This dissertation deals with the evolutionary optimization of ART neural network architectures. ART (adaptive resonance theory) was introduced by a Grossberg in 1976. In the last 20 years (1987-2007) a number of ART neural network architectures were introduced into the literature (Fuzzy ARTMAP (1992), Gaussian ARTMAP (1996 and 1997) and Ellipsoidal ARTMAP (2001)). In this dissertation, we focus on the evolutionary optimization of ART neural network architectures with the intent of optimizing the size and the generalization performance of the ART neural network. A number of researchers have focused on the evolutionary optimization of neural networks, but no research has been performed on the evolutionary optimization of ART neural networks, prior to 2006, when Daraiseh has used evolutionary techniques for the optimization of ART structures. This dissertation extends in many ways and expands in different directions the evolution of ART architectures, such as: (a) uses a multi-objective optimization of ART structures, thus providing to the user multiple solutions (ART networks) with varying degrees of merit, instead of a single solution (b) uses GA parameters that are adaptively determined throughout the ART evolution, (c) identifies a proper size of the validation set used to calculate the fitness function needed for ART's evolution, thus speeding up the evolutionary process, (d) produces experimental results that demonstrate the evolved ART's effectiveness (good accuracy and small size) and efficiency (speed) compared with other competitive ART structures, as well as other classiffiers (CART (Classification and Regression Trees) and SVM (Support Vector Machines)). The overall methodology to evolve ART using a multi-objective approach, the chromosome representation of an ART neural network, the genetic operators used in ART's evolution, and the automatic adaptation of some of the GA parameters in ART's evolution could also be applied in the evolution of other exemplar based neural network classiffiers such as the probabilistic neural network and the radial basis function neural network.