Affine OneMax

A new class of test functions for black box optimization is introduced. Affine OneMax (AOM) functions are defined as compositions of OneMax and invertible affine maps on bit vectors. The black box complexity of the class is upper bounded by a polynomial of large degree in the dimension. The proof relies on discrete Fourier analysis and the Kushilevitz-Mansour algorithm. Tunable complexity is achieved by expressing invertible linear maps as finite products of transvections. The black box complexity of sub-classes of AOM functions is studied. Finally, experimental results are given to illustrate the performance of search algorithms on AOM functions.Comment: An extended two-page abstract of this work will appear in 2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion

Polynomial Time Summary Statistics for a Generalization of MAXSAT

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..