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Optimization with Implicitly Known Objective Functions Using RBF Networks and Genetic Algorithms

  • Hirotaka Nakayama
  • Masao Arakawa
  • Rie Sasaki

Abstract

In many practical engineering design problems, the form of objective function is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective function is obtained by some analysis such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. Usually, these analyses are considerably time consuming to obtain a value of objective function. In order to make the number of analyses as few as possible, we suggest a method by which optimization is performed in parallel with predicting the form of objective function. In this paper, radial basis function networks (RBFN) are employed in predicting the form of objective function, and genetic algorithms (GA) in searching the optimal value of the predicted objective function. The effectiveness of the suggested method will be shown through so me numerical examples.

Keywords

Objective Function Genetic Algorithm Training Data Additional Data Design Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M. Arakawa and I. Hagiwara, “Nonlinear Integer, Discrete and Continuous Optimization Using Adaptive Range Genetic Algorithms”, Proc. of ASME Design Technical Conferences (in CD-ROM), 1997Google Scholar
  2. [2]
    S. Haykin, “Neural Networks: A Comprehensive Foundation”, Macmillan College Publishing Company, 1994Google Scholar
  3. [3]
    M.J.L. Orr, “Introduction to Radial Basis Function Networks”, http://www.cns.ed.ac.uk/people/mark. html, Apr. 1996Google Scholar
  4. [4]
    N.J. Radcliffe, “Forma Analysis and Random Respectful Recombination”, Proceedings of the Forth International Conference on Genetic Algorithms, pp222–229, 1991Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Hirotaka Nakayama
    • 1
  • Masao Arakawa
    • 2
  • Rie Sasaki
    • 1
  1. 1.Department of Applied MathematicsKonan UniversityJapan
  2. 2.Department of Reliability-based Information System EngineeringKagawa UniversityJapan

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