Theoretical Computer Science - Natural computing
On the futility of blind search: An algorithmic view of “no free lunch”
Evolutionary Computation
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
Evolutionary Computation
Free lunches on the discrete Lipschitz class
Theoretical Computer Science
A measure-theoretic analysis of stochastic optimization
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Evolutionary Computation
Adaptive Memetic Differential Evolution with Global and Local neighborhood-based mutation operators
Information Sciences: an International Journal
An analysis on separability for Memetic Computing automatic design
Information Sciences: an International Journal
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This paper investigates extensions of No Free Lunch (NFL) theorems to countably infinite and uncountable infinite domains. The original NFLdue to Wolpert and Macready states that all search heuristics have the same performance when averaged over the uniform distribution over all possible functions. For infinite domains the extension of the concept of distribution over all possible functions involves measurability issues and stochastic process theory. For countably infinite domains, we prove that the natural extension of NFL theorems does not hold, but that a weaker form of NFL does hold, by stating the existence of non-trivial distributions of fitness leading to equal performance forall search heuristics. Our main result is that for continuous domains, NFL does not hold.