Faster Black-Box Algorithms Through Higher Arity Operators

Abstract: We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box model by considering higher arity variation operators. In particular, we show that already for binary operators the black-box complexity of \leadingones drops from $\Theta(n^2)$ for unary operators to $O(n \log n)$. For \onemax, the $\Omega(n \log n)$ unary black-box complexity drops to O(n) in the binary case. For $k$-ary operators, $k \leq n$, the \onemax-complexity further decreases to $O(n/\log k)$.