A PPLICATIONS PPLICATION OF E VOLUTIONARY C OMPUTING ING T ECHNIQUES TO N ON -L INEAR S YSTEMS

Abstract

This dissertation presents an application of heuristic computational intelligence for the solution of non-linear systems in engineering. The design scheme is comprised of mathematical model based on feed-forward artificial neural network (ANN). The linear combination of these networks defines the unsupervised error for the system. The most suitable weights to minimize the error are obtained by training the networks employing stochastic solvers. These techniques are based on nature inspired heuristics including Pattern Search (PS), Simulated Annealing (SA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms. Rapid local convergent algorithms such as Interior Point (IP) and Active Set (AS) methods are hybridized with these global search techniques. To validate the scheme, a number of linear and non-linear initial and boundary value problems have been solved. The design methodology is also applied to a number of problems having special applications in engineering including, singular systems based on non-linear Lane Emden Fowler equation, non-linear van der Pol oscillator with stiff and non-stiff conditions and systems with high nonlinearity governed by Painlevé transcendent I. In addition to that, the scheme also provides an alternate solution for biomedical application like model of heart for low, high and normal blood pressure. It is found that the proposed results are in good agreement with available exact solution and numerical solvers like Adomian decomposition method, Homotopy Perturbation method, Homotopy analysis method and Optimal Homotopy asymptotic method, ODE15i and Runge Kutta method. The comparative studies of stochastic solvers are carried out under a stringent criterion of accuracy, effectiveness, reliability and robustness of the results based on Monte Carlo simulation and its analysis. The solvers based on SA, PS, GA, PSO, GA and PSO hybrid with IP or AS algorithms are used for optimization of neural network. It is found that the GA-IP, GA-AS, PSO-IP and PSO-AS algorithms are the best stochastic optimizers. The other perk up of the scheme have in its simplicity of the concept, ease in use, efficiency and unlike other numerical techniques, it provides the solution on continuous inputs with finite interval instead of predefine discrete grid of inputs.