to determine reasonable values for the usually not explicitly given constants. More precisely, Jägersküpper showed that the expected optimization time of the (1+1) EA for any linear function defined on bit strings of length $n$ is bounded from above by $(1+o(1)) 2.02 {\mathrm{e}\xspace}n \ln(n)$.

Classical Drift Analysis
------------------------

The following method was introduced to the analysis of randomized search heuristics by He and Yao [@HeY04] and builds on a result of Hajek [@Hajek82]. When analyzing the optimization behavior of a randomized search heuristic over a search space, instead of tracking how the objective function improves, one uses an auxiliary potential function and tracks its behavior.

For example, consider the search space $\{0,1\}^n$ of bitstrings of length $n\in\mathbb{N}$.[^2] Suppose we want to analyze the (1+1) EA (which is introduced as Algorithm \[alg:oneoneea\] in Section \[sec:linear\]) minimizing a linear function $f\colon\{0,1\}^n\to\mathbb{R}$ with $$f(x)=\sum_{i=1}^n w_i x_i$$ and arbitrary positive weights $0<w_1\le\dots\le w_n$. (Note that we differ from previous works by always considering minimization problems. See Section \[sec:linear\] for a discussion why this does not influence the runtime analysis.) Then this potential function $h\colon \{0,1\}^n \to \mathbb{R}$ can be chosen as $$\label{eq:logpotential}
h(x)=\ln\Big(1+\sum_{j=1}^{\lfloor \frac{n}{2}\rfloor}x_j+\sum_{j=\lfloor \frac{n}{2}\rfloor +1}^n 2x_j\Big).$$

Though still needing some calculations, one can 