Let $T$ be the optimization time of the $(\mu+1)$ genetic algorithm with crossover probability $p_c$ on $\mathrm{Jump}_k$, started from $\mu$ individuals chosen independently and uniformly at random from $\{0,1\}^n$.

Let $p_c\in(0,1]$ and $a>0$ be constants. If $1\le k\le c\ln\ln n$ for a sufficiently small constant $c>0$, and $Ck(\ln n)^2\le\mu\le n^{a}$ for a sufficiently large constant $C$, then $\mathbb E[T]=O(\mu n)$.

The constants $c$, $C$ and the constant in $O(\mu n)$ depend only on $p_c$ and $a$. The bound holds for all sufficiently large $n$, uniformly in $k$ and $\mu$.