Feedback-Control Operators for Evolutionary Multiobjective Optimization

  • Ricardo H. C. Takahashi
  • Frederico G. Guimarães
  • Elizabeth F. Wanner
  • Eduardo G. Carrano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5467)


New operators for Multi-Objective Evolutionary Algorithms (MOEA’s) are presented here, including one archive-set reduction procedure and two mutation operators, one of them to be applied on the population and the other one on the archive set. Such operators are based on the assignment of “spheres” to the points in the objective space, with the interpretation of a “representative region”. The main contribution of this work is the employment of feedback control principles (PI control) within the archive-set reduction procedure and the archive-set mutation operator, in order to achieve a well-distributed Pareto-set solution sample. An example EMOA is presented, in order to illustrate the effect of the proposed operators. The dynamic effect of the feedback control scheme is shown to explain a high performance of this algorithm in the task of Pareto-set covering.


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  1. 1.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. on Evolutionary Computation 7(2), 117–132 (2003)CrossRefGoogle Scholar
  2. 2.
    Silva, V.L.S., Wanner, E.F., Cerqueira, S.A.A.G., Takahashi, R.H.C.: A new performance metric for multiobjective optimization: The integrated sphere counting. In: Proc. IEEE Congress on Evolutionary Computation, Singapore (2007)Google Scholar
  3. 3.
    Ogata, K.: Modern Control Engineering, 4th edn. Prentice-Hall, Englewood Cliffs (2001)MATHGoogle Scholar
  4. 4.
    de Castro, L.N., Timmis, J.: An artificial immune network for multimodal function optimization. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation, vol. 1, pp. 699–704 (2002)Google Scholar
  5. 5.
    Takahashi, R.H.C., Palhares, R.M., Dutra, D.A., Gonalves, L.P.S.: Estimation of Pareto sets in the mix H 2/H inf control problem. International Journal of Systems Science 35(1), 55–67 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bui, L.T., Deb, K., Abbass, H.A., Essam, D.: Interleaving guidance in evolutionary multi-objective optimization. Journal of Computer Science and Technology 23(1), 44–63 (2008)CrossRefGoogle Scholar
  7. 7.
    Bui, L.T., Abbass, H.A., Essam, D.: Local models – an approach to distributed multi-objective optimization. In: Computational Optimization and Applications (2007) (to appear, published online in 2007), doi:10.1007/s10589-007-9119-8Google Scholar
  8. 8.
    Wanner, E.F., Guimaraes, F.G., Takahashi, R.H.C., Fleming, P.J.: Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria. Evolutionary Computation 16(2), 185–224 (2008)CrossRefGoogle Scholar
  9. 9.
    Takahashi, R.H.C., Vasconcellos, J.A., Ramirez, J.A., Krahenbuhl, L.: A multiobjective methodology for evaluation genetic operators. IEEE Trans. on Magnetics 39, 1321–1324 (2003)CrossRefGoogle Scholar
  10. 10.
    Fonseca, C.M., Fleming, P.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proceedings of the 5th International Conference: Genetic Algorithms, San Mateo, USA, pp. 416–427 (1993)Google Scholar
  11. 11.
    Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation 7(3), 205–230 (1995)Google Scholar
  12. 12.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Tech. Rep. 103 (2001)Google Scholar
  13. 13.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Bader, J., Zitzler, E.: HypE: Fast Hypervolume-Based Multiobjective Search Using Monte Carlo Sampling. Institut für Technische Informatik und Kommunikationsnetze, ETH Zürich, TIK Report 286 (October 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ricardo H. C. Takahashi
    • 1
  • Frederico G. Guimarães
    • 2
  • Elizabeth F. Wanner
    • 3
  • Eduardo G. Carrano
    • 4
  1. 1.Department of MathematicsUniversidade Federal de Minas GeraisBrazil
  2. 2.Department of Computer ScienceUniversidade Federal de Ouro PretoBrazil
  3. 3.Department of MathematicsUniversidade Federal de Ouro PretoBrazil
  4. 4.Centro Federal de Educação Tecnológica de Minas GeraisBrazil

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