function, J[ä]{}gersk[ü]{}pper was able to give a meaningful upper bound on the leading constant (cf. Theorem 2 in [@Jagerskupper08]).

\[thm:upperjagerskupper\] For all positive integers $n\in\mathbb{N}$, the expected optimization time of the (1+1) EA minimizing a linear function on $n$ bits is at most of order $(1+o(1)) 2.02 {\mathrm{e}\xspace}n\ln(n)$.

Using multiplicative drift analysis (Theorem \[thm:multidrift\]) on the result of Lemma \[lem:drift\] and thus replacing the halving argument employed by J[ä]{}gersk[ü]{}pper for the proof of Theorem \[thm:upperjagerskupper\], the constant of $2.02 {\mathrm{e}\xspace}$ in the upper bound of the previous theorem instantly improves to $1.39 {\mathrm{e}\xspace}$. In the light of our lower bound of $1.00{\mathrm{e}\xspace}$, to be proven in the next subsection, this is a considerable progress.

\[thm:upperbound\] For all positive integers $n\in\mathbb{N}$, the expected optimization time of the (1+1) EA minimizing a linear function on $n$ bits is at most of order $(1+o(1))\frac{{\mathrm{e}\xspace}}{{\mathrm{e}\xspace}-2}n\ln(n)\approx (1+o(1)) 1.39 {\mathrm{e}\xspace}n\ln(n)$.

The (1+1) EA Optimizes OneMax Faster than any Function with a Unique Global Optimum
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In this section, we show that the expected optimization time of (1+1) EA on any pseudo-Boolean function with a unique global optimum is at least as large as its expected optimization time on the basic function [<span style="font-variant:small-caps;">OneMax</span>]{}. In particular, this 