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

@article{Doerr2017TheE,
  title={The \$\$(1+1)\$\$(1+1) Elitist Black-Box Complexity of LeadingOnes},
  author={Carola Doerr and J. Lengler},
  journal={Algorithmica},
  year={2017},
  volume={80},
  pages={1579-1603}
}
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 to 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 $$\varOmega (n \log n)$$Ω(nlogn) lower bound for unary unbiased… 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
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
Hyper-heuristics Can Achieve Optimal Performance for Pseudo-Boolean Optimisation
TLDR
This paper generalises the `simple' selection-perturbation mechanisms so success can be measured over some fixed period of time tau, rather than in a single iteration, and rigorously proves that it makes the difference between an efficient and an inefficient algorithm. Expand
Simple Hyper-Heuristics Control the Neighbourhood Size of Randomised Local Search Optimally for LeadingOnes*
TLDR
This article considers the most simple HHs from the literature and rigorously analyse their performance for the LeadingOnes benchmark function, and proves that the Generalised Random Gradient HH has the best possible performance achievable with the low-level heuristics, up to lower-order terms. Expand
Benchmarking discrete optimization heuristics with IOHprofiler
TLDR
This work compiles and assess a selection of 23 discrete optimization problems that subscribe to different types of fitness landscapes, and provides a new module for IOHprofiler which extents the fixed-target and fixed-budget results for the individual problems by ECDF results, which allows one to derive aggregated performance statistics for groups of problems. Expand

References

SHOWING 1-10 OF 23 REFERENCES
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 (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
Ranking-Based Black-Box Complexity
TLDR
A ranking-based black-box algorithm is presented that has a runtime of Θ(n/logn), which shows that the OneMax problem does not become harder with the additional ranking- basedness restriction. Expand
Elitist Black-Box Models: Analyzing the Impact of Elitist Selection on the Performance of Evolutionary Algorithms
TLDR
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
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 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
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
A New Method for Lower Bounds on the Running Time of Evolutionary Algorithms
  • Dirk Sudholt
  • Computer Science, Mathematics
  • IEEE Transactions on Evolutionary Computation
  • 2013
TLDR
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
Faster black-box algorithms through higher arity operators
TLDR
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
Lessons from the black-box: fast crossover-based genetic algorithms
TLDR
A simple genetic algorithm is designed that first creates λ offspring from a single parent by mutation with a mutation probability that is k times larger than the usual one, and is the first time that crossover is shown to give an advantage for the OneMax class that is larger than a constant factor. Expand
...
1
2
3
...