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Maxime Larcher
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Publisher: Journals Gateway
Evolutionary Computation 1–28.
Published: 05 August 2024
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We study the ( 1 : s + 1 ) success rule for controlling the population size of the ( 1 , λ ) -EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large s if the fitness landscape is too easy. They conjectured that this problem is worst for the OneMax benchmark, since in some well-established sense OneMax is known to be the easiest fitness landscape. In this paper, we disprove this conjecture. We show that there exist s and ɛ such that the self-adjusting ( 1 , λ ) -EA with the ( 1 : s + 1 ) -rule optimizes OneMax efficiently when started with ɛ n zero-bits, but does not find the optimum in polynomial time on Dynamic BinVal . Hence, we show that there are landscapes where the problem of the ( 1 : s + 1 ) -rule for controlling the population size of the ( 1 , λ ) -EA is more severe than for OneMax . The key insight is that, while OneMax is the easiest function for decreasing the distance to the optimum, it is not the easiest fitness landscape with respect to finding fitness-improving steps.