A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization

  • Matthieu Basseur
  • Eckart Zitzler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3907)


Real-world optimization problems are often subject to uncertainties, which can arise regarding stochastic model parameters, objective functions and decision variables. These uncertainties can take different forms in terms of distribution, bound and central tendency.

In the multiobjective context, several studies have been proposed to take uncertainty into account, and most of them propose an extension of Pareto dominance to the stochastic case. In this paper, we pursue a slightly different approach where the optimization goal is defined in terms of a quality indicator, i.e., an objective function on the set of Pareto set approximations. We consider the scenario that each solution is inherently associated with a probability distribution over the objective space, without assuming a ’true’ objective vector per solution. We propose different algorithms which optimize the quality indicator, and preliminary simulation results indicate advantages over existing methods such as averaging, especially with many objective functions.


Multiobjective Optimization Objective Space Objective Vector Optimization Goal Pareto Dominance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments - a survey. IEEE Transactions on evolutionary computation 9, 303–317 (2005)CrossRefGoogle Scholar
  3. 3.
    Arnold, D.V.: A comparison of evolution strategies with other direct search methods in the presence of noise. Computational Optimization and Applications 24, 135–159 (2003)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Horn, J., Nafpliotis, N.: Multiobjective optimization using the niched pareto genetic algorithm. Technical report, University of Illinois, Urbana-Champaign, Urbana, Illinois, USA (1993)Google Scholar
  5. 5.
    Hughes, E.: Evolutionary multi-objective ranking with uncertainty and noise. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 329–343. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Teich, J.: Pareto-front exploration with uncertain objectives. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 314–328. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Babbar, M., Lakshmikantha, A., Goldberg, D.E.: A modified NSGA-II to solve noisy multiobjective problems. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 21–27. Springer, Heidelberg (2003)Google Scholar
  8. 8.
    Deb, K., Gupta, H.: Searching for robust pareto-optimal solutions in multi-objective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 150–164. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7, 117–132 (2003)CrossRefGoogle Scholar
  10. 10.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)CrossRefGoogle Scholar
  11. 11.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical report, TIK Report Nr. 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich (2001)Google Scholar
  12. 12.
    Kursawe, F.: A variant of evolution strategies for vector optimization. In: Schwefel, H.P., Männer, R. (eds.) Parallel Problem Solving from Nature, pp. 193–197. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  13. 13.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Abraham, A., et al. (eds.) Evolutionary Computation Based Multi-Criteria Optimization: Theoretical Advances and Applications. Springer, Heidelberg (2004) (to appear)Google Scholar
  14. 14.
    Knowles, J.D., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastive multiobjective optimizers. Technical Report TIK-Report No. 214, Computer Engineering and Networks Laboratory, ETH Zurich (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthieu Basseur
    • 1
  • Eckart Zitzler
    • 2
  1. 1.LIFL/CNRS/INRIAVilleneuve d’AscqFrance
  2. 2.Computer Engineering and Networks LaboratoryETH ZürichZurichSwitzerland

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