Advertisement

Efficient Identification of the Pareto Optimal Set

  • Ingrida Steponavičė
  • Rob J. Hyndman
  • Kate Smith-Miles
  • Laura Villanova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8426)

Abstract

In this paper, we focus on expensive multiobjective optimization problems and propose a method to predict an approximation of the Pareto optimal set using classification of sampled decision vectors as dominated or nondominated. The performance of our method, called EPIC, is demonstrated on a set of benchmark problems used in the multiobjective optimization literature and compared with state-of the-art methods, ParEGO and PAL. The initial results are promising and encourage further research in this direction.

Keywords

Multiobjective optimization Classification Expensive black-box function 

References

  1. 1.
    Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Santana-Quintero, L.V., Montaño, A.A., Coello, C.A.C.: A review of techniques for handling expensive functions in evolutionary multi-objective optimization. In: Tenne, Y., Goh, C.-K. (eds.) Computational Intel. in Expensive Opti. Prob. ALO, vol. 2, pp. 29–59. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  3. 3.
    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4(4), 409–423 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Martin, J.D., Simpson, T.W.: Use of kriging models to approximate deterministic computer models. AIAA J. 43(4), 853–863 (2005)CrossRefGoogle Scholar
  5. 5.
    Box, G.E., Draper, N.R.: Empirical Model-building and Response Surfaces. Wiley, New York (1987)zbMATHGoogle Scholar
  6. 6.
    Fang, H., Horstemeyer, M.F.: Global response approximation with radial basis functions. Eng. Optim. 38(4), 407–424 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Forrester, A.I., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1–3), 50–79 (2009)CrossRefGoogle Scholar
  8. 8.
    Lancaster, P., Salkauskas, K.: Surfaces generated by moving least squares methods. Math. Comput. 37(155), 141–158 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Knowles, J.: Parego: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evol. Comput. 10(1), 50–66 (2006)CrossRefGoogle Scholar
  10. 10.
    Zuluaga, M., Krause, A., Sergent, G., Püschel, M.: Active learning for multi-objective optimization. In: Proceedings of the 30th International Conference on Machine Learning (2013)Google Scholar
  11. 11.
    Jin, R., Chen, W., Simpson, T.: Comparative studies of metamodelling techniques under multiple modelling criteria. Struct. Multi. Optim. 23(1), 1–13 (2001)CrossRefGoogle Scholar
  12. 12.
    Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L.: Pareto Optimality, Game Theory and Equilibria, 2nd edn. Springer, New York (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  14. 14.
    Azevedo, C., Araujo, A.: Correlation between diversity and hypervolume in evolutionary multiobjective optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2743–2750 (2011)Google Scholar
  15. 15.
    Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  16. 16.
    Kursawe, F.: A variant of evolution strategies for vector optimization. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 193–197. Springer, Heidelberg (1991) CrossRefGoogle Scholar
  17. 17.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  18. 18.
    Viennet, R., Fonteix, C., Marc, I.: New multicriteria optimization method based on the use of a diploid genetic algorithm: example of an industrial problem. In: Alliot, J.-M., Ronald, E., Lutton, E., Schoenauer, M., Snyers, D. (eds.) AE 1995. LNCS, vol. 1063, pp. 120–127. Springer, Heidelberg (1996) CrossRefGoogle Scholar
  19. 19.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Congress on Evolutionary Computation (CEC 2002), pp. 825–830. IEEE Press (2002)Google Scholar
  20. 20.
    Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (1999)Google Scholar
  21. 21.
    Bennett, K.P., Bredensteiner, E.J.: Duality and geometry in SVM classifiers. In: Proceedings of 17th International Conference on Machine Learning, pp. 57–64. Morgan Kaufmann (2000)Google Scholar
  22. 22.
    Platt, J.C.: Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: Smola, A.J., Bartlett, P.L., Schölkopf, B., Schurmans, D. (eds.) Advances in Large Margin Classifiers, pp. 61–74. MIT Press, Cambridge (1999)Google Scholar
  23. 23.
    Zadrozny, B., Elkan, C.: Transforming classifier scores into accurate multiclass probability estimates. In: Proceedings of the International Conference on Knowledge Discovery and Data Mining, pp. 694–699 (2002)Google Scholar
  24. 24.
    Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2, 27:1–27:27 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ingrida Steponavičė
    • 1
  • Rob J. Hyndman
    • 2
  • Kate Smith-Miles
    • 1
  • Laura Villanova
    • 3
  1. 1.School of Mathematical SciencesMonash UniversityClaytonAustralia
  2. 2.Department of Econometrics and Business StatisticsMonash UniversityClaytonAustralia
  3. 3.Ceramic Fuel Cells LimitedNoble ParkAustralia

Personalised recommendations