Soft Computing

, Volume 11, Issue 7, pp 655–668 | Cite as

A new hybrid methodology for cooperative-coevolutionary optimization of radial basis function networks

  • A. J. Rivera
  • I. Rojas
  • J. Ortega
  • M. J. del Jesus
Original Article


This paper presents a new multiobjective cooperative–coevolutive hybrid algorithm for the design of a Radial Basis Function Network (RBFN). This approach codifies a population of Radial Basis Functions (RBFs) (hidden neurons), which evolve by means of cooperation and competition to obtain a compact and accurate RBFN. To evaluate the significance of a given RBF in the whole network, three factors have been proposed: the basis function’s contribution to the network’s output, the error produced in the basis function radius, and the overlapping among RBFs. To achieve an RBFN composed of RBFs with proper values for these quality factors our algorithm follows a multiobjective approach in the selection process. In the design process, a Fuzzy Rule Based System (FRBS) is used to determine the possibility of applying operators to a certain RBF. As the time required by our evolutionary algorithm to converge is relatively small, it is possible to get a further improvement of the solution found by using a local minimization algorithm (for example, the Levenberg–Marquardt method). In this paper the results of applying our methodology to function approximation and time series prediction problems are also presented and compared with other alternatives proposed in the bibliography.


Cooperative–coevolution Soft-computing techniques RBF networks Fuzzy rule based system Function approximation 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • A. J. Rivera
    • 1
  • I. Rojas
    • 2
  • J. Ortega
    • 2
  • M. J. del Jesus
    • 1
  1. 1.Department of Computer ScienceUniversity of JaénJaenSpain
  2. 2.Department of Computer Architecture and Computer TechnologyUniversity of GranadaGranadaSpain

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