We study the ( 1 : s + 1 ) success rule for controlling the population size of the ( 1 , λ ) -EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large s if the fitness landscape is too easy. They conjectured that this problem is worst for the OneMax benchmark, since in some well-established sense OneMax is known to be the easiest fitness landscape. In this paper, we disprove this conjecture. We show that there exist s and ɛ such that the self-adjusting ( 1 , λ ) -EA with the ( 1 : s + 1 ) -rule optimizes OneMax efficiently when started with ɛ n zero-bits, but does not find the optimum in polynomial time on Dynamic BinVal . Hence, we show that there are landscapes where the problem of the ( 1 : s + 1 ) -rule for controlling the population size of the ( 1 , λ ) -EA is more severe than for OneMax . The key insight is that, while OneMax is the easiest function for decreasing the distance to the optimum, it is not the easiest fitness landscape with respect to finding fitness-improving steps.

Black-box complexity theory provides lower bounds for the runtime of black-box optimizers like evolutionary algorithms and other search heuristics and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different classes of algorithms exist, each highlighting a different aspect of the algorithms under considerations. In this work we add to the existing black-box notions a new elitist black-box model , in which algorithms are required to base all decisions solely on (the relative performance of) a fixed number of the best search points sampled so far. Our elitist model thus combines features of the ranking-based and the memory-restricted black-box models with an enforced usage of truncation selection. We provide several examples for which the elitist black-box complexity is exponentially larger than that of the respective complexities in all previous black-box models, thus showing that the elitist black-box complexity can be much closer to the runtime of typical evolutionary algorithms. We also introduce the concept of p-Monte Carlo black-box complexity , which measures the time it takes to optimize a problem with failure probability at most p . Even for small p , the p -Monte Carlo black-box complexity of a function class can be smaller by an exponential factor than its typically regarded Las Vegas complexity (which measures the expected time it takes to optimize ).