# Offspring Population Size Matters when Comparing Evolutionary Algorithms with Self-Adjusting Mutation Rates

## TL;DR

This paper empirically compares different self-adjusting mutation rate strategies in evolutionary algorithms on the OneMax problem, revealing how population size influences their relative performance and the impact of mutation rate bounds.

## Contribution

It provides a comprehensive empirical analysis of self-adjusting mutation rate algorithms across various population sizes and problem scales, highlighting the conditions under which each method excels.

## Key findings

- 2-rate EA performs best for small population sizes.
- Multiplicative update rules outperform for larger population sizes.
- Static mutation rate EA matches self-adjusting algorithms around population size 50.

## Abstract

We analyze the performance of the 2-rate $(1+\lambda)$ Evolutionary Algorithm (EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a $(1+\lambda)$~EA variant using multiplicative update rules on the OneMax problem. We compare their efficiency for offspring population sizes ranging up to $\lambda=3,200$ and problem sizes up to $n=100,000$. Our empirical results show that the ranking of the algorithms is very consistent across all tested dimensions, but strongly depends on the population size. While for small values of $\lambda$ the 2-rate EA performs best, the multiplicative updates become superior for starting for some threshold value of $\lambda$ between 50 and 100. Interestingly, for population sizes around 50, the $(1+\lambda)$~EA with static mutation rates performs on par with the best of the self-adjusting algorithms. We also consider how the lower bound $p_{\min}$ for the mutation rate influences the efficiency of the algorithms. We observe that for the 2-rate EA and the EA with multiplicative update rules the more generous bound $p_{\min}=1/n^2$ gives better results than $p_{\min}=1/n$ when $\lambda$ is small. For both algorithms the situation reverses for large~$\lambda$.