Toward Measuring the Scaling of Genetic Programming

TL;DR

This paper investigates how the median number of generations in genetic programming scales with problem difficulty, revealing approximate relationships between generations, program density, and system parallelism.

Contribution

It introduces empirical relationships between evolution time, program density, and system structure in genetic programming, extending understanding of scaling behaviors.

Findings

G ~ 1/√D for program-like systems

G ~ 1/(n ln n) for parallel systems

Analysis of anti-parallel systems

Abstract

Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the problem is increased. In these systems, the density D of working programs in the universe of all possible programs is measured. The relationship G ~ 1/sqrt(D) is observed to approximately hold for two program-like systems. For parallel systems (systems that look like several independent programs evolving in parallel), the relationship G ~ 1/(n ln n) is observed to approximately hold. Finally, systems that are anti-parallel are considered.