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arXiv · 2606.13344

Improved Runtime Bound for the $(\mu + 1)$ EA on BinVal

Joris Belder·Johannes Lengler·Raghu Raman Ravi
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Abstract

We study the $(\mu+1)$ EA on the Binary Value function BinVal. We show that it needs at most $O(\mu \log \mu \cdot n \log n)$ function evaluations to find the optimum when $\mu = o(n/\log n)$. This substantially improves upon the recent upper bound of $O(\mu^5 n \log(n/\mu^4))$ by Krejca, Neumann and Witt. Our results hold for several mutation operators including standard bit mutation. In particular, our bound implies that the $(\mu+1)$ EA is at most a factor $O(\log \mu \cdot \log n)$ slower on BinVal than on OneMax.

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Joris Belder, Johannes Lengler, Raghu Raman Ravi. 2026-06-11. Improved Runtime Bound for the $(\mu + 1)$ EA on BinVal. https://arxiv.org/abs/2606.13344

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