Faster black-box algorithms through higher arity operators

Benjamin Doerr, Daniel Johannsen, Timo Kötzing, Per Kristian Lehre, Markus Wagner, Carola Winzen

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 Θ(n2) for unary operators to O(n log n). For OneMax, the Ω(n log n) 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).