Research Article A New Binary Adaptive Elitist Differential Evolution Based Automatic k-Medoids Clustering for Probability Density Functions D. Pham-Toan , 1 T. Vo-Van, 1 A. T. Pham-Chau, 2,3 T. Nguyen-Trang , 2,3 and D. Ho-Kieu 2,3 1 Natural Science College, Can To University, Can To, Vietnam 2 Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Tang University, Ho Chi Minh City, Vietnam 3 Faculty of Mathematics and Statistics, Ton Duc Tang University, Ho Chi Minh City, Vietnam Correspondence should be addressed to D. Ho-Kieu; hokieudiem@tdtu.edu.vn Received 22 December 2018; Accepted 24 March 2019; Published 22 April 2019 Academic Editor: Elio Masciari Copyright © 2019 D. Pham-Toan et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper proposes an evolutionary computing based automatic partitioned clustering of probability density function, the so-called binary adaptive elitist diferential evolution for clustering of probability density functions (baeDE-CDFs). Herein, the k-medoids based representative probability density functions (PDFs) are preferred to the k-means one for their capability of avoiding outlier efectively. Moreover, addressing clustering problem in favor of an evolutionary optimization one permits determining number of clusters “on the run”. Notably, the application of adaptive elitist diferential evolution (aeDE) algorithm with binary chromosome representation not only decreases the computational burden remarkably, but also increases the quality of solution signifcantly. Multiple numerical examples are designed and examined to verify the proposed algorithm’s performance, and the numerical results are evaluated using numerous criteria to give a comprehensive conclusion. Afer some comparisons with other algorithms in the literature, it is worth noticing that the proposed algorithm reveals an outstanding performance in both quality of solution and computational time in a statistically signifcant way. 1. Introduction Clustering aims to divide input data into multiple groups such that elements in each group are similar and diferent from elements in other groups as much as possible. Tere are two primary objects of clustering, discrete element and probability density function (PDF). Over the past few years, discrete element is preferred in clustering with a lot of works such as [1, 2]. However, with the explosion of digital era, a massive amount of data is created each day [3, 4], and how to present such data well is a challenge task for discrete elements. Te main reason for this is that the discrete element just presents whole data by a representative point so that it is unlikely to fully demonstrate characteristic of whole data, especially fuctuation data [5]. Meanwhile, the remaining object-PDF shows its advantage in such digital era like capturing the distribution of whole data, giving a visible look of characteristic of the estimated objects [5]. However, regardless of the advantages of PDF, works related to clustering for this interesting object are still very limited. Terefore, this paper aims to contribute new approach for clustering of probability density functions (CDFs). Concerning CDFs, two main approaches can be found, nonhierarchical and hierarchical [6]. With respect to non- hierarchical approach, k-means and k-medoids based algo- rithms can be seen as the typical ones [7]. However, k-means based approach shows its disadvantage when addressing out- liers or noises [7]. In contrast, k-medoids based approach can handle outliers efectively as shown in the work of [8] since it directly employs objects in input data as the centers. Te k-medoids is then applied to various felds. For example, in [9], Zhang B et al. presented an improved ranked k-medoids Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 6380568, 16 pages https://doi.org/10.1155/2019/6380568