An artificial neural network, more commonly known as neural network, is a mathematical model for information processing based on the biological nervous system, which has a natural propensity for storing experiential knowledge and making it available for use (Haykin, 1999). The main advantage of a neural network is in its ability to approximate functional relationships, particularly nonlinear relationships. Neural networks have been applied to several classes of optimization problems and have shown promise for solving such problems efficiently. Most of the neural architectures proposed in the literature solve specific types of optimization problems (Dillon & O’Malley, 2002; Kakeya & Okabe, 2000; Xia et al., 2002). In contrast to these neural models, the network proposed here is able to treat several kinds of optimization problems using a unique network architecture. The approach described in this chapter uses a modified Hopfield network, which has equilibrium points representing the solution of the optimization problems. The Hopfield network is modified by presenting an optimization process carried out in two distinct stages, which are represented by two energy functions. The internal parameters of the network have been computed using the valid-subspace technique (Aiyer et al., 1990; Silva et al., 1997). This technique allows us to define a subspace, which contains only those solutions 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. Also in contrast to other neural approaches that use an energy function for each constraint to be satisfied, the mapping of optimization problems using the modified Hopfield network always consists of determining just two energy functions, which are denoted by Econf and Eop. The function Econf is a confinement term that groups all structural constraints associated with the problems, and Eop is an optimization term that leads the network output to the equilibrium points corresponding to optimal solutions. In this chapter, the proposed approach has been applied to solve combinatorial optimization problems, dynamic programming problems and nonlinear optimization problems. In addition to providing a new approach for solving several classes of optimization problems through a unique neural network architecture, the main advantages of using the modified O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m