Corpus ID: 8779809

Recent Results on No-Free-Lunch Theorems for Optimization

  title={Recent Results on No-Free-Lunch Theorems for Optimization},
  author={C. Igel and Marc Toussaint},
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
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
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
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
Universal Induction and Optimisation: No Free Lunch
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
Benchmarks that matter for genetic programming
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
Why Is Optimization Difficult?
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
Effective Adaptive Plans
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
Adaptation and Evolution in Dynamic Persistent Environments
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


On Classes of Functions for which No Free Lunch Results Hold
The main result of this paper is proven that the fraction of subsets that are c.u.p. is negligibly small, which means that classes of objective functions resulting from important classes of real-world problems are likely not to be c. Expand
Optimization with randomized search heuristics - the (A)NFL theorem, realistic scenarios, and difficult functions
An Almost No Free Lunch (ANFL) theorem shows that for each function which can be optimized efficiently by a search heuristic there can be constructed many related functions where the same heuristic is bad. Expand
No free lunch theorems for optimization
A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of "no free lunch" (NFL) theorems are presented whichExpand
No Free Lunch Theorems for Search
We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperformsExpand
Remarks on a recent paper on the "no free lunch" theorems
The present authors explore the issues raised in that paper including the presentation of a simpler version of the NFL proof in accord with a suggestion made explicitly by Koppen (2000) and implicitly by Wolpert and Macready (1997). Expand
Optimization is easy and learning is hard in the typical function
  • T. M. English
  • Computer Science
  • Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512)
  • 2000
Elementary results in algorithmic information theory are invoked to show that almost all finite functions are highly random. That is, the shortest program generating a given function description isExpand
Fundamental Limitations on Search Algorithms: Evolutionary Computing in Perspective
This paper extends results and draws out some of their implications for the design of search algorithms, and for the construction of useful representations, and focuses attention on tailoring alg- orithms and representations to particular problem classes by exploiting domain knowledge. Expand
A Free Lunch Proof for Gray versus Binary Encodings
A measure of complexity is proposed that counts the number of local minima in any given problem representation. A special class of functions with the maximum possible number of optima is also deened.Expand
Neutrality and self-adaptation
It is shown that in the absence of external control neutrality allows a variation of the search distribution independent of phenotypic changes, and the average number of fitness evaluations needed to find a desirable genotype depending on the number of desirable genotypes and the cardinality of the genotypes is derived. Expand
Graph isomorphisms effect on structure optimization of neural networks
  • C. Igel, P. Stagge
  • Mathematics
  • Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290)
  • 2002
Concepts from the graph theory and molecular evolution are proposed for analyzing effects of redundancy induced by graph isomorphisms on the structure optimization of neural networks. It isExpand