Exposing a Bias Toward Short-Length Numbers in Grammatical Evolution

Many automatically-synthesized programs have, like their hand-made counterparts, numerical parameters that need to be set properly before they can show an acceptable performance. Hence, any approach to the automatic synthesis of programs needs the ability to tune numerical parameters efficiently. Grammatical Evolution (GE) is a promising grammar-based genetic programming technique that synthesizes numbers by concatenating digits. In this paper, we show that a naive application of this approach can lead to a serious number length bias that in turn affects efficiency. The root of the problem is the way the context-free grammar used by GE is defined. A simple, yet effective, solution to this problem is proposed.