Reducing the Arity in Unbiased Black-Box Complexity

Benjamin Doerr; Carola Winzen

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arXiv · 1203.4111

Reducing the Arity in Unbiased Black-Box Complexity

Benjamin Doerr·Carola Winzen

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Abstract

We show that for all $1<k \leq \log n$ 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.

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Benjamin Doerr, Carola Winzen. 2012-03-19. Reducing the Arity in Unbiased Black-Box Complexity. https://arxiv.org/abs/1203.4111

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