A hybrid neural network model for solving optimization problems

A hybrid neural network model for solving optimization problems is proposed. An energy function which contains the constraints and cost criteria of an optimization problem is derived, and then the neural network is used to find the global minimum (or maximum) of the energy function, which corresponds to a solution of the optimization problem. The network contains two subnets: a constraint network and a goal network. The constraint network models the constraints of an optimization problem and computes the gradient (updating) value of each neuron such that the energy function monotonically converges to satisfy all constraints of the problem. The goal network points out the direction of convergence for finding an optimal value for the cost criteria. These two subnets ensure that the neural network finds feasible as well as optimal (or near-optimal) solutions. The traveling salesman problem and the Hamiltonian cycle problem are used to demonstrate the method