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={FOGA '11},
  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… Expand
Reducing the arity in unbiased black-box complexity
TLDR
It is shown that the power of higher arity operators is much stronger than what the previous O(n/k) bound by Doerr et al. suggests, and the key to this result is an encoding strategy, which might be of independent interest. Expand
Reducing the arity in unbiased black-box complexity
Abstract We show that for all 1 k ≤ log n the k-ary unbiased black-box complexity of the n-dimensional OneMax function class is O ( n / k ) . This indicates that the power of higher arity operatorsExpand
Better fixed-arity unbiased black-box algorithms
TLDR
This paper proposes an alternative strategy for achieving this unbiased black-box complexity of OneMax when 3 ≤ k ≤ log2 n, and constitutes an algorithm which is conceptually simpler than the one by Doerr and Doerr, and in the same time achieves better constant multiples in the asymptotic notation. Expand
The (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 Ω(n2), a bound that is matched by (1-1)-type evolutionary algorithms. Expand
OneMax in Black-Box Models with Several Restrictions
TLDR
This work shows that the (μ+λ) elitist memory-restricted ranking-based black-box complexity of OneMax is as small as (an advanced version of) the information-theoretic lower bound, and enlivens the quest for natural evolutionary algorithms optimizing OneMax in o(n log n) iterations. Expand
Parallel Black-Box Complexity With Tail Bounds
TLDR
The main result is a general performance limit: it is proved that on every function, the typical optimization time on unimodal and multimodal problems, for the time to find any local optimum, and for the times to even get close to any optimum are reduced. Expand
OneMax in Black-Box Models with Several Restrictions
TLDR
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
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
Black-Box Complexity: Breaking the O(n logn) Barrier of LeadingOnes
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
Unbiased black-box complexities of jump functions: how to cross large plateaus
TLDR
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. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
Black-Box Search by Unbiased Variation
TLDR
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
Black-box search by elimination of fitness functions
TLDR
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
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
TLDR
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
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
List of Figures. List of Tables. Preface. Contributing Authors. Series Foreword. Part I: Foundations. 1. An Introduction to Evolutionary Algorithms J.A. Lozano. 2. An Introduction to ProbabilisticExpand
On the analysis of the (1+1) evolutionary algorithm
TLDR
A step towards a theory on Evolutionary Algorithms, in particular, the so-called (1+1) evolutionary Algorithm, is performed and linear functions are proved to be optimized in expected time O(nlnn) but only mutation rates of size (1/n) can ensure this behavior. Expand
Crossover can provably be useful in evolutionary computation
TLDR
This is the first theoretical analysis proving the usefulness of crossover for a non-artificial problem and it is shown that the natural evolutionary algorithm for the all-pairs shortest path problem is significantly faster with a crossover operator than without. Expand
Ant colony optimization
TLDR
A forage harvester includes four multiple-bladed rotary cutting segments positioned near a shearbar, each including a permanent magnet and a sensing coil to monitor only selected one or ones of the cutting segments. Expand
Swarm intelligence
Introduction to algorithms [2nd ed.]
...
1
2
...