An Enhanced Version of Black Hole Algorithm via Levy Flight for Optimization and Data Clustering Problems

The processes of retrieving useful information from a dataset are an important data mining technique that is commonly applied, known as Data Clustering. Recently, nature-inspired algorithms have been proposed and utilized for solving the optimization problems in general, and data clustering problem in particular. Black Hole (BH) optimization algorithm has been underlined as a solution for data clustering problems, in which it is a population-based metaheuristic that emulates the phenomenon of the black holes in the universe. In this instance, every solution in motion within the search space represents an individual star. The original BH has shown a superior performance when applied on a benchmark dataset, but it lacks exploration capabilities in some datasets. Addressing the exploration issue, this paper introduces the levy flight into BH algorithm to result in a novel data clustering method “Levy Flight Black Hole (LBH)”, which was then presented accordingly. In LBH, the movement of each star depends mainly on the step size generated by the Levy distribution. Therefore, the star explores an area far from the current black hole when the value step size is big, and vice versa. The performance of LBH in terms of finding the best solutions, prevent getting stuck in local optimum, and the convergence rate has been evaluated based on several unimodal and multimodal numerical optimization problems. Additionally, LBH is then tested using six real datasets available from UCI machine learning laboratory. The experimental outcomes obtained indicated the designed algorithm's suitability for data clustering, displaying effectiveness and robustness.