No free lunch theorems for optimization
Wolpert, D.H.; Macready, W.G.
Evolutionary Computation, IEEE Transactions on
Volume 1, Issue 1, Apr 1997 Page(s):67 - 82
Digital Object Identifier 10.1109/4235.585893
Summary: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
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