Population Sizing for Genetic Programming Based on Decision-Making

Abstract

This paper derives a population sizing relationshipfor genetic programming (GP). Following thepopulation-sizing derivation for genetic algorithms inGoldberg, Deb, and Clark (1992), it considers buildingblock decision making as a key facet. The analysisyields a GP-unique relationship because it has toaccount for bloat and for the fact that GP solutionsoften use subsolution multiple times. Thepopulation-sizing relationship depends upon tree size,solution complexity, problem difficulty and buildingblock expression probability. The relationship is usedto analyse and empirically investigate populationsizing for three model GP problems named ORDER, ON-OFFand LOUD. These problems exhibit bloat to differingextents and differ in whether their solutions requirethe use of a building block multiple times.