The modified Hopfield architecture applied in dynamic programming problems and bipartite graph optimization

Abstract

Artificial neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents a modified Hopfield architecture, which has equilibrium points representing the solution of the problems considered, i.e, dynamic programming problems and bipartite graph optimization. The internal parameters of the network have been computed using the valid-subspace technique. This method allows us to define a subspace, which contains only those vectors that represent feasible solutions to the problem analyzed. It has also been demonstrated that with appropriately set parameters, the network confines its output to this subspace, thus ensuring convergence to a valid solution. Simulation results and comparative analyses with other methods are presented to validate the proposed approach.