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No Free Lunch Theorems for Optimization
, 1997
"... 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 which establish that for any algorithm, any elevated performance over one class of problems is offset by performan ..."
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Cited by 961 (10 self)
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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 which establish that for any algorithm, any elevated performance over one class of problems is offset
No Free Lunch Theorems for Search
, 1995
"... 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 outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions wh ..."
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Cited by 292 (2 self)
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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 outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its informationtheoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm 's performance. We also investigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and timevarying cost functions. We conclude with some discussion of the justifiability of biologicallyinspired search methods.
Focused No Free Lunch Theorems
"... Proofs and empirical evidence are presented which show that a subset of algorithms can have identical performance over a subset of functions, even when the subset of functions is not closed under permutation. We refer to these as focused sets. In some cases focused sets correspond to the orbit of a ..."
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Cited by 9 (1 self)
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Proofs and empirical evidence are presented which show that a subset of algorithms can have identical performance over a subset of functions, even when the subset of functions is not closed under permutation. We refer to these as focused sets. In some cases focused sets correspond to the orbit of a permutation group; in other cases, the focused sets must be computed heuristically. In the smallest case, two algorithms can have identical performance over just two functions in a focused set. These results particularly exploit the case where search is limited to m steps, where m is significantly smaller than the size of the search space.
No Free Lunch Theorems for Search
, 1995
"... 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 outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions wh ..."
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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 outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its informationtheoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm's performance. We alsoinvestigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and timevarying cost functions. We conclude with some discussion of the justi ability of biologicallyinspired search methods. 1
The supervised learning nofreelunch Theorems
 In Proc. 6th Online World Conference on Soft Computing in Industrial Applications
, 2001
"... Abstract This paper reviews the supervised learning versions of the nofreelunch theorems in a simplified form. It also discusses the significance of those theorems, and their relation to other aspects of supervised learning. ..."
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Cited by 46 (0 self)
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Abstract This paper reviews the supervised learning versions of the nofreelunch theorems in a simplified form. It also discusses the significance of those theorems, and their relation to other aspects of supervised learning.
Chapter 10 COMPLEXITY THEORY AND THE NO FREE LUNCH THEOREM
"... This tutorial reviews basic concepts in complexity theory, as well as various No Free Lunch results and how these results relate to computational complexity. The tutorial explains basic concepts in an informal fashion that illuminates key concepts. No Free Lunch theorems for ..."
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This tutorial reviews basic concepts in complexity theory, as well as various No Free Lunch results and how these results relate to computational complexity. The tutorial explains basic concepts in an informal fashion that illuminates key concepts. No Free Lunch theorems for
Wolpert and Macready’s No Free Lunch theorem
"... Wolpert and Macready’s No Free Lunch theorem proves that no search algorithm is better than any other over all possible discrete functions. The meaning of the No Free Lunch theorem has, however, been the subject of intense debate. We prove that for local neighborhood search on problems of bounded c ..."
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Wolpert and Macready’s No Free Lunch theorem proves that no search algorithm is better than any other over all possible discrete functions. The meaning of the No Free Lunch theorem has, however, been the subject of intense debate. We prove that for local neighborhood search on problems of bounded
Complexity Theory and the No Free Lunch Theorem
, 2005
"... Introduction This tutorial reviews basic concepts in complexity theory, as well as various No Free Lunch results and how these results relate to computational complexity. The tutorial explain basic concepts in an informal fashion that illuminates key concepts. "No Free Lunch" theorems for ..."
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Cited by 16 (0 self)
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Introduction This tutorial reviews basic concepts in complexity theory, as well as various No Free Lunch results and how these results relate to computational complexity. The tutorial explain basic concepts in an informal fashion that illuminates key concepts. "No Free Lunch" theorems
The No Free Lunch Theorems: Complexity and Security
, 2003
"... One of the main challenges for decision scientists in the 21st century will be managing systems of ever increasing complexity. As systems like electrical power grids, computer networks, and the software that controls it all grow increasingly complex, fragility, bugs, and security flaws are becoming ..."
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Cited by 5 (1 self)
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qualitative nature of decision making. With the Fundamental matrix we explain in a qualitative way many theorems and known results about optimization, complexity, and security. The simplicity of the explanations leads to new insights toward potential research directions. Like other "
Generalization of the NoFreeLunch Theorem
"... Abstract — The NoFreeLunch (NFL) Theorem provides a fundamental limit governing all optimization/search algorithms and has successfully drawn attention to theoretical foundation of optimization and search. However, we find several limitations in the original NFL paper. In this work, using results ..."
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Abstract — The NoFreeLunch (NFL) Theorem provides a fundamental limit governing all optimization/search algorithms and has successfully drawn attention to theoretical foundation of optimization and search. However, we find several limitations in the original NFL paper. In this work, using results
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