Integration of Structural Constraints into TSP Models

Several models based on constraint programming have been proposed to solve the traveling salesman problem (TSP). The most efficient ones, such as the weighted circuit constraint (WCC), mainly rely on the Lagrangian relaxation of the TSP, based on the search for spanning tree or more precisely "1-tree". The weakness of these approaches is that they do not include enough structural constraints and are based almost exclusively on edge costs. The purpose of this paper is to correct this drawback by introducing the Hamiltonian cycle constraint associated with propagators. We propose some properties preventing the existence of a Hamiltonian cycle in a graph or, conversely, properties requiring that certain edges be in the TSP solution set. Notably, we design a propagator based on the research of k-cutsets. The combination of this constraint with the WCC constraint allows us to obtain, for the resolution of the TSP, gains of an order of magnitude for the number of backtracks as well as a strong reduction of the computation time.