Corpus ID: 8779809

Recent Results on No-Free-Lunch Theorems for Optimization

@article{Igel2003RecentRO,
  title={Recent Results on No-Free-Lunch Theorems for Optimization},
  author={C. Igel and Marc Toussaint},
  journal={ArXiv},
  year={2003},
  volume={cs.NE/0303032}
}
The sharpened No-Free-Lunch-theorem (NFL-theorem) states that the performance of all optimization algorithms averaged over any finite set F of functions is equal if and only if F is closed under permutation (c.u.p.) and each target function in F is equally likely. In this paper, we first summarize some consequences of this theorem, which have been proven recently: The average number of evaluations needed to find a desirable (e.g., optimal) solution can be calculated; the number of subsets c.u.p… Expand
A No-Free-Lunch Theorem for Non-Uniform Distributions of Target Functions
The sharpened No-Free-Lunch-theorem (NFL-theorem) states that, regardless of the performance measure, the performance of all optimization algorithms averaged uniformly over any finite set F ofExpand
A No-Free-Lunch theorem for non-uniform distributions of target functions
The sharpened No-Free-Lunch-theorem (NFL-theorem) states that, regardless of the performance measure, the performance of all optimization algorithms averaged uniformly over any finite set F ofExpand
Conditions that Obviate the No-Free-Lunch Theorems for Optimization
TLDR
This paper looks more closely at the NFL results and focuses on their implications for combinatorial problems typically faced by many researchers and practitioners, finding that only trivial subclasses of these problems fall under the NFL implications. Expand
A Study of Some Implications of the No Free Lunch Theorem
TLDR
It is proved that each set of functions based on the distance to a given optimal solution, among which trap functions, onemax or the recently introduced onemix functions, and the NK-landscapes are not c.u.p. and thus the thesis of the sharpened No Free Lunch Theorem does not hold for them. Expand
No Free Lunch Theorems: Limitations and Perspectives of Metaheuristics
  • C. Igel
  • Computer Science
  • Theory and Principled Methods for the Design of Metaheuristics
  • 2014
TLDR
It is not likely that the preconditions of the NFL theorems are fulfilled for a problem class and thus differences between algorithms exist, therefore, tailored algorithms can exploit structure underlying the optimization problem. Expand
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This thesis adapts universal induction to optimisation, and investigates its performance by putting it against the so-called No Free Lunch theorems, which show that under certain conditions, effective optimisation is impossible. Expand
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The aim of this article is to consolidate an emerging theme arising from papers and suggest that benchmarks should not be arbitrarily selected but should instead be drawn from an underlying probability distribution that reflects the problem instances which the algorithm is likely to be applied to in the real-world. Expand
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TLDR
This chapter aims to address some of the fundamental issues that are often encountered in optimization problems, making them difficult to solve, and to help both practitioners and fellow researchers to create more efficient optimization applications and novel algorithms. Expand
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A hypothetical adaptive plan that consists of three base strategies that guarantees a better result with each iteration, one has comparable results, and one guarantees worse results is introduced. Expand
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It is established that indirect interaction is essential to multiagent systems (MASs) and will be useful to researchers in coordination, evolutionary computation, and design of multiagent and adaptive systems. Expand
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