Non-existence of linear universal drift functions

Drift analysis is a powerful tool to prove upper and lower bounds on the runtime of randomized search heuristics. Its most famous application is a simple proof for the classical problem how the (1+1) Evolutionary Algorithm (EA) optimizes linear pseudo-Boolean functions. A relatively simple potential function allows to track the progress of the EA optimizing any linear function. In this work, we show that such beautiful proofs cease to exist if the mutation probability is slightly larger than the standard value of 1/n.