No Free Lunch Theorems for Optimization

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No Free Lunch Theorems for Optimization (1997)

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by David H. Wolpert, et al.

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959 - 10 self

BibTeX

@MISC{Wolpert97nofree,
    author = {David H. Wolpert and et al.},
    title = {No Free Lunch Theorems for Optimization},
    year = {1997}
}

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Abstract

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 performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori “head-to-head” minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems’ enforcing of a type of uniformity over all algorithms.

Keyphrases

free lunch theorem free lunch effective optimization algorithm optimization algorithm benchmark measure optimization problem geometric interpretation information-theoretic aspect elevated performance time-varying optimization problem priori head-to-head minimax distinction

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