No Free Lunch Theorems for Search

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 algo rithm 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 justi ability of biologically inspired search methods