Advancing Model–Building for Many–Objective Optimization Estimation of Distribution Algorithms

  • Luis Martí
  • Jesús García
  • Antonio Berlanga
  • José M. Molina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6024)

Abstract

In order to achieve a substantial improvement of MOEDAs regarding MOEAs it is necessary to adapt their model–building algorithms. Most current model–building schemes used so far off–the–shelf machine learning methods. These methods are mostly error–based learning algorithms. However, the model–building problem has specific requirements that those methods do not meet and even avoid.

In this work we dissect this issue and propose a set of algorithms that can be used to bridge the gap of MOEDA application. A set of experiments are carried out in order to sustain our assertions.

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References

  1. 1.
    Ahn, C.W.: Advances in Evolutionary Algorithms. Theory, Design and Practice. Springer, Heidelberg (2006)MATHGoogle Scholar
  2. 2.
    Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA—A Platform and Programming Language Independent Interface for Search Algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Bosman, P.A.N., Thierens, D.: The naïve MIDEA: A baseline multi–objective EA. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 428–442. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. In: Genetic and Evolutionary Computation, 2nd edn. Springer, New York (2007), http://www.springer.com/west/home/computer/foundations?SGWID=4-156-22-173660344-0 Google Scholar
  5. 5.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  6. 6.
    Fritzke, B.: A growing neural gas network learns topologies. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) Advances in Neural Information Processing Systems, vol. 7, pp. 625–632. 625–632. MIT Press, Cambridge (1995)Google Scholar
  7. 7.
    Grossberg, S.: Studies of Mind and Brain: Neural Principles of Learning, Perception, Development, Cognition, and Motor Control. Reidel, Boston (1982)MATHGoogle Scholar
  8. 8.
    Hartigan, J.A.: Clustering Algorithms. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York (1975)MATHGoogle Scholar
  9. 9.
    Huband, S., Hingston, P., Barone, L., While, L.: A Review of Multiobjective Test Problems and a Scalable Test Problem Toolkit. IEEE Transactions on Evolutionary Computation 10(5), 477–506 (2006)CrossRefGoogle Scholar
  10. 10.
    Igel, C., Hansen, N., Roth, S.: Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation 15(1), 1–28 (2007)CrossRefGoogle Scholar
  11. 11.
    Kibler, D., Aha, D.W., Albert, M.K.: Instance–based prediction of real–valued attributes. Computational Intelligence 5(2), 51–57 (1989)CrossRefGoogle Scholar
  12. 12.
    Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2006)Google Scholar
  13. 13.
    Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms. A new tool for Evolutionary Computation. In: Genetic Algorithms and Evolutionary Computation. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  14. 14.
    Martí, L., García, J., Berlanga, A., Molina, J.M.: Introducing MONEDA: Scalable multiobjective optimization with a neural estimation of distribution algorithm. In: Thierens, D., Deb, K., Pelikan, M., Beyer, H.G., Doerr, B., Poli, R., Bittari, M. (eds.) GECCO 2008: 10th Annual Conference on Genetic and Evolutionary Computation, pp. 689–696. ACM Press, New York (2008); EMO Track “Best Paper” NomineeCrossRefGoogle Scholar
  15. 15.
    Martí, L., García, J., Berlanga, A., Molina, J.M.: Scalable continuous multiobjective optimization with a neural network–based estimation of distribution algorithm. In: Giacobini, M., Brabazon, A., Cagnoni, S., Di Caro, G.A., Drechsler, R., Ekárt, A., Esparcia-Alcázar, A.I., Farooq, M., Fink, A., McCormack, J., O’Neill, M., Romero, J., Rothlauf, F., Squillero, G., Uyar, A.Ş., Yang, S. (eds.) EvoWorkshops 2008. LNCS, vol. 4974, pp. 535–544. Springer, Heidelberg (2008), http://dx.doi.org/10.1007/978-3-540-78761-7_59 CrossRefGoogle Scholar
  16. 16.
    Martí, L., García, J., Berlanga, A., Molina, J.M.: Solving complex high–dimensional problems with the multi–objective neural estimation of distribution algorithm. In: Thierens, D., Deb, K., Pelikan, M., Beyer, H.G., Doerr, B., Poli, R., Bittari, M. (eds.) GECCO 2009: 11th Annual Conference on Genetic and Evolutionary Computation. ACM Press, New York (2009) (to appear)Google Scholar
  17. 17.
    Pelikan, M., Sastry, K., Goldberg, D.E.: Multiobjective estimation of distribution algorithms. In: Pelikan, M., Sastry, K., Cantú-Paz, E. (eds.) Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications. Studies in Computational Intelligence, pp. 223–248. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Purshouse, R.C., Fleming, P.J.: On the evolutionary optimization of many conflicting objectives. IEEE Transactions on Evolutionary Computation 11(6), 770–784 (2007), http://dx.doi.org/10.1109/TEVC.2007.910138 CrossRefGoogle Scholar
  19. 19.
    Qin, A.K., Suganthan, P.N.: Robust growing neural gas algorithm with application in cluster analysis. Neural Networks 17(8–9), 1135–1148 (2004), http://dx.doi.org/10.1016/j.neunet.2004.06.013 MATHCrossRefGoogle Scholar
  20. 20.
    Sarle, W.S.: Why statisticians should not FART. Tech. rep., SAS Institute, Cary, NC (1995)Google Scholar
  21. 21.
    Williamson, J.R.: Gaussian ARTMAP: A neural network for fast incremental learning of noisy multidimensional maps. Neural Networks 9, 881–897 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Luis Martí
    • 1
  • Jesús García
    • 1
  • Antonio Berlanga
    • 1
  • José M. Molina
    • 1
  1. 1.Group of Applied Artificial IntelligenceUniversidad Carlos III de MadridMadridSpain

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