Towards a Sound Theory of Adaptation for the Simple Genetic Algorithm

TL;DR

This paper argues that a comprehensive theory explaining the simple genetic algorithm's strong adaptive capacity can overcome current limitations in evolutionary computation and machine learning, challenging existing beliefs about its constraints.

Contribution

It identifies and refutes the supposed limitations of the SGA's adaptability, and proposes a method to analyze its search distribution over generations.

Findings

The SGA's adaptive ability is more powerful than previously believed.

The negative impact of the building block hypothesis (BBH) is overstated.

Conditions are provided for approximating the search distribution of the SGA.

Abstract

The pace of progress in the fields of Evolutionary Computation and Machine Learning is currently limited -- in the former field, by the improbability of making advantageous extensions to evolutionary algorithms when their capacity for adaptation is poorly understood, and in the latter by the difficulty of finding effective semi-principled reductions of hard real-world problems to relatively simple optimization problems. In this paper we explain why a theory which can accurately explain the simple genetic algorithm's remarkable capacity for adaptation has the potential to address both these limitations. We describe what we believe to be the impediments -- historic and analytic -- to the discovery of such a theory and highlight the negative role that the building block hypothesis (BBH) has played. We argue based on experimental results that a fundamental limitation which is widely believed to constrain the SGA's adaptive ability (and is strongly implied by the BBH) is in fact illusionary and does not exist. The SGA therefore turns out to be more powerful than it is currently thought to be. We give conditions under which it becomes feasible to numerically approximate and study the multivariate marginals of the search distribution of an infinite population SGA over multiple generations even when its genomes are long, and explain why this analysis is relevant to the riddle of the SGA's remarkable adaptive abilities.