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

ACM Transactions on Evolutionary Learning and Optimization 2023年第4期2卷 1–39页

作者： Hevia Fajardo, Mario Alejandro Sudholt, Dirk Department of Computer Science University of Sheffield Sheffield United Kingdom Chair of Algorithms for Intelligent Systems University of Passau Passau Germany

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 *** study this problem for the standard Jumpk 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 Jumpk 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 *** 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 Jumpk. 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. © 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM.

关键词： Genetic algorithms

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