no code implementations • 21 Jun 2019 • Hsien-Kuei Hwang, Carsten Witt
This paper revisits drift analysis for the (1+1) EA on OneMax and obtains that the expected running time $E(T)$, starting from $\lceil n/2\rceil$ one-bits, is determined by the sum of inverse drifts up to logarithmic error terms, more precisely $$\sum_{k=1}^{\lfloor n/2\rfloor}\frac{1}{\Delta(k)} - c_1\log n \le E(T) \le \sum_{k=1}^{\lfloor n/2\rfloor}\frac{1}{\Delta(k)} - c_2\log n,$$ where $\Delta(k)$ is the drift (expected increase of the number of one-bits from the state of $n-k$ ones) and $c_1, c_2 >0$ are explicitly computed constants.
