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

@inproceedings{Droste2002ANF, title={A New Framework for the Valuation of Algorithms for Black-Box Optimization}, author={Stefan Droste and T. Jansen and Karsten Tinnefeld and Ingo Wegener}, booktitle={FOGA}, year={2002} }

Black-box optimization algorithms optimize a fitness function f without knowledge of the specific parameters of the problem instance. Their run time is measured as the number of f -evaluations. This implies that the usual algorithmic complexity of a problem cannot be applied in the black-box scenario. Therefore, a new framework for the valuation of algorithms for black-box optimization is presented allowing the notion of the black-box complexity of a problem. For several problems upper and… Expand

#### Topics from this paper

#### 71 Citations

Black-Box Complexity for Bounding the Performance of Randomized Search Heuristics

- Computer Science
- Theory and Principled Methods for the Design of Metaheuristics
- 2014

This chapter gives a precise and accessible introduction to the notion of black-box complexity, explains important properties and discusses several concrete examples. Expand

On the Black-Box Complexity of Example Functions: The Real Jump Function

- Computer Science, Mathematics
- FOGA
- 2015

It is argued that the problem is not with the notion of black-box complexity but with the extension to a function class and it is shown that for this extension there is a much better agreement even between the performance of an extremely simple evolutionary algorithm and the most general notion ofBlackbox complexity. Expand

Ranking-Based Black-Box Complexity

- Mathematics, Computer Science
- Algorithmica
- 2012

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

- Computer Science, Mathematics
- GECCO
- 2015

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

OneMax in Black-Box Models with Several Restrictions

- Mathematics, Computer Science
- Algorithmica
- 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. Expand

Black-box complexities of combinatorial problems

- Computer Science
- GECCO '11
- 2011

This work reveals that the choice of how to model the optimization problem is non-trivial here and comes true where the search space does not consist of bit strings and where a reasonable definition of unbiasedness has to be agreed on. 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

Introducing Elitist Black-Box Models: When Does Elitist Behavior Weaken the Performance of Evolutionary Algorithms?

- Computer Science, Medicine
- Evolutionary Computation
- 2017

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

General Limits in Black-Box Optimization

- Computer Science
- 2013

This chapter makes precise what it means when talking of black-box optimization, and considers a very general framework without concrete references to evolutionary algorithms that covers an enormous array of optimization algorithms. Expand

From black-box complexity to designing new genetic algorithms

- Mathematics, Computer Science
- Theor. Comput. Sci.
- 2015

This work designs a new crossover-based genetic algorithm that uses mutation with a higher-than-usual mutation probability to increase the exploration speed and crossover with the parent to repair losses incurred by the more aggressive mutation. Expand

#### References

SHOWING 1-10 OF 23 REFERENCES

Fitness Landscapes Based on Sorting and Shortest Paths Problems

- Computer Science
- PPSN
- 2002

Fitness landscapes based on important computer science problems as sorting and shortest paths problems are investigated here and it cannot be expected that evolutionary algorithms outperform the well-known problem specific algorithms on these simple problems. Expand

Long Path Problems

- Mathematics, Computer Science
- PPSN
- 1994

It is demonstrated that simple paths to the global optimum can be so long that climbing the path is intractable, which means that a unimodal search space, which consists of a single hill, can be difficult for a hillclimber to optimize. Expand

The time complexity of maximum matching by simulated annealing

- Mathematics, Computer Science
- JACM
- 1988

It is shown for arbitrary graphs that a degenerate form of the basic annealing algorithm (obtained by letting “temperature” be a suitably chosen constant) produces matchings with nearly maximum cardinality in polynomial average time. Expand

Computers and Intractability: A Guide to the Theory of NP-Completeness

- Computer Science, Mathematics
- 1978

Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge… Expand

Modern heuristic techniques for combinatorial problems

- Mathematics
- 1993

Part 1 Introduction: combinatorial problems local and global optima heuristics. Part 2 Simulated annealing: the basic method enhancements and modifications applications conclusions. Part 3 Tabu… Expand

Probabilistic computations: Toward a unified measure of complexity

- Computer Science
- 18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
- 1977

Two approaches to the study of expected running time of algoritruns lead naturally to two different definitions of intrinsic complexity of a problem, which are the distributional complexity and the randomized complexity, respectively. Expand

On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm

- Computer Science
- PPSN
- 1998

It is shown that unimodal functions can be very difficult to be optimized for the (1+1) EA, and it is proved that a little modification in the selection method can lead to huge changes in the expected running time. Expand

On the analysis of the (1+1) evolutionary algorithm

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2002

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

A Framework for Adaptive Sorting

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1995

It is shown that there exists a natural partial order on the set of measures, which makes it possible to say that some measures are superior to others, and insert all known measures of presortedness into the partial order, and thereby provide a powerful tool for evaluating both measures and adaptive sorting algorithms. Expand

Theoretical Aspects of Evolutionary Algorithms

- Computer Science
- ICALP
- 2001

Some fundamental results on evolutionary algorithms are presented in order to show how theoretical results on randomized search heuristics can be proved and how they contribute to the understanding of evolutionary algorithms. Expand