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Black-box complexity theory provides lower bounds for the runtime ofblack-box optimizers like evolutionary algorithms and serves as an inspirationfor the design of new genetic algorithms. Several black-box models coveringdifferent classes of algorithms exist, each highlighting a different aspect ofthe algorithms under considerations. In this work we add to the existingblack-box notions a new \emph{elitist black-box model}, in which algorithms arerequired to base all decisions solely on (a fixed number of) the best searchpoints sampled so far. Our model combines features of the ranking-based and thememory-restricted black-box models with elitist selection.  We provide several examples for which the elitist black-box complexity isexponentially larger than that the respective complexities in all previousblack-box models, thus showing that the elitist black-box complexity can bemuch closer to the runtime of typical evolutionary algorithms.  We also introduce the concept of $p$-Monte Carlo black-box complexity, whichmeasures the time it takes to optimize a problem with failure probability atmost $p$. Even for small~$p$, the $p$-Monte Carlo black-box complexity of afunction class $\mathcal F$ can be smaller by an exponential factor than itstypically regarded Las Vegas complexity (which measures the \emph{expected}time it takes to optimize $\mathcal F$).

Introducing Elitist Black-Box Models: When Does Elitist Selection Weaken the Performance of Evolutionary Algorithms?