We analyze the unbiased black-box complexity of jump functions with small,
medium, and large sizes of the fitness plateau surrounding the optimal
solution.
Among other results, we show that when the jump size is (1/2−ε)n, that is, only a small constant fraction of the fitness values
is visible, then the unbiased black-box complexities for arities 3 and higher
are of the same order as those for the simple \textsc{OneMax} function. Even
for the extreme jump function, in which all but the two fitness values n/2
and n are blanked out, polynomial-time mutation-based (i.e., unary unbiased)
black-box optimization algorithms exist. This is quite surprising given that
for the extreme jump function almost the whole search space (all but a
Θ(n−1/2) fraction) is a plateau of constant fitness.
To prove these results, we introduce new tools for the analysis of unbiased
black-box complexities, for example, selecting the new parent individual not by
comparing the fitnesses of the competing search points, but also by taking into
account the (empirical) expected fitnesses of their offspring.Comment: This paper is based on results presented in the conference versions
[GECCO 2011] and [GECCO 2014