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

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