Faster Black-Box Algorithms Through Higher Arity Operators

摘要

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 Θ(n2) for unary operators to O(nlogn). For OneMax; the Ω(nlogn) unary black-box complexity drops to O(n) in the binary case. For k-ary operators, k ≥ n, the OneMax-complexity further decreases to O(n/log k).