# Faster black-box algorithms through higher arity operators

@inproceedings{Doerr2011FasterBA, title={Faster black-box algorithms through higher arity operators}, author={Benjamin Doerr and Daniel Johannsen and Timo K{\"o}tzing and P. Lehre and Markus Wagner and Carola Doerr}, booktitle={Foundations of Genetic Algorithms}, year={2011} }

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(<i>n</i><sup>2</sup>) for unary operators to <i>O</i>(<i>n</i> log <i>n</i>). For OneMax, the Ω(<i>n</i> log <i>n</i>) unary black-box complexity drops to <i>O</i>(<i>n</i>) in the binary case. For <i>k</i>-ary operators, <i>k</i> ≤ <i>n</i>, the OneMax…

## 56 Citations

### Reducing the arity in unbiased black-box complexity

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### The (1+1) Elitist Black-Box Complexity of LeadingOnes

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The permutation- and bit-invariant version of LeadingOnes is regarded and it is proved that its (1+1) elitist black-box complexity is Ω(n2), a bound that is matched by (1-1)-type evolutionary algorithms.

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This work shows that the (1+1) memory-restricted ranking-based black-box complexity of OneMax is linear, and provides improved lower bounds for the complexity of the OneMax in the regarded models.

### The $$(1+1)$$(1+1) Elitist Black-Box Complexity of LeadingOnes

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- 2017

The permutation- and bit-invariant version of LeadingOnes is regarded and it is proved that its(1+1) elitist black-box complexity is VarOmega (n^2)Ω(n2), a bound that is matched by(1-1)-type evolutionary algorithms, a bound which shows that for LeadingOns the memory-restriction, together with the selection requirement, has a substantial impact on the best possible performance.

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We show that the unrestricted black-box complexity of the n-dimensional XOR- and permutation-invariant LeadingOnes function class is O(n log(n) / loglogn). This shows that the recent natural looking…

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It is shown that when the jump size is (1/2 - epsilon)n, that is, only a small constant fraction of the fitness values is visible, then the unbiased black-box complexities for arities 3 and higher are of the same order as those for the simple OneMax function.

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