Polynomial time summary statistics for a generalization of MAXSAT
Robert B. Heckendorn, Soraya Rana, Darrell Whitley · 1999
MAXSAT problems are notoriously difficult for genetic algorithms to solve. NKlandscapes are often used as test problems of scalable difficulty for genetic algorithms. In this paper we exploit the similar structure of the two problems to create an encompassing class of problems called embedded landscapes. Then we use Walsh analysis to explore the nonlinear bit interactions of these important test functions. We show that by applying Walsh analysis to embedded landscapes, several important summary statistics can be generated in polynomial time. We then use these techniques to discuss the statistical "shape" of both MAXSAT and NKlandscapes. 1 INTRODUCTION MAXSAT problems are notoriously difficult for genetic algorithms to solve. Even relatively old algorithms such as Davis-Putnam [Davis and Putnam, 1960] which are deterministic and exact are orders of magnitude faster than GAs. Understanding what makes MAXSAT so difficult for GAs gives us important clues about mechanisms of...