  We propose and develop a novel framework for analyzing permutation-based
combinatorial optimization problems, which could eventually be extended to
other types of problems. Our approach is based on the decomposition of the
objective functions via the generalized Fourier transform. We characterize the
Fourier coefficients of three different problems: the Traveling Salesman
Problem, the Linear Ordering Problem and the Quadratic Assignment Problem. This
implies that these three problems can be viewed in a homogeneous space, such as
the Fourier domain. Our final target would be to create a taxonomy of problem
instances, so that functions which are treated similarly under the same search
algorithms are grouped together. For this purpose, we simplify the
representations of the objective functions by considering them as permutations
of the elements of the search space, and study the permutations that are
associated with different problems.
