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Dealing with Epistemic Uncertainty in Multi-objective Optimization: A Survey

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2018)

Abstract

Multi-objective optimization under epistemic uncertainty is today present as an active research area reflecting reality of many practical applications. In this paper, we try to present and discuss relevant state-of-the-art related to multi-objective optimisation with uncertain-valued objective. In fact, we give an overview of approaches that have already been proposed in this context and limitations of each one of them. We also present recent researches developed for taking into account uncertainty in the Pareto optimality aspect.

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References

  1. Barrico, C., Antunes, C.H.: Robustness analysis in multi-objective optimization using a degree of robustness concept. In: IEEE CEC, pp. 1887–1892 (2006)

    Google Scholar 

  2. Bahri, O., Ben Amor, N., El-Ghazali, T.: New Pareto approach for ranking triangular fuzzy numbers. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014, Part II. CCIS, vol. 443, pp. 264–273. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08855-6_27

    Chapter  Google Scholar 

  3. Bahri, O., Ben Amor N., Talbi E.-G.: Optimization algorithms for multi-objective problems with fuzzy data. In: IEEE International Symposium on MCDM, pp. 194–201 (2014)

    Google Scholar 

  4. Binois, M., Ginsbourger, D., Roustant, O.: Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations. Eur. J. Oper. Res. 243(2), 386–394 (2015)

    Article  MathSciNet  Google Scholar 

  5. Basseur, M., Zitzler, E.: Handling uncertainty in indicator-based multiobjective optimization. Int. J. Comput. Intell. Res. 2(3), 255–272 (2006)

    Article  MathSciNet  Google Scholar 

  6. Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.): EMO 2005. LNCS, vol. 3410. Springer, Heidelberg (2005). https://doi.org/10.1007/b106458

    Book  MATH  Google Scholar 

  7. Sánchez, L., Couso, I., Casillas, J.: A multiobjective genetic fuzzy system with imprecise probability fitness for vague data. In: IEEE International Symposium on Evolving Fuzzy Systems, pp. 131–136 (2006)

    Google Scholar 

  8. Goncalves, G., Hsu, T., Xu, J.: Vehicle routing problem with time windows and fuzzy demands: an approach based on the possibility theory. Int. J. Adv. Oper. Manage. 1(4), 312–330 (2009)

    Google Scholar 

  9. 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). https://doi.org/10.1007/978-3-540-31880-4_11

    Chapter  MATH  Google Scholar 

  10. Diwekar, U.: Optimization under uncertainty. Introduction to Applied Optimization. SOIA, vol. 22, pp. 1–54. Springer, Boston (2008). https://doi.org/10.1007/978-0-387-76635-5_5

    Chapter  MATH  Google Scholar 

  11. Fieldsend, J.E., Everson, R.M.: Multi-objective optimisation in the presence of uncertainty. In: IEEE CEC, vol. 1, pp. 243–250 (2005)

    Google Scholar 

  12. Goh, C.K., Tan, K.C.: Evolutionary multi-objective optimization in uncertain environments. J. Stud. Comput. Intell. 186, 5–18 (2009)

    MATH  Google Scholar 

  13. Hughes, E.J.: Evolutionary multi-objective ranking with uncertainty and noise. In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., Corne, D. (eds.) EMO 2001. LNCS, vol. 1993, pp. 329–343. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44719-9_23

    Chapter  Google Scholar 

  14. Haubelt, C., Teich, J.: Accelerating design space exploration using Pareto-front arithmetics. In: ACM Conference on Asia and South Pacific Design Automation, pp. 525–531 (2003)

    Google Scholar 

  15. Hendriks, M., Geile, M., Basten, T.: Pareto analysis with uncertainty. In: 9th International Conference on EUC, pp. 189–196 (2011)

    Google Scholar 

  16. Köppen, M., Vicente-Garcia, R., Nickolay, B.: Fuzzy-Pareto-dominance and its application in evolutionary multi-objective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 399–412. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31880-4_28

    Chapter  MATH  Google Scholar 

  17. Limbourg, P.: Multi-objective optimization of problems with epistemic uncertainty. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 413–427. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31880-4_29

    Chapter  MATH  Google Scholar 

  18. Limbourg, P., Aponte, D.E.S.: An optimization algorithm for imprecise multi-objective problem functions. In: IEEE CEC, vol. 1, pp. 459–466 (2005)

    Google Scholar 

  19. Liefooghe, A.: Methodes pour l’optimisation multiobjectif: Approche cooperative, prise en compte de l’incertitude et application logistique. PHD thesis, Universit de Lille 1, pp. 13–20 (2009)

    Google Scholar 

  20. Liefooghe, A., Jourdan, L., Talbi, E.G.: Indicator-based approaches for multiobjective optimization in uncertain environments. In: 25th Mini-EURO Conference URPDM (2010)

    Google Scholar 

  21. Meng, Z., Shen, R., Jiang, M.: An objective penalty functions algorithm for multiobjective optimization problem. J. Oper. Res. 1(4), 229 (2011)

    Google Scholar 

  22. Petrone, G.: Optimization under Uncertainty: theory, algorithms and industrial applications. PHD thesis, Università degli Studi di Napoli Federico II, pp. 77–122 (2011)

    Google Scholar 

  23. Talbi, E.-G.: Metaheuristics: From design to implementation, vol. 74, pp. 309–373. John Wiley and Sons (2009)

    Google Scholar 

  24. Teich, J.: Pareto-front exploration with uncertain objectives. In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., Corne, D. (eds.) EMO 2001. LNCS, vol. 1993, pp. 314–328. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44719-9_22

    Chapter  Google Scholar 

  25. Sahinidis, N.V.: Optimization under uncertainty: state-of-the-art and opportunities. J. Comput. Chem. Eng. 28(6), 971–983 (2004)

    Article  Google Scholar 

  26. Saka, M.P., Dogan, E.: Recent developments in metaheuristic algorithms: a review. J. Comput. Technol. Rev. 5(4), 31–78 (2012)

    Article  Google Scholar 

  27. Silva, R.C., Yamakami, A.: Definition of fuzzy Pareto-optimality by using possibility theory. In: IFSA/EUSFLAT Conference, pp. 1234–1239. Citeseer (2009)

    Google Scholar 

  28. Wang, G., Huawei, J.: Fuzzy-dominance and its application in evolutionary many objective optimization. In: IEEE International Conference on Computational Intelligence and Security Workshops CISW, pp. 195–198 (2007)

    Google Scholar 

  29. Zadeh, L.A.: Fuzzy sets. In: Fuzzy Sets, Fuzzy Logic and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh, pp. 394–432 (1996)

    Google Scholar 

  30. Zhou, J., Yang, F., Wang, K.: Multi-objective optimization in uncertain random environments. J. Fuzzy Optim. Decis. Mak. 13(4), 397–413 (2014)

    Article  MathSciNet  Google Scholar 

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Correspondence to Oumayma Bahri .

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Bahri, O., Talbi, EG. (2018). Dealing with Epistemic Uncertainty in Multi-objective Optimization: A Survey. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_22

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  • DOI: https://doi.org/10.1007/978-3-319-91479-4_22

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  • Online ISBN: 978-3-319-91479-4

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