Eur. Phys. J. Plus (2019) 134: 122
https://doi.org/10.1140/epjp/i2019-12530-5

Regular Article

Design of cascade artificial neural networks optimized with the memetic computing paradigm for solving the nonlinear Bratu system

¹ Research in Modeling and Simulation (RIMS) Group, Department of Physics, COMSATS University Islamabad, Islamabad, Pakistan
² Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

^* e-mail: sirajisl@yahoo.co.uk

Received: 20 November 2018
Accepted: 23 January 2019
Published online: 26 March 2019

Abstract

A nature-inspired, integrated computational heuristic paradigm is developed for the piecewise solution of the nonlinear Bratu problem arising in fuel ignition model, electrically conducting solids and related fields, by exploiting the strength of Cascade Artificial Neural Networks (CANN) modeling, optimized with the memetic computing procedure based on global search efficacy of genetic algorithms (GAs), aided with the efficient local search of teaching learning based optimization (TLBO). The proposed technique incorporates the log-sigmoid activation function in the CANN model, trained by GAs hybridized with TLBO, i.e., CANN-GA-TLBO. As a first application of CANN-GA-TLBO, 1D nonlinear Bratu's system represented with a boundary value problem of the second-order ordinary different equation has been solved, which is a benchmark for testing new algorithms. Comparison of the results with exact solution and previously reported solutions, including Adomian decomposition method, Laplace transformed decomposition method, B-Spline method and artificial neural network solutions, confirms the superiority of the designed stochastic solver CANN-GA-TLBO in terms of accuracy and convergence measures.