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Evolutionary Computation

Spring 2009, Vol. 17, No. 1, Pages 117-129
(doi: 10.1162/evco.2009.17.1.117)
© 2009 by the Massachusetts Institute of Technology
Reinterpreting No Free Lunch
Article PDF (115.04 KB)

Since its inception, the “No Free Lunch” theorem (NFL) has concerned the application of symmetry results rather than the symmetries themselves. In our view, the conflation of result and application obscures the simplicity, generality, and power of the symmetries involved. This paper separates result from application, focusing on and clarifying the nature of underlying symmetries. The result is a general set-theoretic version of NFL which speaks to symmetries when arbitrary domains and co-domains are involved. Although our framework is deterministic, we note situations where our deterministic set-theoretic results speak nevertheless to stochastic algorithms.