Determination of Parameters in Relaxation-search Neural Networks for Optimization Problems

We propose a method to define constraint weight parameters of the Hopfield network in order to establish the solutions of the optimization problem as stable equilibrium points in the state space. Application of the methodology is demonstrated on a well known benchmark problem, the Traveling Salesman Problem. Simulation results indicate that the proposed bounds on the constraint weight parameters establish the solutions as stable points and consequently, the Hopfield network consistently converges to a solution after each relaxation.