# OneMax in Black-Box Models with Several Restrictions

@article{Doerr2015OneMaxIB, title={OneMax in Black-Box Models with Several Restrictions}, author={Carola Doerr and Johannes Lengler}, journal={Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation}, year={2015} }

As in classical runtime analysis the OneMax problem is the most prominent test problem also in black-box complexity theory. It is known that the unrestricted, the memory-restricted, and the ranking-based black-box complexities of this problem are all of order n/log n, where n denotes the length of the bit strings. The combined memory-restricted ranking-based black-box complexity of OneMax, however, was not known. We show in this work that it is Θ(n) for the smallest possible size bound, that is…

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## 5 Citations

OneMax in Black-Box Models with Several Restrictions

- Mathematics, Computer ScienceAlgorithmica
- 2016

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.

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A rigorous runtime analysis concerning the update strength, a vital parameter in PMBGAs such as the step size 1 / K in the so-called compact Genetic Algorithm and the evaporation factor $$\rho $$ρ in ant colony optimizers (ACO).

Theory of estimation-of-distribution algorithms

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An up-to-date overview of the most commonly analyzed EDAs and the most recent theoretical results in this area is provided, with emphasis put on the runtime analysis of simple univariate EDAs.

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