In this paper we revisit the question how hard it can be for the \((1+1)\) Evolutionary Algorithm to optimize monotone pseudo-Boolean functions. By introducing a more pessimistic stochastic process, the partially-ordered evolutionary algorithm (PO-EA) model, Jansen first proved a runtime bound of \(O(n^{3/2})\) . More recently, Lengler, Martinsson and Steger improved this upper bound to \(O(n \log ^2 n)\) by an entropy compression argument. In this work, we analyze monotone functions that may adversarially vary at each step of the optimization, so-called dynamic monotone functions. We introduce the function Switching Dynamic BinVal (SDBV) and prove, using a combinatorial argument, that for the \((1 + 1)\) -EA with any mutation rate \(p \in [0,1]\) , SDBV is drift minimizing within the class of dynamic monotone functions. We further show that the \((1 + 1)\) -EA optimizes SDBV in \(\Theta (n^{3/2})\) generations. Therefore, our construction provides the first explicit example which realizes the pessimism of the PO-EA model. Our simulations demonstrate matching runtimes for both the static and the self-adjusting \((1, \lambda )\) -EA and \((1 + \lambda )\) -EA. Moreover, devising an example for fixed dimension, we illustrate that drift minimization does not equal maximal runtime beyond asymptotic analysis.
