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Dynamic programming has provided a powerful approach to optimization problems, but its applicability has been somewhat limited because of the large computational requirements of the standard computational algorithm. In recent years a number of new procedures with reduced computational requirements have been developed. This paper presents a association of a modified Hopfield neural network, which is a computing model capable of solving a large class of optimization problems, with a genetic algorithm, that to make possible cover nonlinear and extensive search spaces, which guarantees the convergence of the system to the equilibrium points that represent solutions for the optimization problems. Experimental results are presented and discussed.