after $X^{(0)}/\delta$ steps the expected potential is zero. Thus, one might expect the expected number of steps until the (random) potential reaches zero to be $X^{(0)}/\delta$, too. This is indeed the case in the setting of the previous theorem.

In order to apply the previous theorem to the analysis of randomized search heuristics over a (finite) search space $\mathcal{S}$, we define a potential function $h\colon\mathcal{S}\to\mathbb{R}$ which maps all optimal search points to zero and all non-optimal search points to values strictly larger than zero. We choose the random variable $X^{(t)}$ as the potential $h(x^{(t)})$ of the search point (or population) in the $t$-th iteration of the algorithm. Then the random variable $T$ becomes the optimization time of the algorithm, that is, the number of iterations until the algorithm finds an optimum.

When applying Theorem \[thm:additivedrift\], we call the expected difference between $h(x^{(t)})$ and $h(x^{(t+1)})$ the *drift* of the random process $\{x^{(t)}\}_{t\in\mathbb{N}}$ with respect to $h$. We say this drift is *additive* if condition (\[eq:additivedrift\]) holds.

Ideal Potential Functions for Additive Drift Analysis
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The application of additive drift analysis (Theorem \[thm:additivedrift\]) to the runtime analysis of randomized search heuristics requires a suitable potential function. The following lemma (Lemma 3 in 