Drift analysis yields E(T) bounded between sum 1/Δ(k) minus c1 log n and sum 1/Δ(k) minus c2 log n, with the difference exactly (e/2) log n + O(1) for the (1+1) EA on OneMax from n/2 ones.
Probabilistic analysis of the (1+1)-evolutionary algorithm
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abstract
We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations for the mean and the variance represent the strongest of their kind. The approach we develop is also applicable to characterize the limit laws and is based on asymptotic resolution of the underlying recurrence. While most approximations have their simple formal nature, we elaborate on the delicate error analysis required for rigorous justifications.
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cs.NE 1years
2019 1verdicts
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Sharp Bounds on the Runtime of the (1+1) EA via Drift Analysis and Analytic Combinatorial Tools
Drift analysis yields E(T) bounded between sum 1/Δ(k) minus c1 log n and sum 1/Δ(k) minus c2 log n, with the difference exactly (e/2) log n + O(1) for the (1+1) EA on OneMax from n/2 ones.