Box and Jenkins Nonlinear System Modelling Using RBF Neural Networks Designed by NSGAII

  • Kheireddine Lamamra
  • Khaled Belarbi
  • Souaad Boukhtini
Part of the Studies in Computational Intelligence book series (SCI, volume 575)


In this work, we use radial basis function neural network for modeling nonlinear systems. Generally, the main problem in artificial neural network is often to find a better structure. The choice of the architecture of artificial neural network for a given problem has long been a problem. Developments show that it is often possible to find architecture of artificial neural network that greatly improves the results obtained with conventional methods. We propose in this work a method based on No Sorting Genetic Algorithm II (NSGA II) to determine the best parameters of a radial basis function neural network. The NSGAII should provide the best connection weights between the hidden layer and output layer, find the parameters of the radial function of neurons in the hidden layer and the optimal number of neurons in the hidden layers and thus ensure learning necessary. Two functions are optimized by NSGAII: the number of neurons in the hidden layer of the radial basis function neural network, and the error which is the difference between desired input and the output of the radial basis function neural network. This method is applied to modeling Box and Jenkins system. The obtained results are very satisfactory.


NSGAII Radial basis function (RBF) neural networks Optimization Modelling Non linear system Box and Jenkins system 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Kheireddine Lamamra
    • 1
    • 2
  • Khaled Belarbi
    • 3
  • Souaad Boukhtini
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Oum El BouaghiOum El BouaghiAlgeria
  2. 2.Laboratory of Mastering of Renewable EnergiesUniversity of BejaiaBejaiaAlgeria
  3. 3.University of ConstantineConstantineAlgeria

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