In this paper, a hybrid approach that combines a population-based method, adaptive elitist differential evolution (aeDE), with a powerful gradient-based method, spherical quadratic steepest descent (SQSD), is proposed and then applied for clustering analysis. This combination not only helps inherit the advantages of both the aeDE and SQSD but also helps reduce computational cost significantly. First, based on the aeDE’s global explorative manner in the initial steps, the proposed approach can quickly reach to a region that contains the global optimal value. Next, based on the SQSD’s locally effective exploitative manner in the later steps, the proposed approach can find the global optimal solution rapidly and accurately and hence helps reduce the computational cost. The proposed method is first tested over 32 benchmark functions to verify its robustness and effectiveness. Then, it is applied for clustering analysis which is one of the problems of interest in statistics, machine learning, and data mining. In this application, the proposed method is utilized to find the positions of the cluster centers, in which the internal validity measure is optimized. For both the benchmark functions and clustering problem, the numerical results show that the hybrid approach for aeDE (HaeDE) outperforms others in both accuracy and computational cost.

This paper proposes an evolutionary computing based automatic partitioned clustering of probability density function, the so-called binary adaptive elitist differential 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 effectively. 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 differential evolution (aeDE) algorithm with binary chromosome representation not only decreases the computational burden remarkably, but also increases the quality of solution significantly. 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. After 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 significant way.

Image enhancement is an adjusting process to make an image more appropriate for certain applications. The contrast enhancement is one of the most frequently used image enhancement methods. In this study, we introduce a new image contrast enhancement method using a link between sigmoid function and Differential Evolution (DE) algorithm. DE algorithm is performed to identify the parameters in sigmoid function so that they can maximize the measure of contrast. The experimental results show that the proposed method not only retains the original image features but also enhances the contrast effectively. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

The contrast is a major factor influencing the image quality; therefore, image contrast enhancement technique is more and more widely applied in the field of image processing. In this paper, a new fuzzy rule-based contrast enhancement method using the two-steps automatic clustering algorithm is proposed. Specifically, based on the Automatic clustering algorithm, a state-of-art method in cluster analysis and data mining, this paper proposes a two-steps Automatic clustering method to determine the number of fuzzy sets and locate the critical point in membership functions so that they are suitable for the distribution of pixel intensity values. The experiments on the "Lena" image and other natural images demonstrate that the new method can effectively enhance the contrast of the images and meet the demands of human eyes perception at the same time.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.