Runtime Analysis of Evolutionary Algorithms via Symmetry Arguments

TL;DR

This paper provides a mathematical analysis of a genetic algorithm, showing it requires exponential time to find specific solutions, and improves previous bounds using symmetry arguments.

Contribution

It introduces a new group action-based approach to analyze the runtime of a selection-free genetic algorithm, establishing tighter lower bounds.

Findings

The algorithm takes at least 2^n / 0000 iterations on average.

The new bound applies for all population sizes 0.

Improves previous lower bounds significantly.

Abstract

We use an elementary argument building on group actions to prove that the selection-free steady state genetic algorithm analyzed by Sutton and Witt (GECCO 2019) takes an expected number of $\Omega(2^n / \sqrt n)$ iterations to find any particular target search point. This bound is valid for all population sizes $\mu$. Our result improves over the previous lower bound of $\Omega(\exp(n^{\delta/2}))$ valid for population sizes $\mu = O(n^{1/2 - \delta})$, $0 < \delta < 1/2$.