Now that’s more like it for a disclaimer …

That's perfect. Time is always the best judge. But: 1) how did NDE side comment the new results (if they did at all); and more important: 2) did Wolpert provide further comments? Finally perhaps it could be useful to correct the related information contained withine the Wiki page: http://en.wikipedia.org/wiki/No-free-lunch_theorem kairos

See the new preface to my book No Free Lunch at www.designinference.com. I address exactly your point and that paper by Wolpert and Macready: http://www.designinference.com/documents/2006.06.NFL_paperback_preface.pdf William Dembski

Bill, I have an important question concerning the following paper: "Coevolutionary Free Lunches", by David H. Wolpert and William G. Macready, IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 9, NO. 6, DECEMBER 2005 In the Abstract: "... In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. However, in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold...." In the Introduction: "... In this paper, we present a mathematical framework, generalized optimization (GO), that covers both traditional optimization and coevolutionary scenarios. GO also covers other scenarios such as multiarmed bandits. We then use GO to explore the differences between traditional optimization and coevolution. We find dramatic differences between the traditional optimization and coevolutoin scenarios. In particular, unlike the fundamental NFL result for traditional optimization, in the self-play version of coevolution there are algorithms that are superior to other algorithms for all problems. However, in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold, i.e., uniformly averaged over all objective functions, all algorithms perform identically. ..." In the CONCLUSION: "We have introduced a general framework for analyzing NFL issues in a variety of contexts, GO. When applied to self-play GO establishes the existence of pairs of algorithms in which one is superior for all possible joint payoff functions . This result stands in marked contrast to similar analyzes for optimization in nonself-play settings. Basically, the result arises because under a maximin criteria the sum over all payoff functions is not . We have equivalent to a sum over all functions shown that for simple algorithms, we can calculate expected performance over all possible payoff functions and in some cases determine the fraction of functions where one algorithm outperforms another. On the other hand, we have also shown that for the more general biological coevolutionary settings, where there is no sense of a "champion" like there is in self-play, the NFL theorems still hold. ..." But if I remember well one of the main arguments against your NFL work was that results are non appliable to biology and that Wolpert and Macready did agree on this. Is this paper an implicit recognition of your work or I am missing something? kairos

Evolutionary computation is intelligently-designed trial and error with a pre-specified goal, and this can be a useful tool for arriving at approximate solutions to problems within a limited domain, assuming that the initial assumptions and algorithms are valid. This has no relevance to biological evolution. GilDodgen