On parameter settings of Hopfield networks applied to traveling salesman problems

Parameter setting is a critical step in the Hopfield networks solution of the traveling salesman problem (TSP), which is often prone to extraneous solutions. This paper presents some stability criteria that ensure the convergence of valid solutions and suppression of infeasible solutions. Our theory is based on an enhanced parametric formulation that maps TSP onto a continuous-time Hopfield network (CHN), which is more advantageous than the Hopfield-Tank (H-T) formulation. A set of analytical conditions for optimal parameter settings of the CHN is then derived, and the resulting performance is validated by simulations.