Quadratic Bloat in Genetic Programming ¹

W. B. Langdon
Centrum voor Wiskunde en Informatica,
Kruislaan 413, NL-1098 SJ Amsterdam
W. B. Langdon

Abstract:

In earlier work we predicted program size would grow in the limit at a quadratic rate and up to fifty generations we measured bloat O(generations ^1.2-1.5). On two simple benchmarks we test the prediction of bloat O(generations^2.0) up to generation 600. In continuous problems the limit of quadratic growth is reached but convergence in the discrete case limits growth in size. Measurements indicate subtree crossover ceases to be disruptive with large programs (1,000,000) and the population effectively converges (even though variety is near unity). Depending upon implementation, we predict run time O(no. generations ^2.0-3.0) and memory O(no. generations ^1.0-2.0).