We propose and analyze a self-adaptive version of the $(1,\lambda)$
evolutionary algorithm in which the current mutation rate is part of the
individual and thus also subject to mutation. A rigorous runtime analysis on
the OneMax benchmark function reveals that a simple local mutation scheme for
the rate leads to an expected optimization time (number of fitness evaluations)
of $O(n\lambda/\log\lambda+n\log n)$ when $\lambda$ is at least $C \ln n$ for
some constant $C > 0$. For all values of $\lambda \ge C \ln n$, this
performance is asymptotically best possible among all $\lambda$-parallel
mutation-based unbiased black-box algorithms.
Our result shows that self-adaptation in evolutionary computation can find
complex optimal parameter settings on the fly. At the same time, it proves that
a relatively complicated self-adjusting scheme for the mutation rate proposed
by Doerr, Gie{\ss}en, Witt, and Yang~(GECCO~2017) can be replaced by our simple
endogenous scheme.
On the technical side, the paper contributes new tools for the analysis of
two-dimensional drift processes arising in the analysis of dynamic parameter
choices in EAs, including bounds on occupation probabilities in processes with
non-constant drift.

本文提出了一个自适应版本的 (1,λ) 进化算法，并进行了严格的运行时间分析。结果表明，进化计算中的自适应可以在飞行中找到复杂的最优参数设置。同时，它证明了 Doerr、Gie?en、Witt 和 Yang~(GECCO~2017) 提出的相对复杂的自适应性变异率调整方案可以用我们简单的内生性方案代替。