Given the rapid growth of data and the reduced implementation quality of data mining and pattern extraction techniques, the use of feature reduction has become an important challenge of data mining and pattern recognition. An important goal of data reduction techniques is to make the minimum effort and achieve the maximum efficiency of data selection for the implementation of data mining process. The two primary objectives of feature selection are to minimize the errors of the patterns identified in the reduced subset and minimize the number of features. The majority of available feature selection algorithms adopts a single-objective approach. This is the first paper focused on clustering used as the identifier of unsupervised hidden patterns. It is also focused on the principal component analysis (PCA) to analyze the values of the features. The goals of the new multi-objective feature selection problem are to minimize the coefficient of PCA, maximize the accuracy of k-medoids clustering, and minimize the number of selected features. Another innovation of this study was to select the best subset of features at the best performance by using the electromagnetism-like mechanism (EM) algorithm. The proposed method was tested on 14 standard UCI datasets. The results indicated the competitive advantage of this algorithm over other algorithms implemented to solve this problem.