On Classes of Functions for which No Free Lunch Results Hold
<|reference_start|>On Classes of Functions for which No Free Lunch Results Hold: In a recent paper it was shown that No Free Lunch results hold for any subset F of the set of all possible functions from a finite set X to a finite set Y iff F is closed under permutation of X. In this article, we prove that the number of those subsets can be neglected compared to the overall number of possible subsets. Further, we present some arguments why problem classes relevant in practice are not likely to be closed under permutation.<|reference_end|>
@article{igel2001on,
    title={On Classes of Functions for which No Free Lunch Results Hold},
    author={Christian Igel and Marc Toussaint},
    journal={arXiv preprint arXiv:cs/0108011},
    year={2001},
    archivePrefix={arXiv},
    eprint={cs/0108011},
    primaryClass={cs.NE math.OC nlin.AO}
}