benefit from very broad and shallow searches (as broad as 10 million individuals). We also explore stepped population sizes that start with large populations and drop to small populations to balance the breadth and depth of search.

Problem

• population size
• genetic programming
• symbolic regression
• GPU computing
• search strategy

Innovation

• GPU-based Genetic Programming
• population size
• symbolic regression
• search breadth and depth
• stepped population strategy