Some information theoretic results on evolutionary optimization

The body of theoretical results regarding conservation of information ("no free lunch") in optimization has not related directly to evolutionary computation. Prior work has assumed that an optimizer traverses a sequence of points in the domain of a function without revisiting points. The present work reduces the difference between theory and practice by a) allowing points to be revisited, b) reasoning about the set of visited points instead of the sequence, and c) considering the impact of bounded memory and revisited points upon optimizer performance. Fortuitously, this leads to clarification of the fundamental results in conservation of information. Although most work in this area emphasizes the futility of attempting to design a generally superior optimizer, the present work highlights possible constructive use of the theory in restricted problem domains.