论文标题
跳跃功能上的$（1 +（λ，λ））$ ga的严格运行时分析
A Rigorous Runtime Analysis of the $(1 + (λ, λ))$ GA on Jump Functions
论文作者
论文摘要
$（1 +（λ，λ））$遗传算法是一种年轻的进化算法，试图从下溶液中获利。对单峰健度函数进行严格的运行时分析表明，它确实可以比经典的进化算法更快，尽管在这些简单问题上，收益仅是中等的。 在这项工作中，我们对多模式问题类（跳跃功能基准测试）进行了该算法的第一个运行时分析。我们表明，使用正确的参数，\ ollga优化了任何跳跃尺寸$ 2 \ le K \ le K \ le k \ le n/4 $在预期的时间$ o（n^{（k+1）/2} e^{o（k）k^{ - k^{ - k/2}）$，并且已经很重要，并且已经很重要，并且已经对常量的〜$ k $ offermith ungrith ungrith ungrith ungrith k）基于交叉的算法，其$ \ tilde {o}（n^{k-1}）$运行时保证。 对于离开本地最佳函数的孤立问题，我们确定可证明导致$（n/k）^{k/2} e^{θ（k）} $的最佳参数。这暗示了有关如何设置\ ollga参数的一些一般建议，这可能会减轻此算法的进一步使用。
The $(1 + (λ,λ))$ genetic algorithm is a younger evolutionary algorithm trying to profit also from inferior solutions. Rigorous runtime analyses on unimodal fitness functions showed that it can indeed be faster than classical evolutionary algorithms, though on these simple problems the gains were only moderate. In this work, we conduct the first runtime analysis of this algorithm on a multimodal problem class, the jump functions benchmark. We show that with the right parameters, the \ollga optimizes any jump function with jump size $2 \le k \le n/4$ in expected time $O(n^{(k+1)/2} e^{O(k)} k^{-k/2})$, which significantly and already for constant~$k$ outperforms standard mutation-based algorithms with their $Θ(n^k)$ runtime and standard crossover-based algorithms with their $\tilde{O}(n^{k-1})$ runtime guarantee. For the isolated problem of leaving the local optimum of jump functions, we determine provably optimal parameters that lead to a runtime of $(n/k)^{k/2} e^{Θ(k)}$. This suggests some general advice on how to set the parameters of the \ollga, which might ease the further use of this algorithm.
