Population Sizing for Genetic Programming Based Upon Decision Making

TL;DR

This paper develops a new population sizing formula for genetic programming that accounts for bloat, solution complexity, and building block reuse, supported by empirical analysis on three model problems.

Contribution

It introduces a GP-specific population sizing relationship considering bloat and subsolution reuse, extending prior GA-based models.

Findings

Population size depends on tree size, problem difficulty, and building block probability.

Empirical results validate the population sizing relationship across three model problems.

Analysis highlights the impact of bloat and multiple building block usage on population requirements.

Abstract

This paper derives a population sizing relationship for genetic programming (GP). Following the population-sizing derivation for genetic algorithms in Goldberg, Deb, and Clark (1992), it considers building block decision making as a key facet. The analysis yields a GP-unique relationship because it has to account for bloat and for the fact that GP solutions often use subsolution multiple times. The population-sizing relationship depends upon tree size, solution complexity, problem difficulty and building block expression probability. The relationship is used to analyze and empirically investigate population sizing for three model GP problems named ORDER, ON-OFF and LOUD. These problems exhibit bloat to differing extents and differ in whether their solutions require the use of a building block multiple times.