# Ranking-Based Black-Box Complexity

@article{Doerr2012RankingBasedBC, title={Ranking-Based Black-Box Complexity}, author={Benjamin Doerr and Carola Doerr}, journal={Algorithmica}, year={2012}, volume={68}, pages={571-609} }

Randomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a growing field. While several strong runtime analysis results have appeared in the last 20 years, a powerful complexity theory for such algorithms is yet to be developed. We enrich the existing notions of black-box complexity by the additional restriction… Expand

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#### 39 Citations

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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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This work proposes a new elitist black-box model, in which algorithms are required to base all decisions solely on (a fixed number of) the best search points sampled so far, and introduces the concept of $p-Monte Carlo black- box complexity, which measures the time it takes to optimize a problem with failure probability at most p. Expand

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The elitist model is added, in which algorithms are required to base all decisions solely on (the relative performance of) a fixed number of the best search points sampled so far, and the concept of p-Monte Carlo black-box complexity is introduced, which measures the time it takes to optimize a problem with failure probability at most p. Expand

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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. Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

Towards a Complexity Theory of Randomized Search Heuristics: Ranking-Based Black-Box Complexity

- Computer Science, Mathematics
- CSR
- 2011

This work enrichs the two existing black-box complexity notions due to Wegener and other authors by the restrictions that not actual objective values, but only the relative quality of the previously evaluated solutions may be taken into account by the algorithm. Expand

A New Framework for the Valuation of Algorithms for Black-Box Optimization

- Mathematics, Computer Science
- FOGA
- 2002

It can be concluded that randomized search heuristics whose (worst-case) expected optimization time for some problem is close to the black-box complexity of the problem are provably efficient (in theblack-box scenario). Expand

Black-Box Search by Unbiased Variation

- Computer Science, Mathematics
- GECCO '10
- 2010

This paper introduces a more restricted black-box model for optimisation of pseudo-Boolean functions which it is claimed captures the working principles of many randomised search heuristics including simulated annealing, evolutionary algorithms, randomised local search, and others. Expand

Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

- Computer Science, Mathematics
- Theory of Computing Systems
- 2004

Lower bounds on the black-box complexity of problems are derived without complexity theoretical assumptions and are compared with upper bounds in this scenario. Expand

Too fast unbiased black-box algorithms

- Mathematics, Computer Science
- GECCO '11
- 2011

This work gives mutation-only unbiased black-box algorithms having complexity O(n log n) for the classical JumpK test function class and for a subclass of the well-known Partition problem. Expand

Black-box search by elimination of fitness functions

- Mathematics, Computer Science
- FOGA '09
- 2009

Though in its early stages, it is believed that there is utility in search methods based on ideas from the elimination of functions method, and that the viewpoint provides promise and new insight about black-box optimization. Expand

General Lower Bounds for Evolutionary Algorithms

- Mathematics, Computer Science
- PPSN
- 2006

It is proved that, at least in some particular cases, using the full ranking information can improve these lower bounds, and ultimately provide superlinear convergence results. Expand

Algorithmics for hard problems - introduction to combinatorial optimization, randomization, approximation, and heuristics

- Computer Science
- 2001

This book discusses thoroughly all of the above approaches to attack hard problems in an absolutely fascinating way that can serve as a pattern for theory textbooks with a high level of generality. Expand

New upper and lower bounds for randomized and quantum local search

- Mathematics, Computer Science
- STOC '06
- 2006

A new quantum algorithm using O(☂n(log log n)<sup>1.5</sup>) queries is given, which improves the previous best known upper bound of O(n<sup>(n/3) (Aaronson, [2]), and implies that Local Search on grids exhibits different properties in low dimensions. Expand

Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem

- Computer Science
- GECCO
- 2004

It is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms. Expand