Abstract
This paper proposes a new approach to cope with multi-objective optimization problems in presence of noise. In the first place, since considering the worst-case performance is important in many real-world optimization problems, a solution is evaluated based on the upper bounds of respective noisy objective functions predicted statistically by multiple sampling. Secondary, a rational way to decide the maximum sample size for the solution is shown. Thirdly, to allocate the computing budget of a proposed evolutionary algorithm only to promising solutions, two pruning techniques are contrived to judge hopeless solutions only by a few sampling and skip the evaluation of the upper bounds for them.
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Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Springer (2005)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments - a survey. IEEE Trans. on Evolutionary Computation 9(3), 303–317 (2005)
Gunawan, S., Azarm, S.: Multi-objective robust optimization using a sensitivity region concept. Structural and Multidisciplinary Optimization 29(1), 50–60 (2005)
Voß, T., Trautmann, H., Igel, C.: New uncertainty handling strategies in multi-objective evolutionary optimization. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6239, pp. 260–269. Springer, Heidelberg (2010)
Rakshit, P., Konar, A., Das, S., Jain, L.C., Nagar, A.K.: Uncertainty management in differential evolution induced multiobjective optimization in presence of measurement noise. IEEE Trans. on Systems, Man, and Cybernetics: Systems 44(7), 922–937 (2013)
Hughes, E.J.: 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. 329–342. Springer, Heidelberg (2001)
Fieldsend, J.E., Everson, R.M.: Multi-objective optimization in the presence of uncertainty. In: Proc. IEEE CEC 2005, pp. 243–250 (2005)
Shim, V.A., Tan, K.C., Chia, J.Y., Mamun, A.A.: Multi-objective optimization with estimation of distribution algorithm in a noisy environment. Evolutionary Computation 21(1), 149–177 (2013)
Bui, L.T., Abbass, H.A., Essam, D.: Localization for solving noisy multi-objective optimization problems. Evolutionary Computation 17(3), 379–409 (2009)
Eskandari, H., Geiger, C.D.: Evolutionary multiobjective optimization in noisy problem environments. Journal of Heuristics 15(6), 559–595 (2009)
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)
Kuroiwa, D., Lee, G.M.: On robust multiobjective optimization. Vietnam Journal of Mathematics 40(2&3), 305–317 (2012)
Avigad, G., Branke, J.: Embedded evolutionary multi-objective optimization for worst case robustness. In: Proc. GECCO 2008, pp. 617–624 (2008)
Branke, J., Avigad, G., Moshaiov, A.: Multi-objective worst case optimization by means of evolutionary algorithms. Working Paper, Coventry UK: WBS, University of Warwick (2013), http://wrap.warwick.ac.uk/55724
Ehrgott, M., Ide, J., Schöbel, A.: Minmax robustness for multi-objective optimization problems. European Journal of Operation Research (2014), http://dx.doi.org/10.1016/j.ejor.2014.03.013
Wackerly, D.D., Mendenhall, W., Scheaffer, R.L.: Mathematical Statistics with Applications, 7th edn. Thomson Learning, Inc. (2008)
Fisher, R.A.: On the interpretation of χ 2 from contingency tables, and calculation of \({\cal P}\). Journal of the Royal Statistical Society 85(1), 87–94 (1922)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6(2), 182–197 (2002)
Robič, T., Filipič, B.: DEMO: Differential evolution for multiobjective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)
Brest, J., Greiner, S., Bošković, B., Merink, M., Žumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. on Evolutionary Computation 10(6), 646–657 (2006)
Köppen, M., Yoshida, K.: Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 727–741. Springer, Heidelberg (2007)
Tagawa, K., Imamura, A.: Many-hard-objective optimization using differential evolution based on two-stage constraint-handling. In: Proc. GECCO 2013, pp. 671–678 (2013)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. TIK-Technical Report, 112, 1–27 (2001)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)
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Tagawa, K., Harada, S. (2014). Multi-Noisy-objective Optimization Based on Prediction of Worst-Case Performance. In: Dediu, AH., Lozano, M., Martín-Vide, C. (eds) Theory and Practice of Natural Computing. TPNC 2014. Lecture Notes in Computer Science, vol 8890. Springer, Cham. https://doi.org/10.1007/978-3-319-13749-0_3
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DOI: https://doi.org/10.1007/978-3-319-13749-0_3
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