2001/08/21 by Christian Igel, Igel, Christian, Marc Toussaint +1
Computer Science · Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #G.1.6 #Neural and Evolutionary Computing (cs.NE) #Optimization and Control (math.OC) #cs.NE #math.OC #nlin.AO
paper · pdf · doi:10.48550/arxiv.cs/0108011
8 pages, 1 figure, see http://www.neuroinformatik.ruhr-uni-bochum.de/
arxiv created 2001/08/21 · arxiv updated 2009/11/30
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.