In this paper, we introduce the methodological system design via feature selection using Principal Component Analysis and Particle Swarm Optimization algorithms. The overall methodological system design comes from three kinds of modules such as preprocessing module, feature extraction module, and recognition module. First, Histogram equalization enhance the quality of image by exploiting contrast effect based on the normalized function generated from histogram distribution values of 2D face image. Secondly, PCA extracts feature vectors to be used for face recognition by using eigenvalues and eigenvectors obtained from covariance matrix. Finally the feature selection for face recognition among the entire feature vectors is considered by means of the Particle Swarm Optimization. The optimized Polynomial-based Radial Basis Function Neural Networks are used to evaluate the face recognition performance. This study shows that the proposed methodological system design is effective to the analysis of preferred face recognition.