An improved differential evolution algorithm using Archimedean spiral and neighborhood search based mutation approach for cluster analysis

Abstract

This study proposes an improved Differential Evolution (DE) algorithm utilizing Archimedean Spiral, Mantegna Lévy Distribution, and Neighborhood Search (NS). The proposed algorithm is denoted as Adaptive Differential Evolution with Neighborhood Search (ADENS). The aim of the ADENS algorithm is to enhance the convergence speed and keeping a balance between exploration and exploitation of the DE algorithm. It uses a new mutation strategy to generate robust solutions by combining the Archimedean Spiral (AS) with the Mantegna Lévy flight. In order to enhance the efficiency of ADENS, a replacement method combines Lévy flight with neighborhood search to generate solutions that replace poorly performing ones. A self-adaptive strategy is applied to fine-tune one of the control parameters of DE and an initialization method is employed to initialize the algorithm. These strategies help the algorithm achieve good efficiency in terms of convergence speed and both local and global search. The performance is evaluated using twelve well-known standard data sets to show the algorithm’s superior performance, confirmed to be statistically significant. In order to test the proposed approach statistically, this paper applied Wilcoxon ranked sum test as well as Friedman test. Our results also shed light on the comparative performance of some recently published clustering heuristics. The results show that the algorithm is a robust algorithm and has a great superiority with respect to the employed algorithms. The proposed algorithm can be applied in different applications such as medical diagnosis and image segmentation according to the conducted experiments.