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No Free Lunch Theorems for Search
, 1995
"... 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 wh ..."
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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 informationtheoretic 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 timevarying cost functions. We conclude with some discussion of the justifiability of biologicallyinspired search methods.
Lectures on Polytopes: Updates, Corrections, and More
, 1999
"... be identied within Blind & Blind's [542] classication of all cubical dpolytopes with 2 d+1 vertices. (new 11/98) Pages 131132, Piles of Cubes: More interesting structure connected with the \piles of cubes" polytopes constructed and studied here has recently been uncovered by Athanasiadis [540]. ..."
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be identied within Blind & Blind's [542] classication of all cubical dpolytopes with 2 d+1 vertices. (new 11/98) Pages 131132, 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 275277, 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 nonshellable 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],