On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism

TL;DR

This paper provides a rigorous runtime analysis of the clearing diversity-preserving mechanism, demonstrating its efficiency in optimizing certain functions with phenotypic distances and highlighting its practical characteristics through empirical analysis.

Contribution

It offers the first theoretical proof of clearing's polynomial runtime performance on specific functions, contrasting phenotypic and genotypic distances, and supports findings with empirical data.

Findings

Phenotypic distance enables polynomial-time optimization of unitation functions.

Genotypic distance leads to exponential runtime in similar scenarios.

Clearing effectively finds multiple optima in bimodal functions like Twomax.

Abstract

Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis has been focused on experimental approaches that have shown that clearing is a powerful diversity-preserving mechanism. Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic distance function always succeeds in optimising all functions of unitation for small niches in polynomial time, while a genotypic distance function requires exponential time. Finally, we prove that with phenotypic and genotypic distances clearing is able to find both optima for Twomax and several general classes of bimodal functions in polynomial expected time. We use empirical analysis to highlight some of the characteristics that makes it a useful mechanism and to support the theoretical results.