Evolutionary Algorithms with Self-adjusting Asymmetric Mutation

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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Evolutionary Algorithms with Self-adjusting Asymmetric Mutation

Cited by 4 publications

References 25 publications

Self-adjusting Population Sizes for the $$(1, \lambda )$$-EA on Monotone Functions

Self-adjusting Population Sizes for the $$(1, \lambda )$$-EA on Monotone Functions

Self-adjusting offspring population sizes outperform fixed parameters on the cliff function

Theoretical and Empirical Analysis of Parameter Control Mechanisms in the (1 + (λ, λ)) Genetic Algorithm

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