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The self-adjusting (1+( λ , λ )) GA is the best known genetic algorithm for problems with a good fitness-distance correlation as in OneMax . It uses a parameter control mechanism for the parameter  λ that governs the mutation strength and the number of offspring. However, on multimodal problems, the parameter control mechanism tends to increase λ uncontrollably. We study this problem for the standard \({Jump}_k \) benchmark problem class using runtime analysis. The self-adjusting (1+( λ , λ )) GA behaves like a (1+ n ) EA whenever the maximum value for λ is reached. This is ineffective for problems where large jumps are required. Capping λ at smaller values is beneficial for such problems. Finally, resetting λ to 1 allows the parameter to cycle through the parameter space. We show that resets are effective for all \({Jump}_k \) problems: the self-adjusting (1+( λ , λ )) GA performs as well as the (1+1) EA with the optimal mutation rate and evolutionary algorithms with heavy-tailed mutation, apart from a small polynomial overhead. Along the way, we present new general methods for translating existing runtime bounds from the (1+1) EA to the self-adjusting (1+( λ , λ )) GA. We also show that the algorithm presents a bimodal parameter landscape with respect to λ on \({Jump}_k \) . For appropriate n and k , the landscape features a local optimum in a wide basin of attraction and a global optimum in a narrow basin of attraction. To our knowledge this is the first proof of a bimodal parameter landscape for the runtime of an evolutionary algorithm on a multimodal problem.

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