Unbiased black-box complexities of jump functions
Benjamin Doerr, Carola Doerr, Timo Kötzing · 2014
We analyze the unbiased black-box complexity of jump functions with large jump sizes. Among other results, we show that when the jump size is (1/2 - epsilon)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 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 Theta(n-1/2) fraction) is a plateau of constant fitness.