On the Structure of Sequential Search: Beyond "No Free Lunch"

In sequential, deterministic, non-redundant search the algorithm permutes a test function to obtain the search result. The mapping from test functions to search results is a one-to-one correspondence. There is a partition of the set of functions into maximal blocks of functions that are permutations of one another. This permits reasoning about search to be reduced to reasoning about search within blocks of functions. It also leads to the definition of the block uniform distribution, in which functions within the same block have the same probability. It is established that the Kullback-Leibler distance to the nearest block uniform distribution is identical for the distributions of test functions and search results. The distance is zero if and only if all search algorithms have identically distributed search results. That is, a block uniform distribution of test functions is necessary and sufficient for “no free lunch.”

• Type: Conference
• Year: 2004
• Where: EVOW
• Authors: Thomas M. English
• Keywords: Artificial Intelligence, Block Uniform Distribution, EVOW 2004, Non-redundant Search, Test Functions