An Efficient Hybrid Optimization Approach Using Adaptive Elitist Differential Evolution and Spherical Quadratic Steepest Descent and Its Application for Clustering

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.