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，针对最常见的多目标进化算法NSGA-II首次开展了数学运行时分析。延续这一研究方向，我们证明当采用交叉操作时，NSGA-II能渐近更快地优化OneJumpZeroJump基准问题。与Dang、Opris、Salehi和Sudholt的平行独立工作一道，这是首次为NSGA-II证明交叉操作具有如此优势。我们的论证可迁移至单目标优化，由此证明交叉操作能以不同于已知方式且更显著地加速$(\mu+1)$遗传算法。实验验证了交叉操作的附加价值，并表明实际观测到的优势甚至大于理论证明所能保证的范围。