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

Abstract

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.

Hybridized Extreme Learning Machine Model with Salp Swarm Algorithm: A Novel Predictive Model for Hydrological Application

“…In addition, inspecting longer data span of historical data information is highly recommended to be devoted as it is a limitation of the current research. On the algorithmic level, the proposed model can be extended in a way that other parameters in the ELM network can be optimized and such parameters include the number of hidden nodes in the hidden layer, the transfer functions, and the activation functions [51][52][53].…”

Training Feedforward Neural Network Using Enhanced Black Hole Algorithm: A Case Study on COVID-19 Related ACE2 Gene Expression Classification

“…Under the same conditions as our experiments, the parameters setting and experimental results for other evolutionary algorithms, including ABC, PSO, LFFA, GWO, GSA, CSA, BB-BC, BHA, and LBH, were derived from Ref. [ 61 ]. The experimental results are tabulated in Table 2 .…”

“…Levy flight is a type of random walk, where its step-size is based on Levy distribution. Levy flight enhances the efficiency of the BHA by improving BHA’s global search capability and avoiding local optima [ 61 ]. The stars’ new position using Levy flight random walk can be calculated by: is an array of normally distributed random numbers, and indicates the steps of Levy flight which is calculated as follows: where and are drawn from a normal distribution with zero mean and standard deviations and .…”

“…It is also worth noting that a hybrid of Levy flight and BHA, called LBH [ 61 ], has been considered in the literature for empowering the BHA’s global search capability to solve function and clustering problems. In LBH, levy flight is used in the updating of all-stars’ positions without any constraints, while in the BHACRW, complementary learning operator and levy flight are utilized sequentially for updating the position of half-worst solutions, if the BHA get stuck in local optima.…”

Shallow Foundation Settlement Quantification: Application of Hybridized Adaptive Neuro‐Fuzzy Inference System Model

“…is is a very useful probabilistic approach in the sense that it can overcome the problems of the deterministic techniques and provide some guidance to the geotechnical engineers about the level of risk (i.e., degree of uncertainty) associated with the predicted settlement. Exploring other nature-inspired algorithms for optimizing ANFIS model can be further studied for better prediction accuracy [78][79][80].…”