Model-Based Multi-objective Optimization: Taxonomy, Multi-Point Proposal, Toolbox and Benchmark

  • Daniel HornEmail author
  • Tobias Wagner
  • Dirk Biermann
  • Claus Weihs
  • Bernd Bischl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9018)


Within the last 10 years, many model-based multi-objective optimization algorithms have been proposed. In this paper, a taxonomy of these algorithms is derived. It is shown which contributions were made to which phase of the MBMO process. A special attention is given to the proposal of a set of points for parallel evaluation within a batch. Proposals for four different MBMO algorithms are presented and compared to their sequential variants within a comprehensive benchmark. In particular for the classic ParEGO algorithm, significant improvements are obtained. The implementations of all algorithm variants are organized according to the taxonomy and are shared in the open-source R package mlrMBO.


Expected improvement Hypervolume Kriging Performance indicator Surrogate model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bautista, D.C.: A Sequential Design For Approximating The Pareto Front Using the Expected Pareto Improvement Function. Ph.D. thesis, Ohio State University (2009)Google Scholar
  2. 2.
    Binois, M., Ginsbourger, D., Roustant, O.: Quantifying uncertainty on pareto fronts with gaussian process conditional simulations. European Journal of Operational Research, 1–9 (2014) (accepted, available online)Google Scholar
  3. 3.
    Bischl, B., Wessing, S., Bauer, N., Friedrichs, K., Weihs, C.: MOI-MBO: multiobjective infill for parallel model-based optimization. In: Pardalos, P.M., Resende, M.G.C., Vogiatzis, C., Walteros, J.L. (eds.) LION 2014. LNCS, vol. 8426, pp. 173–186. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  4. 4.
    Bischl, B., Horn, D., Bossek, J., Richter, J., Lang, M.:Package mlrMBO (2014).
  5. 5.
    Bischl, B., Horn, D., Wagner, T.: Model-Based Multi-Objective Optimization: Taxonomy, Multi-Point Proposal, Toolbox and Benchmark: Supplementary Material (2014).
  6. 6.
    Bischl, B., Lang, M., Bossek, J., Judt, L., Richter, J., Kuehn, T., Studerus, E.: Package mlr: Machine Learning in R (2014).
  7. 7.
    Brockhoff, D., Wagner, T., Trautmann, H.: On the properties of the R2 indicator. In: Soule, T., et al. (eds.) Proc. 2012 Genetic and Evolutionary Computation Conference (GECCO 2012), Philadelphia, US, pp. 465–472 (2012)Google Scholar
  8. 8.
    Couckuyt, I., Deschrijver, D., Dhaene, T.: Fast calculation of multiobjective probability of improvement and expected improvement criteria for pareto optimization. Journal of Global Optimization, 1–21 (2014) (accepted, available online)Google Scholar
  9. 9.
    Emmerich, M.T.M., Deutz, A., Klinkenberg, J.W.: Hypervolume-based expected improvement: Monotonicity properties and exact computation. In: Corne, D., et al. (eds.) Proc. IEEE Congress on Evolutionary Computation (CEC), pp. 2147–2154. IEEE (2011)Google Scholar
  10. 10.
    Janusevskis, J., Le Riche, R., Ginsbourger, D., Girdziusas, R.: Expected improvements for the asynchronous parallel global optimization of expensive functions: Potentials and challenges. In: Hamadi, Y., Schoenauer, M. (eds.) LION 2012. LNCS, vol. 7219, pp. 413–418. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  11. 11.
    Jeong, S., Obayashi, S.: Efficient global optimization (EGO) for multi-objective problem and data mining. In: Corne, D., et al. (eds.) Proc. IEEE Congress on Evolutionary Computation (CEC 2005), pp. 2138–2145. IEEE (2005)Google Scholar
  12. 12.
    Jones, D.R.: A taxonomy of global optimization methods based on response surfaces. Journal of Global Optimization 21(4), 345–383 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13(4), 455–492 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Keane, A.J.: Statistical improvement criteria for use in multiobjective design optimization. AIAA Journal 44(4), 879–891 (2006)CrossRefGoogle Scholar
  15. 15.
    Knowles, J.: ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation 10(1), 50–66 (2006)CrossRefGoogle Scholar
  16. 16.
    Knowles, J.D., Nakayama, H.: Meta-modeling in multiobjective optimization. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 245–284. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    Ponweiser, W., Wagner, T., Biermann, D., Vincze, M.: Multiobjective optimization on a limited amount of evaluations using model-assisted \(\cal S\)-metric selection. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN X. LNCS, vol. 5199, pp. 784–794. Springer, Heidelberg (2008) Google Scholar
  19. 19.
    Voutchkov, I., Keane, A.J.: Multiobjective optimization using surrogates. In: Parmee, I.C. (ed.) Proc. 7th Int’l. Conf. Adaptive Computing in Design and Manufacture (ACDM), Bristol, UK, pp. 167–175 (2006)Google Scholar
  20. 20.
    Wagner, T.: Planning and Multi-Objective Optimization of Manufacturing Processes by Means of Empirical Surrogate Models. Vulkan Verlag, Essen (2013) Google Scholar
  21. 21.
    Wagner, T., Emmerich, M., Deutz, A., Ponweiser, W.: On expected-improvement criteria for model-based multi-objective optimization. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 718–727. Springer, Heidelberg (2010) Google Scholar
  22. 22.
    Zaefferer, M., Bartz-Beielstein, T., Naujoks, B., Wagner, T., Emmerich, M.: A case study on multi-criteria optimization of an event detection software under limited budgets. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds.) EMO 2013. LNCS, vol. 7811, pp. 756–770. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  23. 23.
    Zhang, Q., Liu, W., Tsang, E., Virginas, B.: Expensive multiobjective optimization by MOEA/D with gaussian process model. IEEE Transactions on Evolutionary Computation 4(3), 456–474 (2010)CrossRefGoogle Scholar
  24. 24.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. Transactions on Evolutionary Computation 8(2), 117–132 (2003)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Daniel Horn
    • 1
    Email author
  • Tobias Wagner
    • 2
  • Dirk Biermann
    • 2
  • Claus Weihs
    • 1
  • Bernd Bischl
    • 1
  1. 1.Chair of Computational StatisticsTechnische Universität DortmundDortmundGermany
  2. 2.Institute of Machining Technology (ISF)Technische Universität DortmundDortmundGermany

Personalised recommendations