Multi-objective Optimization of a Composite Material Spring Design Using an Evolutionary Algorithm

  • Frédéric Ratle
  • Benoît Lecarpentier
  • Richard Labib
  • François Trochu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)


A multi-objective evolutionary algorithm is applied to optimize the design of a helical spring made out of a composite material. The criteria considered are the minimization of the mass along with the maximization of the stiffness of the spring. Considering the computation time required for finite element analyses, the optimization is performed using approximate relations between design parameters. Dual kriging interpolation allows improving the accuracy of the classical model of spring stiffness by estimating the error between the model and the results of finite element analyses. This error is taken into account by adding a correction function to the stiffness function. The NSGA-II algorithm is applied and shows satisfactory results, while using the correction function induces a displacement of the Pareto front.


Pareto Front Multiobjective Optimization Correction Function Helix Angle Multiobjective Evolutionary Algorithm 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yokota, T., Taguchi, T., Gen, M.: A solution method for optimal weight design problem of helical spring using genetic algorithms. Computers Ind. Engng. 33(1-2), 71–76 (1997)CrossRefGoogle Scholar
  2. 2.
    Gobbi, M., Mastinu, G.: On the optimal design of composite material tubular helical springs. In: Meccanica, vol. 36, pp. 525–553. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  3. 3.
    Srinivas, D., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Journal of Evolutionary Computation 2(3), 221–248 (1995)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer, M., et al. (eds.) Parallel Problem Solving from Nature, vol. 6, pp. 849–858 (2000)Google Scholar
  5. 5.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar
  6. 6.
    Hamda, H., Roudenko, O., Schoenauer, M.: Application of a multi-objective evolutionary algorithm to topological optimum design. In: Parmee, I. (ed.) Fifth International Conference on Adaptive Computing in Design and Manufacture (2002)Google Scholar
  7. 7.
    Lahanas, M., Baltas, D., Zamboglou, N.: A hybrid evolutionary multiobjective algorithm for anatomy based dose optimization algorithm in HDR brachytherapy. Physics in Medecine and Biology 48, 399–415 (2003)CrossRefGoogle Scholar
  8. 8.
    Wu, J.-L., Agogino, A.M.: Automating keyphrase extraction with multi-objective genetic algorithms. In: Proceedings of the 37th Hawaii International Conference on Systems Sciences (2004)Google Scholar
  9. 9.
    Jin, Y.: Fitness approximation in evolutionary computation: a survey. Soft Computing Journal 4 (2003) (in press)Google Scholar
  10. 10.
    Cressie, N.: Statistics for Spatial Data. Wiley, Chichester (1993)Google Scholar
  11. 11.
    Trochu, F.: A contouring program based on dual kriging interpolation. Engineering with Computers 9, 160–177 (1993)CrossRefGoogle Scholar
  12. 12.
    Cohn, D.A., Ghahramani, Z., Jordan, M.I.: Active learning with statistical models. Journal of Artificial Intelligence Research 4, 129–145 (1996)MATHGoogle Scholar
  13. 13.
    Abe, N., Mamitsuka, H.: Query learning strategies using boosting and bagging. In: Proceedings of The Fifteenth International Conference on Machine Learning, pp. 1–9 (1998)Google Scholar
  14. 14.
    Parmee, I.: Evolutionary and Adaptive Computing in Engineering Design. Springer, Heidelberg (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Frédéric Ratle
    • 1
  • Benoît Lecarpentier
    • 1
  • Richard Labib
    • 2
  • François Trochu
    • 1
  1. 1.Centre de Recherche Appliquée Sur les Polymères, Département de Génie MécaniqueÉcole Polytechnique de MontréalMontréalCanada
  2. 2.Département de Mathématiques et de Génie IndustrielÉcole Polytechnique de MontréalMontréalCanada

Personalised recommendations