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Recent Results on No-Free-Lunch Theorems for Optimization [article]

Christian Igel, Marc Toussaint
2003 arXiv   pre-print
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  ...  This yields the most general NFL-theorem for optimization presented so far.  ...  We thank Stefan Wiegand for fruitful discussions.  ... 
arXiv:cs/0303032v1 fatcat:dvmc2jp3g5cn7ccfs36yc4huue

FREE LUNCH OR NO FREE LUNCH: THAT IS NOT JUST A QUESTION?

XIN-SHE YANG
2012 International journal on artificial intelligence tools  
This paper discusses the recent results on no-free-lunch theorems and algorithm convergence, as well as their important implications for algorithm development in practice.  ...  No-free-lunch theorems are of both theoretical and practical importance, while many important studies on convergence analysis of various metaheuristic algorithms have proven to be fruitful.  ...  Free lunches: No-free-lunch theorems have not been proved for continuous domains for multiobjective optimization.  ... 
doi:10.1142/s0218213012400106 fatcat:3eixjjeskbf7ffog7ptnyueosy

Ioannis C. Demetriou and Panos M. Pardalos (eds): Approximation and Optimization: Algorithms, Complexity and Applications

Oleg Burdakov
2020 SN Operations Research Forum  
Toint) considers evaluation complexity for solving constrained optimization. This paper presents theoretical results on a subject where the authors have made important contributions.  ...  The collection of individual papers is a mix of state of the art research articles on Approximation and Optimization, surveys of new work, and relevant applications in science, engineering, and social  ...  For a reader who is interested in evolutionary optimization for machine learning and the no free lunch theorems, the survey articles would be useful sources of recent results.  ... 
doi:10.1007/s43069-020-0006-9 fatcat:wqennjmsr5csxlpfpbhhxrx4ju

Swarm-Based Metaheuristic Algorithms and No-Free-Lunch Theorems [chapter]

Xin-She Yang
2012 Theory and New Applications of Swarm Intelligence  
Free lunches: No-free-lunch theorems have not been proved for continuous domains for multiobjective optimization.  ...  to provide a state-of-the-art review of the recent studies of no-free-lunch theory and also free lunch scenarios.  ... 
doi:10.5772/30852 fatcat:b7qycekf2repjjliwsd6fkmyey

A no-free-lunch framework for coevolution

Travis C. Service, Daniel R. Tauritz
2008 Proceedings of the 10th annual conference on Genetic and evolutionary computation - GECCO '08  
The No-Free-Lunch theorem is a fundamental result in the field of black-box function optimization. Recent work has shown that coevolution can exhibit free lunches.  ...  in the original No-Free-Lunch theorem.  ...  INTRODUCTION The No-Free-Lunch (NFL) theorem is a fundemental result in the field of function optimization [11] .  ... 
doi:10.1145/1389095.1389163 dblp:conf/gecco/ServiceT08 fatcat:rnrgwdr4jrfidh2nor7uod7zja

Gain-loss pricing under ambiguity of measure

Mustafa Ç. Pınar
2008 E S A I M: Control, Optimisation and Calculus of Variations  
Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of measure, and illustrate its use.  ...  Korf proved that if the market has no free lunches, then the problem P f satisfies the direction-free feasibility constraint qualification, and gave the following theorem (see also Shapiro [27] for a  ...  In a recent paper that inspired the present one, Korf [20] gave a one-step variant of the fundamental theorem of asset pricing (FTAP) in mathematical finance [17, 18] (in the context of arbitrage free  ... 
doi:10.1051/cocv:2008068 fatcat:zjvel7wuvbhvvddsumjx6dr7xm

The Implications of the No-Free-Lunch Theorems for Meta-induction [article]

David H. Wolpert
2022 arXiv   pre-print
The important recent book by G. Schurz appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction.  ...  Importantly though, in addition to the NFL theorems, there are many free lunch theorems.  ...  I would like to thank the Santa Fe Institute for support.  ... 
arXiv:2103.11956v3 fatcat:re6xvwtbt5d7xeehhnl7ntt5mq

Conditions that Obviate the No-Free-Lunch Theorems for Optimization

Gary J. Koehler
2007 INFORMS journal on computing  
Roughly speaking, the No Free Lunch theorems state that any blackbox algorithm has the same average performance as random search. These results have largely been ignored by algorithm researchers.  ...  We derive necessary conditions for the NFL results to hold based on common problem structures.  ...  Introduction Roughly speaking, the No Free Lunch (NFL) theorem for optimization by Macready (1995, 1997) states that any two blackbox algorithms (deterministic or stochastic) have the same average performance  ... 
doi:10.1287/ijoc.1060.0194 fatcat:oav73j2u7nawjcqaulm5omgqti

No Free Lunch Theorem and Bayesian probability theory: two sides of the same coin. Some implications for black-box optimization and metaheuristics [article]

Loris Serafino
2013 arXiv   pre-print
I will stress how an interpretation of the No Free Lunch theorem leads naturally to a general Bayesian optimization framework.  ...  This paper will focus on some theoretical issues that have strong implications for practice.  ...  Figure 1 . 1 Some basic strategies for hard optimization. Figure 2 . 2 The No Free Lunch Theorem.  ... 
arXiv:1311.6041v3 fatcat:vn6fu6r7eba6ji7lskvrbuaes4

A No-Free-Lunch theorem for non-uniform distributions of target functions

Christian Igel, Marc Toussaint
2005 Journal of Mathematical Modelling and Algorithms  
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 of functions  ...  Second, as the main result, the NFL-theorem is extended. Necessary and sufficient conditions for NFL-results to hold are given for arbitrary distributions of target functions.  ...  We thank Stefan Wiegand for fruitful discussions.  ... 
doi:10.1007/s10852-005-2586-y fatcat:z6gtfw3o4ne6fhp6pv3h4hfrma

A No-Free-Lunch Theorem for Non-Uniform Distributions of Target Functions

Christian Igel, Marc Toussaint
2004 Journal of Mathematical Modelling and Algorithms  
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 of functions  ...  Second, as the main result, the NFL-theorem is extended. Necessary and sufficient conditions for NFL-results to hold are given for arbitrary distributions of target functions.  ...  We thank Stefan Wiegand for fruitful discussions.  ... 
doi:10.1023/b:jmma.0000049381.24625.f7 fatcat:zt5wtywjq5ds3ipxqqzoq5ztga

Stochastic Convex Programming: Relatively Complete Recourse and Induced Feasibility

R. T. Rockafellar, R. J-B. Wets
1976 SIAM Journal of Control and Optimization  
Theorem 5 . 3 . 53 Suppose that the market admits no free lunch.  ...  FUNDAMENTAL THEOREM OF ASSET PRICING In order to state a characterization of no free lunch in the framework of finitelyadditive martingale measures, we present the following multistage stochastic optimization  ... 
doi:10.1137/0314038 fatcat:gtifr3tdardqxipigpqscpyhxi

No Free Lunch and Free Leftovers Theorems for Multiobjective Optimisation Problems [chapter]

David W. Corne, Joshua D. Knowles
2003 Lecture Notes in Computer Science  
; the other theme concerns classes of problems for which NFL doesn't hold (i.e. proofs of 'Free Lunch' theorems).  ...  The classic NFL theorems are invariably cast in terms of single objective optimization problems.  ...  Introduction The so-called 'No Free Lunch' theorem (NFL) is a class of theorems concerning the average behaviour of 'black-box' optimization algorithms over given spaces of optimisation problems.  ... 
doi:10.1007/3-540-36970-8_23 fatcat:63tbxrqi4fa6lbt4u4d6ijnb3u

No Free Lunch in the Search for Creativity

Dan Ventura
2011 International Conference on Computational Creativity  
We consider computational creativity as a search process and give a No Free Lunch result for computational creativity in this context.  ...  That is, we show that there is no a priori "best" creative strategy. We discuss some implications of this result and suggest some additional questions to be explored.  ...  Acknowledgments This material is based upon work that is partially supported by the National Science Foundation under Grant No. IIS-0856089.  ... 
dblp:conf/icccrea/Ventura11 fatcat:po7olvsdfbcljgny5jplhbklwy

Arbitrage and Existence of Equilibrium in Infinite Asset Markets

Donald J. Brown, Jan Werner
1995 The Review of Economic Studies  
For more information about JSTOR, please contact support@jstor.org.  ...  JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.  ...  LeRoy for helpful remarks. We have also received helpful comments from the editor and three anonymous referees. In comments on an earlier draft of this paper  ... 
doi:10.2307/2297843 fatcat:c33eoo2t4vcrlglvsirepjtoea
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