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A Non-parametric Statistical Dominance Operator for Noisy Multiobjective Optimization

  • Dung H. Phan
  • Junichi Suzuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7673)

Abstract

This paper describes and evaluates a new noise-aware dominance operator for evolutionary algorithms to solve the multiobjective optimization problems (MOPs) that contain noise in their objective functions. This operator is designed with the Mann-Whitney U-test, which is a non-parametric (i.e., distribution-free) statistical significance test. It takes objective value samples of given two individuals, performs a U-test on the two sample sets and determines which individual is statistically superior. Experimental results show that it operates reliably in noisy MOPs and outperforms existing noise-aware dominance operators particularly when many outliers exist under asymmetric noise distributions.

Keywords

Evolutionary multiobjective optimization algorithms noisy optimization uncertainties in objective functions 

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References

  1. 1.
    Babbar, M., Lakshmikantha, A., Goldberg, D.: A modified NSGA-II to solve noisy multiobjective problems. In: Proc. ACM Genet. Evol. Computat. Conf. (2003)Google Scholar
  2. 2.
    Bianchi, L., Dorigo, M., Gambardella, L., Gutjahr, W.J.: A survey on metaheuristics for stochastic combinatorial optimization. Nat. Comput. 8(2) (2009)Google Scholar
  3. 3.
    Boonma, P., Suzuki, J.: A confidence-based dominance operator in evolutionary algorithms for noisy multiobjective optimization problems. In: Proc. IEEE Int’l Conference on Tools with Artificial Intelligence (2009)Google Scholar
  4. 4.
    Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, R., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. Springer (2005)Google Scholar
  6. 6.
    Delibrasis, K., Undrill, P., Cameron, G.: Genetic algorithm implementation of stack filter design for image restoration. In: Proc. Vis., Image, Sign. Proc. (1996)Google Scholar
  7. 7.
    Durillo, J., Nebro, A., Alba, E.: The jMetal framework for multi-objective optimization: Design and architecture. In: Proc. IEEE Congress on Evol. Computat. (2010)Google Scholar
  8. 8.
    Eskandari, H., Geiger, C., Bird, R.: Handling uncertainty in evolutionary multiobjective optimization: SPGA. In: Proc. IEEE Congress Evol. Computat. (2007)Google Scholar
  9. 9.
    Goh, C.K., Tan, K.C.: Noise handling in evolutionary multi-objective optimization. In: Proc. of IEEE Congress on Evolutionary Computation (2006)Google Scholar
  10. 10.
    Hughes, E.: Evolutionary multi-objective ranking with uncertainty and noise. In: Proc. Int’l Conf. on Evolutionary Multi-Criterion Optimization (2001)Google Scholar
  11. 11.
    Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments-a survey. IEEE Trans. Evol. Computat. 9(3) (2005)Google Scholar
  12. 12.
    Mann, H., Whitney, D.: On a test of whether one of two random variables is stochastically larger than the other. Annals of Math. Stat. 18(1) (1947)Google Scholar
  13. 13.
    Park, T., Ryu, K.: Accumulative sampling for noisy evolutionary multi-objective optimization. In: Proc. of ACM Genetic and Evol. Computat. Conference (2011)Google Scholar
  14. 14.
    Teich, J.: Pareto-front exploration with uncertain objectives. In: Proc. of Int’l Conf. on Evol. Multi-Criterion Optimization (2001)Google Scholar
  15. 15.
    Veldhuizen, D.A.V., Lamont, G.B.: Multiobjective evolutionary algorithm test suites. In: Proc. ACM Symposium on Applied Computing (1999)Google Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Wormington, M., Panaccione, C., Matney, K.M., Bowen, D.K.: Characterization of structures from x-ray scattering data using genetic algorithms. Phil. Trans. R. Soc. Lond. A 357(1761) (1999)Google Scholar
  18. 18.
    Zhu, B., Suzuki, J., Boonma, P.: Solving the probabilistic traveling salesperson problem with profits (pTSPP) with a noise-aware evolutionary multiobjective optimization algorithm. In: Proc. IEEE Congress on Evol. Computat. (2011)Google Scholar
  19. 19.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Computat. 8(2) (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dung H. Phan
    • 1
  • Junichi Suzuki
    • 1
  1. 1.Deptartment of Computer ScienceUniversity of MassachusettsBostonUSA

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