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}
}
  • Carola Doerr, J. Lengler
  • Published 2016
  • Computer Science, Mathematics
  • Proceedings of the Genetic and Evolutionary Computation Conference 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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This chapter collects several probabilistic tools that have proven to be useful in the analysis of randomized search heuristics. This includes classic material such as the Markov, Chebyshev, andExpand
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The $$(1+1)$$(1+1) Elitist Black-Box Complexity of LeadingOnes
TLDR
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 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. Expand
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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 lookingExpand
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The work of Lehre and Witt (GECCO 2010) on the unbiased black- box model is extended by considering higher arity variation operators by showing 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-i> log <i*n> log<i+i>) in the binary case. Expand
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A new method based on fitness-level partitions and an additional condition on transition probabilities between fitness levels allows us to determine the optimal mutation-based algorithm for LO and OneMax, i.e., the algorithm that minimizes the expected number of fitness evaluations. Expand
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