No free lunch theorems for optimization

Author

Wolpert, David H. ; Macready, William G.

Author_Institution

IBM Almaden Res. Center, San Jose, CA, USA

Volume

1

Issue

1

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

67

Lastpage

82

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

Keywords

combinatorial mathematics; genetic algorithms; information theory; search problems; a priori head-to-head minimax distinctions; elevated performance; geometric interpretation; information-theoretic aspects; no free lunch theorems; optimization; time-varying optimization; Algorithm design and analysis; Bayesian methods; Evolutionary computation; Helium; Information theory; Iron; Minimax techniques; Performance analysis; Probability distribution; Simulated annealing;

fLanguage

English

Journal_Title

Evolutionary Computation, IEEE Transactions on

Publisher

ieee

ISSN

1089-778X

Type

jour

DOI

10.1109/4235.585893

Filename

585893