No free lunch theorems for optimization
Wolpert, D.H.
Macready, W.G.
IBM Almaden Res. Center, San Jose, CA;
This paper appears in: Evolutionary Computation, IEEE Transactions on
Publication Date: Apr 1997
Volume: 1,
Issue: 1
On page(s): 67-82
ISSN: 1089-778X
References Cited: 15
CODEN: ITEVF5
INSPEC Accession Number: 5611374
Digital Object Identifier: 10.1109/4235.585893
Current Version Published: 2002-08-06
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
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