Recursion-Based Biases in Stochastic Grammar Model Genetic Programming

Abstract—Estimation of distribution algorithms applied to genetic programming have been studied by a number of authors. Like all estimation of distribution algorithms, they suffer from biases induced by the model building and sampling process. However, the biases are amplified in the algorithms for genetic programming. In particular, many systems use stochastic grammars as their model representation, but biases arise due to grammar recursion. We define and estimate the bias due to recursion in grammar-based estimation of distribution algorithms in genetic programming, using methods derived from computational linguistics. We confirm the extent of bias in some simple experimental examples. We then propose some methods to repair this bias. We apply the estimation of bias, and its repair, to some more practical applications. We experimentally demonstrate the extent of bias arising from recursion, and the performance improvements that can result from correcting it.