Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function

  • Carlos M. Fonseca
  • Viviane Grunert da Fonseca
  • Luís Paquete
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3410)

Abstract

The attainment function has been proposed as a measure of the statistical performance of stochastic multiobjective optimisers which encompasses both the quality of individual non-dominated solutions in objective space and their spread along the trade-off surface. It has also been related to results from random closed-set theory, and cast as a mean-like, first-order moment measure of the outcomes of multiobjective optimisers. In this work, the use of more informative, second-order moment measures for the evaluation and comparison of multiobjective optimiser performance is explored experimentally, with emphasis on the interpretability of the results.

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References

  1. 1.
    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
  2. 2.
    Goutsias, J.: Modeling random shapes: An introduction to random closed set theory. In: Haralick, R.M. (ed.) Mathematical Morphology: Theory and Hardware. Oxford Series in Optical & Imaging Sciences. Oxford University Press, New York (1996)Google Scholar
  3. 3.
    Grunert da Fonseca, V., Fonseca, C.M., Hall, A.O.: Inferential performance assessment of stochastic optimisers and the attainment function. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D. (eds.) EMO 2001. LNCS, vol. 1993, p. 213. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Justel, A., Peña, D., Zamar, R.: A multivariate Kolmogorov-Smirnov test of goodness of fit. Statistics and Probability Letters 35, 251–259 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fonseca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  6. 6.
    Shaw, K.J., Nortcliffe, A.L., Thompson, M., Love, J., Fleming, P.: Assessing the performance of multiobjective genetic algorithms for optimization of a batch process scheduling problem. In: Proceedings of the Congress on Evolutionary Computation (CEC1999), Washington DC, vol. 1, pp. 37–45 (1999)Google Scholar
  7. 7.
    Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications, 2nd edn. Wiley Series in Probability and Statistics. Wiley & Sons, Chichester (1995)MATHGoogle Scholar
  8. 8.
    Good, P.I.: Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd edn. Springer Series in Statistics. Springer, New York (2000)MATHGoogle Scholar
  9. 9.
    Bickel, P.J.: A distribution free version of the Smirnov two sample test in the p-variate case. The Annals of Mathematical Statistics 40, 1–23 (1969)MATHCrossRefGoogle Scholar
  10. 10.
    Barratt, C., Boyd, S.: Example of exact trade-offs in linear control design. IEEE Control Systems Magazine 9, 46–52 (1989)CrossRefGoogle Scholar
  11. 11.
    Fonseca, C.M., Fleming, P.J.: Multiobjective optimal controller design with genetic algorithms. In: Proc. IEE Control 1994 International Conference, Warwick, U.K, vol. 1, pp. 745–749 (1994)Google Scholar
  12. 12.
    Fonseca, C.M., Fleming, P.J.: Multiobjective genetic algorithms made easy: selection, sharing and mating restriction. In: First IEE/IEEE International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, Sheffield, U.K., pp. 45–52 (1995)Google Scholar
  13. 13.
    Paquete, L., Chiarandini, M., Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: An experimental study. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, vol. 535, pp. 177–200. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Bentley, J.: Fast algorithms for geometric traveling salesman problems. ORSA Journal on Computing 4, 387–411 (1992)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carlos M. Fonseca
    • 1
  • Viviane Grunert da Fonseca
    • 1
    • 2
  • Luís Paquete
    • 3
    • 4
  1. 1.CSI – Centro de Sistemas Inteligentes, Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal
  2. 2.INUAF – Instituto Superior D. Afonso IIILouléPortugal
  3. 3.Fachgebiet Intellektik, Fachbereich InformatikTechnische Universität DarmstadtDarmstadtGermany
  4. 4.Faculdade de EconomiaUniversidade do AlgarveFaroPortugal

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