*multiplicative* if condition (\[eq:multidrift\]) holds for the associated random variables $x^{(t)}:=g(x^{(t)})$.

The advantage of the multiplicative approach is that it allows to use potential functions which are more natural. The most natural potential function, obviously, is the distance of the objective value of the current solution to the optimum. This often is a good choice in the analysis of combinatorial optimization problems. For example, in Section \[sec:combinatorial\] we see that the runtimes of the (1+1) EA on finding a minimum spanning tree, a shortest path tree, or an Euler tour can be bounded by analyzing this potential function.

Another potential function for which drift analysis has been successfully applied is the *distance in the search space* between the current search points and a (global) optimum.

The typical example for this is the drift analysis for linear functions in Section \[sec:linear\], where we use the (weighted) Hamming distance to the optimum as potential for all functions of this class. While being more difficult to analyze, this approach often gives tighter bounds which are independent of range of potential fitness values.

Note that multiplicative drift analysis applies to all situations where previously the so-called *method of expected weight decrease* was used. This 