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

@article{Doerr2016TheE, title={The (1+1) Elitist Black-Box Complexity of LeadingOnes}, author={Carola Doerr and J. Lengler}, journal={Proceedings of the Genetic and Evolutionary Computation Conference 2016}, year={2016} }

One important goal of black-box complexity theory is the development of complexity models allowing to derive meaningful lower bounds for whole classes of randomized search heuristics. Complementing classical runtime analysis, black-box models help us understand how algorithmic choices such as the population size, the variation operators, or the selection rules influence the optimization time. One example for such a result is the Ω(n log n) lower bound for unary unbiased algorithms on functions… Expand

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#### 13 Citations

The $$(1+1)$$(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 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. Expand

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This work experiments with a multiplicative, comparison-based update rule to adjust the mutation probability of a (1+1)~Evolutionary Algorithm and shows that this simple self-adjusting rule outperforms the best static unary unbiased black-box algorithm on LeadingOnes, achieving an almost optimal speedup. Expand

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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 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. Expand

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