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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 ..."
Abstract

Cited by 247 (2 self)
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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.
The Mathematics of Search
, 1996
"... We show that all algorithms that search for an extremum of a cost function perform exactly the same, according to any performance measure, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must ex ..."
Abstract

Cited by 9 (0 self)
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We show that all algorithms that search for an extremum of a cost function perform exactly the same, according to any performance measure, 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.
No Free Lunch Theorem for Search, SFITR9502010, The Santa Fe Institute, Santa Fe
 JPL
, 1995
"... We show that all algorithms that search for an extremum of a cost function perform exactly the same, according to any performance measure, when averaged over all possible cost functions. In particular, if algorithm A outperforms algorithm B on some cost functions, then loosely speaking there must e ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We show that all algorithms that search for an extremum of a cost function perform exactly the same, according to any performance measure, 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 justiability of biologicallyinspired search methods. 1