Reducing the Arity in Unbiased Black-Box Complexity

Abstract

We show that for all 1<k ≤q \log n the k-ary unbiased black-box complexity of the n-dimensional \onemax function class is O(n/k). This indicates that the power of higher arity operators is much stronger than what the previous O(n/\log k) bound by Doerr et al. (Faster black-box algorithms through higher arity operators, Proc. of FOGA 2011, pp. 163--172, ACM, 2011) suggests. The key to this result is an encoding strategy, which might be of independent interest. We show that, using k-ary unbiased variation operators only, we may simulate an unrestricted memory of size O(2^k) bits