Forecasting Chaotic Time Series Using an Artificial Immune System Algorithm-based BPNN

Based on the steepest descent method, back-propagation neural networks (BPNNs) minimize an energy function for errors occurring between desired and actual outputs. Therefore, conventional BPNNs obtain local optimum weights. Stochastic search optimization methods, such as genetic algorithms, particle swarm optimization methods and artificial immune system (AIS) algorithms, have been extensively used to solve optimization problems. The weight optimization of a BPNN can be considered as a highly dimensional and unconstrained optimization problem. To overcome the limitation of conventional BPNN, this work presents an AIS algorithm-based BPNN (named AIS-BPNN). The weights of BPNN are optimized using an AIS algorithm. Performance of the proposed AIS-BPNN is then evaluated using a benchmark chaotic time series and compared with those of conventional BPNN and advanced simulated annealing (ASA) algorithm-based BPNN (named ASA-BPNN). Numerical results indicate that the proposed AIS-BPNN can yield acceptable training and generalization results and are superior to those of standard BPNN and ASA-BPNN for the test case. The proposed AIS-BPNN is thus considered as an alternative forecasting tool for chaotic time series.