A tight runtime analysis for the (μ + λ) EA

Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of true population-based evolutionary algorithms remains challenging and only few rigorous results exist. Already for the most basic problem, the determination of the asymptotic runtime of the (μ + λ) evolutionary algorithm on the simple OneMax benchmark function, only the special cases μ = 1 and λ = 1 have been solved. In this work, we analyze this long-standing problem and show the asymptotically tight result that the runtime T, the number of iterations until the optimum is found, satisfies [EQUATION] where log+ x := max{1, log x} for all x > 0.

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