Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted. Continuing this research direction, we prove that the NSGA-II optimizes the OneJumpZeroJump benchmark asymptotically faster when crossover is employed. Together with a parallel independent work by Dang, Opris, Salehi, and Sudholt, this is the first time such an advantage of crossover is proven for the NSGA-II. Our arguments can be transferred to single-objective optimization. They then prove that crossover can speed up the $(\mu+1)$ genetic algorithm in a different way and more pronounced than known before. Our experiments confirm the added value of crossover and show that the observed advantages are even larger than what our proofs can guarantee.

翻译：最近,为第二代NSGA-II(最常见的多客观进化算法)首次进行了数学运行时间分析。 继续这一研究方向,我们证明第二代NSGA-II(NSGA-II)在使用交叉重叠时,会以简单更快的速度优化一个JumpZeroJumb基准。 加上Dang、Opris、Salehi和Sudholt(Sudholt)的平行独立工作,这是第一次为第二代NSGA-II(NSGA-II)证明这种交叉重叠的好处。 我们的论点可以转移到单一目标优化。 然后它们证明交叉重叠可以以不同的方式加速( mu+1) $( mu+1) 的遗传算法。 我们的实验证实了交叉重叠的附加值,并表明所观察到的优势甚至比我们的证据能保证的还要大。</s>