Advertisement

Statistics of Pareto Fronts

  • Mohamed BassiEmail author
  • Emmanuel Pagnacco
  • Eduardo Souza de Cursi
  • Rachid Ellaia
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

We consider multiobjective optimization problems affected by uncertainty, where the objective functions or the restrictions involve random variables. We are interested in the evaluation of statistics such as medians, quantiles and confidence intervals for the Pareto front. We present a method for the determination of such statistics which is independent of the representation used to describe the Pareto front. In a second step, we start from a sample of Pareto fronts and we use a Generalized Fourier Series approach to generate a larger sample of about 105 Pareto fronts with a reasonable computational cost. These large samples are used to obtain more accurate statistics. Examples show that the method is effective to calculate.

Keywords

Optimization under uncertainty Uncertainty quantification Multiobjective optimization 

References

  1. 1.
    Croquet, R., Souza de Cursi, E.: Statistics of uncertain dynamical systems. In: Topping, B.H.V., Adam, J.M., Pallarés, F.J., Bru, R., Romero, M.L. (eds.) Proceedings of the Tenth International Conference on Computational Structures Technology, Paper 173, Civil-Comp Press, Stirlingshire, UK (93), pp. 541–561.  https://doi.org/10.4203/ccp.93.173 (2010)
  2. 2.
    Bassi, M., Souza de Cursi, E., Ellaia, R.: Generalized fourier series for representing random variables and application for quantifying uncertainties in optimization. In: 3rd International Symposium on Uncertainty Quantification and Stochastic Modeling, Maresias, SP, Brazil, 15–19 February (2016). http://www.swge.inf.br/PDF/USM-2016-0037_027656.PDF
  3. 3.
    Bassi, M.: Quantification d’Incertitudes et Objets en Dimension Infinie. Ph.D. Thesis, INSA Rouen Normandie, Normandie Université, Saint-Etienne du Rouvray (2019)Google Scholar
  4. 4.
    Souza de Cursi, E., Sampaio, R.: Uncertainty Quantification and Stochastic Modelling with Matlab. ISTE Press, London, UK (2015)Google Scholar
  5. 5.
    Bassi, M., Souza de Cursi, E., Pagnacco, E., Ellaia, R.: Statistics of the pareto front in multi-objective optimization under uncertainties. Lat. Am. J. Solids Struct. 15(11), e130. Epub November 14, 2018.  https://doi.org/10.1590/1679-78255018 (2018)
  6. 6.
    Dubuisson, M., Jain, A.K.: A modified hausdorff distance for object matching. In: Proceedings of 12th International Conference on Pattern Recognition, October 9–13, Jerusalem, pp. 566–568,  https://doi.org/10.1109/icpr.1994.576361 (1994)

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LMNINSA Rouen Normandie, Normandie UniversitéSt-Etienne du RouvrayFrance
  2. 2.LERMA LaboratoryEngineering for Smart & Sustainable Systems Research Center, E3S, Mohammed V University of Rabat, EMIRabatMorocco

Personalised recommendations