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We re-investigate a fundamental question: how effective is crossover inGenetic Algorithms in combining building blocks of good solutions? Althoughthis has been discussed controversially for decades, we are still lacking arigorous and intuitive answer. We provide such answers for royal road functionsand OneMax, where every bit is a building block. For the latter we show thatusing crossover makes every ($\mu$+$\lambda$) Genetic Algorithm at least twiceas fast as the fastest evolutionary algorithm using only standard bit mutation,up to small-order terms and for moderate $\mu$ and $\lambda$. Crossover isbeneficial because it effectively turns fitness-neutral mutations intoimprovements by combining the right building blocks at a later stage. Comparedto mutation-based evolutionary algorithms, this makes multi-bit mutations moreuseful. Introducing crossover changes the optimal mutation rate on OneMax from$1/n$ to $(1+\sqrt{5})/2 \cdot 1/n \approx 1.618/n$. This holds both foruniform crossover and $k$-point crossover. Experiments and statistical testsconfirm that our findings apply to a broad class of building-block functions.

How Crossover Speeds Up Building-Block Assembly in Genetic Algorithms