An encoding scheme for generating λ-expressions in genetic programming

Abstract

To apply genetic programming (GP) to evolve λ-expressions, we devised an encoding scheme that encodes λ-expressions into trees. This encoding has closure property, i.e., any combination of terminal and non-terminal symbols forms a valid λ-expression. We applied this encoding to a simple symbolic regression problem over Church numerals and the objective function f(x) = 2x was successfully obtained. This encoding scheme will provide a good foothold for exploring fundamental properties of GP by making use of lambda-calculus. © Springer-Verlag Berlin Heidelberg 2003.