Linear Optimization over Permutation Groups

For a permutation group given by a set of generators, the problem of finding "special" group members is NP-hard in many cases. E.g., this is true for the problem of finding a permutation with a minimum number of fixed points or a permutation with a minimal Hamming distance from a given permutation. Many of these problems can be modeled as linear optimization problems over permutation groups. We develop a polyhedral approach to this general problem and derive an exact and practically fast algorithm based on the branch&cut-technique