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Well-Distributed Pareto Front by Using the \(\epsilon \hskip-0.9em \nearrow \hskip-0.4em-MOGA\) Evolutionary Algorithm

  • J. M. Herrero
  • M. Martínez
  • J. Sanchis
  • X. Blasco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4507)

Abstract

In the field of multiobjective optimization, important efforts have been made in recent years to generate global Pareto fronts uniformly distributed. A new multiobjective evolutionary algorithm, called \(\epsilon \hskip-0.9em \nearrow \hskip-0.4em-MOGA\), has been designed to converge towards \(\mathbf{\Theta}_P^*\), a reduced but well distributed representation of the Pareto set Θ P . The algorithm achieves good convergence and distribution of the Pareto front J(Θ P ) with bounded memory requirements which are established with one of its parameters. Finally, a optimization problem of a three-bar truss is presented to illustrate the algorithm performance.

Keywords

Pareto Front Multiobjective Optimization Pareto Frontier Multiobjective Evolutionary Algorithm Normalize Normal Constraint 
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.
    Batill, S.M.: Course: ME/AE 446. Finite Element Methods in Structural Analysis, Planar truss applications (1995), http://www.nd.edu
  2. 2.
    Coello, C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in applied Mechanics and Engineering 191, 1245–1287 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Coello, C., Veldhuizen, D., Lamont, G.: Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, Boston (2002)zbMATHGoogle Scholar
  4. 4.
    Herrero, J.M.: Non-linear Robust identification using evolutionary algorithms, PhD thesis, Polytechnic University of Valencia (2006)Google Scholar
  5. 5.
    Herrero, J.M., Blasco, X., Martínez, M., Sanchis, J.: Robust identification of a biomedical process by evolutionary algorithms. RIAI 3(4), 75–86 (2006)Google Scholar
  6. 6.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary computation 10(3), 263–282 (2002)CrossRefGoogle Scholar
  7. 7.
    Martínez, M., Blasco, X., Sanchis, J.: Global and well-distributed pareto frontier by modified normalized constraint methods. Struct. Multidisc. Optim. 34(3) (2006), doi:10.1007/S00158-006-0071-5Google Scholar
  8. 8.
    Messac, A., Ismail, A., Mattson, C.A.: The normalized normal constraint method for generating the Pareto frontier. Struct. Multidisc. Optim. 25, 86–98 (2003)CrossRefGoogle Scholar
  9. 9.
    Zitzler, E.: Evolutionary algorithms for multiobjective optimization: Methods and applications, PhD thesis, Swiss Federal Institute of Technology Zurich (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • J. M. Herrero
    • 1
  • M. Martínez
    • 1
  • J. Sanchis
    • 1
  • X. Blasco
    • 1
  1. 1.Department of Systems Engineering and Control, Polytechnic University of ValenciaSpain

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