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The $(1 + (\lambda,\lambda))$ genetic algorithm is a younger evolutionaryalgorithm trying to profit also from inferior solutions. Rigorous runtimeanalyses on unimodal fitness functions showed that it can indeed be faster thanclassical evolutionary algorithms, though on these simple problems the gainswere only moderate.  In this work, we conduct the first runtime analysis of this algorithm on amultimodal problem class, the jump functions benchmark. We show that with theright parameters, the \ollga optimizes any jump function with jump size $2 \lek \le n/4$ in expected time $O(n^{(k+1)/2} e^{O(k)} k^{-k/2})$, whichsignificantly and already for constant~$k$ outperforms standard mutation-basedalgorithms with their $\Theta(n^k)$ runtime and standard crossover-basedalgorithms with their $\tilde{O}(n^{k-1})$ runtime guarantee.  For the isolated problem of leaving the local optimum of jump functions, wedetermine provably optimal parameters that lead to a runtime of $(n/k)^{k/2}e^{\Theta(k)}$. This suggests some general advice on how to set the parametersof the \ollga, which might ease the further use of this algorithm.

A Rigorous Runtime Analysis of the $(1 + (\lambda, \lambda))$ GA on Jump Functions