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Citation

Woodward J (2003) Modularity in Genetic Programming. In: Ryan C, Soule T, Keijzer M, Tsang E, Poli R & Costa E (eds.) Genetic Programming: 6th European Conference, EuroGP 2003 Essex, UK, April 14–16, 2003 Proceedings. Lecture Notes in Computer Science, 2610. 6th European Conference, EuroGP 2003, Essex, UK, 14.04.2003-16.04.2003. Berlin Heidelberg: Springer, pp. 254-263. http://link.springer.com/chapter/10.1007/3-540-36599-0_23#

Abstract
Genetic Programming uses a tree based representation to express solutions to problems. Trees are constructed from a primitive set which consists of a function set and a terminal set. An extension to GP is the ability to define modules, which are in turn tree based representations defined in terms of the primitives. The most well known of these methods is Koza's Automatically Defined Functions. In this paper it is proved that for a given problem, the minimum number of nodes in the main tree plus the nodes in any modules is independent of the primitive set (up to an additive constant) and depends only on the function being expressed. This reduces the number of user defined parameters in the run and makes the inclusion of a hypothesis in the search space independent of the primitive set.