No Free Lunch Theorem: A Review

@inproceedings{Adam2019NoFL,
  title={No Free Lunch Theorem: A Review},
  author={Stavros P. Adam and Stamatios-Aggelos N. Alexandropoulos and Panos M. Pardalos and Michael N. Vrahatis},
  year={2019}
}
The “No Free Lunch” theorem states that, averaged over all optimization problems, without re-sampling, all optimization algorithms perform equally well. Optimization, search, and supervised learning are the areas that have benefited more from this important theoretical concept. Formulation of the initial No Free Lunch theorem, very soon, gave rise to a number of research works which resulted in a suite of theorems that define an entire research field with significant results in other scientific… Expand
The Evidence of the “No Free Lunch” Theorems and the Theory of Complexity in Business Artificial Intelligence
TLDR
The evidence of the “No-Free-Lunch” (NFL) theorems is proposed to understand ML use’s applicability in business organizations. Expand
Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
TLDR
This work shows that entangled data sets lead to an apparent violation of the (classical) NFL theorem and proves a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. Expand
Are Humans Bayesian in the Optimization of Black-Box Functions?
TLDR
This paper focuses on Bayesian Optimization and analyse experimentally how it compares to humans while searching for the maximum of an unknown 2D function and confirms that Gaussian Processes provide a general model to explain different patterns of learning enabled search and optimization in humans. Expand
Gravitational search algorithm based strategy for combinatorial t-way test suite generation
TLDR
The primary contribution of this paper is that GSA has adapted for the first time to t-way test data generation, and benchmarking results showcase that GSTG obtains competitive results in most system configurations compared to other existing strategies and addresses higher combination coverage. Expand
Global Optimisation through Hyper-Heuristics: Unfolding Population-Based Metaheuristics
TLDR
This work proposes a heuristic-based solver model for continuous optimisation problems by extending the existing concepts present in the literature and utilised a hyper-heuristic based on Simulated Annealing as a high-level strategy. Expand
Hyper-Heuristics to customise metaheuristics for continuous optimisation
TLDR
This work proposes a strategy based on a hyper-heuristic model powered by Simulated Annealing for customising population-based metaheuristics that solve continuous optimisation problems with different characteristics, similar to those from practical engineering scenarios. Expand
A Primary Study on Hyper-Heuristics to Customise Metaheuristics for Continuous optimisation
TLDR
This work proposes a strategy based on a hyper-heuristic for tailoring population-based metaheuristics, and considers search operators from well-known techniques as building blocks for new ones. Expand
Three novel quantum-inspired swarm optimization algorithms using different bounded potential fields
TLDR
This paper presents three novel quantum-inspired algorithms, which scenario is a particle swarm that is excited by a Lorentz, Rosen–Morse, and Coulomb-like square root potential fields, respectively, and finds that a strong potential field inside a well with weak asymptotic behavior leads to better exploitation and exploration attributes for unimmodal, multimodal, and fixed-multimodal functions. Expand
Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems
TLDR
This work introduces a first step to a generalised and mathematically formal metaheuristic model, which can be used for studying and improving metaheuristics and outlines and discusses several future extensions of this model to various problem and solver domains. Expand
Genetic programming performance prediction and its application for symbolic regression problems
TLDR
A theoretical analysis of GP performance prediction problem is presented and an upper bound for GP performance is suggested that the error of the best solution that is found by GP for a given problem is less than the proposed upper bound. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 68 REFERENCES
The No Free Lunch and problem description length
The No Free Lunch theorem is reviewed and cast within a simple framework for black-box search. A duality result which relates functions being optimized to algorithms optimizing them is obtained andExpand
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
Continuous Lunches Are Free Plus the Design of Optimal Optimization Algorithms
TLDR
It is proved that the natural extension of NFL theorems, for the current formalization of probability, does not hold, but that a weaker form of NFL does hold, by stating the existence of non-trivial distributions of fitness leading to equal performances for all search heuristics. Expand
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
Optimization, block designs and No Free Lunch theorems
TLDR
This work provides tight connections between such ''No Free Lunch'' conditions and the structure of t-designs and t-wise balanced designs for arbitrary values t, and obtains a nontrivial family of n-variate Boolean functions that satisfies the '' no-free-lunch'' condition with respect to searches of length @W(n^1^/^2/log^1+2n). Expand
A no-free-lunch framework for coevolution
TLDR
A novel framework for analyzing No-Free-Lunch like results for classes of coevolutionary algorithms based upon the solution concept which they implement and a new instance of free lunches in coevolved which demonstrates the applicability of the framework. Expand
Remarks on a recent paper on the "no free lunch" theorems
TLDR
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
Beyond No Free Lunch: Realistic algorithms for arbitrary problem classes
TLDR
A new approach to reasoning about search algorithm performance is proposed, treating search algorithms as stochastic processes and thereby admitting revisiting; for this approach the authors need only make a simple assumption that search algorithms are applied for optimisation (i.e. maximisation or minimisation), rather than considering arbitrary performance measures. Expand
Coevolutionary free lunches
TLDR
This paper presents a general framework covering most optimization scenarios and shows that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. Expand
The no free lunch theorem and the human-machine interface
  • Y. Ho
  • Computer Science
  • 1999
TLDR
The twin purposes of the article are to explore the implications of NFL and to address the proper allocation of natural and computational intelligence in optimization problem solving. Expand
...
1
2
3
4
5
...