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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)
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)
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4(4), 409–423 (1989)
Martin, J.D., Simpson, T.W.: Use of kriging models to approximate deterministic computer models. AIAA J. 43(4), 853–863 (2005)
Box, G.E., Draper, N.R.: Empirical Model-building and Response Surfaces. Wiley, New York (1987)
Fang, H., Horstemeyer, M.F.: Global response approximation with radial basis functions. Eng. Optim. 38(4), 407–424 (2006)
Forrester, A.I., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1–3), 50–79 (2009)
Lancaster, P., Salkauskas, K.: Surfaces generated by moving least squares methods. Math. Comput. 37(155), 141–158 (1981)
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)
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)
**, R., Chen, W., Simpson, T.: Comparative studies of metamodelling techniques under multiple modelling criteria. Struct. Multi. Optim. 23(1), 1–13 (2001)
Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L.: Pareto Optimality, Game Theory and Equilibria, 2nd edn. Springer, New York (2008)
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)
Azevedo, C., Araujo, A.: Correlation between diversity and hypervolume in evolutionary multiobjective optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2743–2750 (2011)
Okabe, T., **, 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)
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)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)
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)
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)
Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (1999)
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)
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)
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)
Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2, 27:1–27:27 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Steponavičė, I., Hyndman, R.J., Smith-Miles, K., Villanova, L. (2014). Efficient Identification of the Pareto Optimal Set. In: Pardalos, P., Resende, M., Vogiatzis, C., Walteros, J. (eds) Learning and Intelligent Optimization. LION 2014. Lecture Notes in Computer Science(), vol 8426. Springer, Cham. https://doi.org/10.1007/978-3-319-09584-4_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-09584-4_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09583-7
Online ISBN: 978-3-319-09584-4
eBook Packages: Computer ScienceComputer Science (R0)