Abstract
A learning method of the Hopfield neural network is presented for efficiently solving combinatorial optimization problems. The learning method adjusts the balance between the constraint term and the cost term of the energy function so as to keep the Hopfield network updating in a gradient descent direction of energy.This paper describes and analyzes the learning method and shows its application to the traveling salesman problem (TSP). The performance is evaluated through simulating 100 randomly generated instances of the 10-city traveling salesman problem and some TSPLIB benchmark problems. The simulation results show that the performance of the proposed learning method on these test problems is very satisfactory in terms of both solution quality and running time. The proposed learning method finds the optimal solutions on the test TSPLIB benchmark problems in very short computation time.
