Dual-mode dynamics neural network (D2NN) for the traveling salesman problem

This paper presents an approach for solving TSP based on dual-mode dynamic neural network (D2NN). The dual modes dynamics includes state dynamics and weight dynamics. The state dynamics defines the state trajectories in a direction to minimize the network energy toward an equilibrium specified by the current weights. The weight dynamics generates the weight trajectories in a direction toward the minimum of the preassigned external cost function. The external cost function is defined to represent the desired objective function and the constraints to be satisfied. The two modes of dynamics govern the network alternately until the weight dynamics reaches its own equilibrium. With a nonconvex objective function, the gradient of the external cost function may be zero at its local minima such that no weight trajectory can be defined toward a global minimum. Therefore, a projection method is proposed in this paper as a solution to avoid such local minima. The simulation results show excellent performance of D2NN for TSP with the quality of solution enhanced by the proposed projection method