Abstract
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.
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References
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)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments - a survey. IEEE Transactions on evolutionary computation 9, 303–317 (2005)
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)
Horn, J., Nafpliotis, N.: Multiobjective optimization using the niched pareto genetic algorithm. Technical report, University of Illinois, Urbana-Champaign, Urbana, Illinois, USA (1993)
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)
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)
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)
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)
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)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)
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)
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)
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)
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)
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Basseur, M., Zitzler, E. (2006). A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization. In: Rothlauf, F., et al. Applications of Evolutionary Computing. EvoWorkshops 2006. Lecture Notes in Computer Science, vol 3907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11732242_71
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DOI: https://doi.org/10.1007/11732242_71
Publisher Name: Springer, Berlin, Heidelberg
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