Remarks on a recent paper on the "no free lunch" theorems

This letter discusses the recent paper "Some technical remarks on the proof of the 'No Free Lunch' theorem," In that paper, some technical issues related to the formal proof of the no free lunch (NFL) theorem for search were given by Wolpert and Macready (1995 and 1997). As a result of a discussion among the authors, this letter explores the issues raised in that paper more thoroughly. This includes the presentation of a simpler version of the NFL proof in accord with a suggestion made explicitly by Koppen (2000) and implicitly by Wolpert and Macready (1997). It also includes the correction of an incorrect claim made by Koppen (2000) of a limitation of the NFL theorem. Finally, some thoughts on future research directions for research into algorithm performance are given.