Computer-Aided Diagnosis (CAD) represents a relevant instrument to automatically classify between patients with and without Alzheimer's Disease (AD) using several actual imaging techniques. This study analyzes the optimization of volumes of interest (VOIs) to extract three-dimensional (3D) textures from Magnetic Resonance Image (MRI) in order to diagnose AD, Mild Cognitive Impairment converter (MCIc), Mild Cognitive Impairment nonconverter (MCInc) and Normal subjects. A relevant feature of the proposed approach is the use of 3D features instead of traditional two-dimensional (2D) features, by using 3D discrete wavelet transform (3D-DWT) approach for performing feature extraction from T-1 weighted MRI. Due to the high number of coefficients when applying 3D-DWT to each of the VOIs, a feature selection algorithm based on mutual information is used, as is the minimum Redundancy Maximum Relevance (mRMR) algorithm. Region optimization has been performed in order to discover the most relevant regions (VOIs) in the brain with the use of Multi-Objective Genetic Algorithms, being one of the objectives to be optimize the accuracy of the system. The error index of the system is computed by the confusion matrix obtained by the multi-class support vector machine (SVM) classifier. Principal Component Analysis (PCA) is used with the purpose of reducing the number of features to the classifier. The cohort of subjects used in the study consisted of 296 different patients. A first group of 206 patients was used to optimize VOI selection and another group of 90 independent subjects (that did not belong to the first group) was used to test the solutions yielded by the genetic algorithm. The proposed methodology obtains excellent results in multi-class classification achieving accuracies of 94.4% and also extracting significant information on the location of the most relevant points of the brain. This suggests that the proposed method could aid in the research of other neurodegenerative diseases, improving the accuracy of the diagnosis and finding the most relevant regions of the brain associated with them.