Skip to main content
SpringerLink
Log in
Book cover

International Conference on Evolutionary Multi-Criterion Optimization

EMO 2011: Evolutionary Multi-Criterion Optimization pp 298–312Cite as

Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6576))

Abstract

The objective values information can be incorporated into the evolutionary algorithms based on probabilistic modeling in order to capture the relationships between objectives and variables. This paper investigates the effects of joining the objective and variable information on the performance of an estimation of distribution algorithm for multi-objective optimization. A joint Gaussian Bayesian network of objectives and variables is learnt and then sampled using the information about currently best obtained objective values as evidence. The experimental results obtained on a set of multi-objective functions and in comparison to two other competitive algorithms are presented and discussed.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abraham, A., Jain, L., Goldberg, R. (eds.): Evolutionary Multiobjective Optimization: Theoretical Advances and Applications. Advanced Information and Knowledge Processing. Springer, Berlin (2005)

    Google Scholar 

  2. Bielza, C., Li, G., Larrañaga, P.: Multi-dimensional classification with Bayesian networks. Technical Report UPM-FI/DIA/2010-1, Artificial Intelligence Department, Technical University of Madrid, Madrid, Spain (2010)

    Google Scholar 

  3. Brockhoff, D., Zitzler, E.: Dimensionality reduction in multiobjective optimization: The minimum objective subset problem. In: Waldmann, K.-H., Stocker, U.M. (eds.) Operations Research Proceedings 2006, pp. 423–429. Springer, Berlin (2007)

    Chapter  Google Scholar 

  4. Brockhoff, D., Zitzler, E.: Objective reduction in evolutionary multiobjective optimization: Theory and applications. Evolutionary Computation 17(2), 135–166 (2009)

    Article  Google Scholar 

  5. Buntine, W.: Theory refinement on Bayesian networks. In: Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence, vol. 91, pp. 52–60. Morgan Kaufmann, San Francisco (1991)

    Google Scholar 

  6. Coello, C.: An updated survey of evolutionary multiobjective optimization techniques: State of the art and future trends. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 1999), vol. 1, pp. 3–13 (1999)

    Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825–830 (2002)

    Google Scholar 

  9. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 105–145. Springer, Heidelberg (2005)

    Google Scholar 

  10. Garza-Fabre, M., Pulido, G., Coello, C.: Ranking methods for many-objective optimization. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds.) MICAI 2009. LNCS, vol. 5845, pp. 633–645. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Huband, S., Barone, L., While, L., Hingston, P.: A scalable multi-objective test problem toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. 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)

    Article  MATH  Google Scholar 

  13. Ishibuchi, H., Tsukamoto, N., Hitotsuyanagi, Y., Nojima, Y.: Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), pp. 649–656. ACM, New York (2008)

    Google Scholar 

  14. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. In: Adaptive Computation and Machine Learning. The MIT Press, Cambridge (2009)

    Google Scholar 

  15. Larrañaga, P., Etxeberria, R., Lozano, J., Peña, J.: Optimization in continuous domains by learning and simulation of Gaussian networks. In: Wu, A. (ed.) Proceedings of the 2000 Genetic and Evolutionary Computation Conference (GECCO 2000) Workshop Program, pp. 201–204. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  16. Larrañaga, P., Lozano, J. (eds.): Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  17. Lauritzen, S.L.: Propagation of probabilities, means, and variances in mixed graphical association models. Journal of the American Statistical Association 87(420), 1098–1108 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. López Jaimes, A., Coello Coello, C.A., Chakraborty, D.: Objective reduction using a feature selection technique. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), pp. 673–680. ACM, New York (2008)

    Google Scholar 

  19. Lozano, J., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.): Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Studies in Fuzziness and Soft Computing, vol. 192. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  20. Martí, L., Garcia, J., Antonio, B., Coello, C.A., Molina, J.: On current model-building methods for multi-objective estimation of distribution algorithms: Shortcommings and directions for improvement. Technical Report GIAA2010E001, Department of Informatics, Universidad Carlos III de Madrid, Madrid, Spain (2010)

    Google Scholar 

  21. Miquélez, T., Bengoetxea, E., Larrañaga, P.: Evolutionary computation based on Bayesian classifiers. International Journal of Applied Mathematics and Computer Science 14(3), 335–350 (2004)

    MathSciNet  MATH  Google Scholar 

  22. Miquélez, T., Bengoetxea, E., Larrañaga, P.: Evolutionary Bayesian Classifier-Based Optimization in Continuous Domains. In: Wang, T.-D., Li, X., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 529–536. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  23. Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions i. binary parameters. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  24. Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Yao, X., Burke, E., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J., Tino, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Pelikan, M., Sastry, K., Cantú-Paz, E. (eds.): Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications. SCI. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  26. Pelikan, M., Sastry, K., Goldberg, D.: Multiobjective estimation of distribution algorithms. In: Pelikan, et al. (eds.) [25], pp. 223–248

    Google Scholar 

  27. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. In: Adaptive Computation and Machine Learning. The MIT Press, Cambridge (2005)

    Google Scholar 

  28. Santana, R., Bielza, C., Larrañaga, P., Lozano, J.A., Echegoyen, C., Mendiburu, A., Armañanzas, R., Shakya, S.: Mateda-2.0: Estimation of distribution algorithms in MATLAB. Journal of Statistical Software 35(7), 1–30 (2010)

    Article  Google Scholar 

  29. Sbalzarini, I., Mueller, S., Koumoutsakos, P.: Multiobjective optimization using evolutionary algorithms. In: Proceedings of the 2000 Summer Program of Studying Turbulence Using Numerical Simulation Databases–VIII, vol. 1, pp. 63–74. Center for Turbulence Research (November 2000)

    Google Scholar 

  30. Schäfer, J., Strimmer, K.: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology 4(1) (2005)

    Google Scholar 

  31. Schmidt, M., Niculescu-Mizil, A., Murphy, K.: Learning graphical model structure using L1-regularization paths. In: Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2007), vol. 2, pp. 1278–1283. AAAI Press, Menlo Park (2007)

    Google Scholar 

  32. Thierens, D., Bosman, P.: Multi-objective mixture-based iterated density estimation evolutionary algorithms. In: Spector, L., Goodman, E.D., Wu, A., Langdon, W.B., Voigt, H.-M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M.H., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 663–670. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  33. Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: A regularity model based multiobjective estimation of distribution algorithm. IEEE Transactions on Evolutionary Computation 12(1), 41–63 (2008)

    Article  Google Scholar 

  34. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computational Intelligence Group, School of Computer Science, Technical University of Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain

    Hossein Karshenas, Roberto Santana, Concha Bielza & Pedro Larrañaga

Authors
  1. Hossein Karshenas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Santana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Concha Bielza
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Larrañaga
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Federal University of Minas Gerais, Av. Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil

    Ricardo H. C. Takahashi

  2. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208 016, Kanpur, India

    Kalyanmoy Deb

  3. Department of Computer Engineering, Centro Federal de Educaçao Tecnológica de Minas Gerais, Av. Amazonas 5253, 30421-169, Belo Horizonte, MG, Brazil

    Elizabeth F. Wanner

  4. Faculty of Economics, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Karshenas, H., Santana, R., Bielza, C., Larrañaga, P. (2011). Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19893-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19892-2

  • Online ISBN: 978-3-642-19893-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation