Levy flight and chaos theory based gravitational search algorithm for multilayer perceptron training

In this paper, a modified version of the Gravitational Search Algorithm (GSA) based on levy flight and chaos theory namely LCGSA has been used to train Multilayer Perceptron (MLP) neural network for feature classification and function approximation. In LCGSA, the diversification of the search space is carried out by levy flight while chaotic maps have been utilized for the intensification of the candidate solutions towards the global optimum. Besides, the sigmoid function acts as an objective function for LCGSA based MLP pair in order to minimize the neural bias and error. Moreover, the matrix encoding scheme is used for representing the candidate solutions. To verify the effectiveness of LCGSA, it has been applied to three well-known classification datasets namely XOR, Balloon, and Heart. Besides, two function approximation benchmarks including Sigmoid and Cosine functions are also considered for the performance evaluation. Furthermore, the quantitative and qualitative analysis of the simulation results has been carried out. The quantitative performance metrics include statistical measures, run time, mean square error (MSE), and average test error (ATE). Also, the simulation analysis is benchmarked by utilizing various qualitative measures such as convergence rate, box plot analysis, and approximation curves. The signed Wilcoxon rank-sum test is employed to statistically verify the experimental outcomes. In addition, ten LCGSA versions are compared with various hybrid and recent heuristic optimization techniques. The simulation results indicate that LCGSA provides better performance than standard GSA and most of the competing algorithms.