Neutral Fitness Landscape in the Cellular Automata Majority Problem

TL;DR

This paper analyzes the complex fitness landscape of the cellular automata majority problem, revealing high neutrality and identifying a key subspace called the 'Olympus' where optimal solutions tend to concentrate.

Contribution

It provides a detailed characterization of the fitness landscape, highlighting the role of neutrality and introducing the 'Olympus' subspace as a focus for solution concentration.

Findings

High neutrality in the fitness landscape explains search difficulty.

The 'Olympus' subspace contains most good solutions.

Quantitative measures characterize the 'Olympus' and landscape complexity.

Abstract

We study in detail the fitness landscape of a difficult cellular automata computational task: the majority problem. Our results show why this problem landscape is so hard to search, and we quantify the large degree of neutrality found in various ways. We show that a particular subspace of the solution space, called the "Olympus", is where good solutions concentrate, and give measures to quantitatively characterize this subspace.