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

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.