On Classes of Functions for which No Free Lunch Results Hold

@article{Igel2003OnCO,
  title={On Classes of Functions for which No Free Lunch Results Hold},
  author={C. Igel and Marc Toussaint},
  journal={ArXiv},
  year={2003},
  volume={cs.NE/0108011}
}

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References

SHOWING 1-10 OF 12 REFERENCES
No free lunch theorems for optimization
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
Perhaps Not a Free Lunch But At Least a Free Appetizer
TLDR
It is argued why the scenario on which the No Free Lunch Theorem is based does not model real life optimization, and why optimization techniques differ in their efficiency.
A Free Lunch Proof for Gray versus Binary Encodings
TLDR
A measure of complexity is proposed that counts the number of local minima in any given problem representation and it is shown that reeected Gray code induce more optima than Binary over this special class of functions.
The no free lunch and description length
  • Genetic and Evolutionary Computation Conference (GECCO
  • 2001
The No Free Lun and description length
  • in: L. Spector, E. Goodman, A. W W. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo S. Pezeshk, M. Garzon, E. Burke (Eds.), Genetic and Evolut ary Computation Conference
  • 2001
An Introduction to Probability Theory and its Applications, Volume I
Optimization with randomi search heuristics — The ( A ) NFL theorem , realistic scenar and difficult functions , Theoret
  • Comput . Sci . An Introduction to Probability Theory and i Applications
  • 1971
to IEEE Transactions on Evolutionary Computation Los Alamos e-Print Archive cs
  • to IEEE Transactions on Evolutionary Computation Los Alamos e-Print Archive cs
The No Free Lunch and description length
  • 2001
...
...