A Note on Characterizing the k-OPTNeighborhood Via Group Theory

Group theory can be used to model and synthesize the neighborhood of Traveling Salesman tours reachable through k-OPT exchanges. A primary concept is that a dihedral group action partitions the sets of cut arcs so that k-OPT exchanges of orbital elements are conjugate. Also presented is a method to produce all k-OPT exchanges for a given set of cut arcs.