We show that all algorithms that search for an extremum of a cost function perform exactly the same, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must exist exactly as many other functions where B outperforms A. Starting from this we analyze a number of the other a priori characteristics of the search problem, like its geometry and its information-theoretic aspects. This analysis allows us to derive mathematical benchmarks for assessing a particular search algorithm 's performance. We also investigate minimax aspects of the search problem, the validity of using characteristics of a partial search over a cost function to predict future behavior of the search algorithm on that cost function, and time-varying cost functions. We conclude with some discussion of the justifiability of biologically-inspired search methods.

be identied within Blind & Blind's [542] classication of all cubical d-polytopes with 2 d+1 vertices. (new 11/98) Pages 131-132, Piles of Cubes: More interesting structure connected with the \piles of cubes" polytopes constructed and studied here has recently been uncovered by Athanasiadis [540]. (new 11/98) Chapter 6: See Eisenbud & Popescu [544] for an entirely dierent (algebraic geometry) view of Gale diagrams. (new 7/98) Pages 275-277, Nonshellable balls: Masahiro Hachimori [547, 548] has studied constructibility of simplicial balls (a concept that is weaker than shellability). He found, for example, that while my 10 vertex example of a non-shellable ball [539] is constructible, Furch/Bing's knotted hole balls are not constructible | this is stronger than just saying that they are not shellable. (Hachimori also found that the facet list of Grunbaum's nonshellable ball, as given in [164],