We show that for all 1<k≤logn 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/logk) 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(2k) bits.Comment: An extended abstract of this paper has been accepted for inclusion in
the proceedings of the Genetic and Evolutionary Computation Conference (GECCO
2012