Average Convergence Rate of Evolutionary Algorithms

TL;DR

This paper introduces a new, simple measure called average convergence rate to evaluate how quickly evolutionary algorithms approach the optimum, applicable to various types of optimization problems.

Contribution

It proposes the average convergence rate as a novel, normalized measure and provides theoretical analysis including bounds and asymptotic behavior for discrete optimization.

Findings

The average convergence rate is easy to compute and broadly applicable.

Lower bounds on the convergence rate are derived.

Asymptotic behavior of the convergence rate is analyzed.

Abstract

In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average convergence rate. It is a normalised geometric mean of the reduction ratio of the fitness difference per generation. The calculation of the average convergence rate is very simple and it is applicable for most evolutionary algorithms on both continuous and discrete optimization. A theoretical study of the average convergence rate is conducted for discrete optimization. Lower bounds on the average convergence rate are derived. The limit of the average convergence rate is analysed and then the asymptotic average convergence rate is proposed.