Skip to main content

Multi-Noisy-objective Optimization Based on Prediction of Worst-Case Performance

  • Conference paper
Theory and Practice of Natural Computing (TPNC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8890))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Springer (2005)

    Google Scholar 

  2. Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments - a survey. IEEE Trans. on Evolutionary Computation 9(3), 303–317 (2005)

    Article  Google Scholar 

  3. Gunawan, S., Azarm, S.: Multi-objective robust optimization using a sensitivity region concept. Structural and Multidisciplinary Optimization 29(1), 50–60 (2005)

    Article  Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Fieldsend, J.E., Everson, R.M.: Multi-objective optimization in the presence of uncertainty. In: Proc. IEEE CEC 2005, pp. 243–250 (2005)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Bui, L.T., Abbass, H.A., Essam, D.: Localization for solving noisy multi-objective optimization problems. Evolutionary Computation 17(3), 379–409 (2009)

    Article  Google Scholar 

  10. Eskandari, H., Geiger, C.D.: Evolutionary multiobjective optimization in noisy problem environments. Journal of Heuristics 15(6), 559–595 (2009)

    Article  MATH  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. Kuroiwa, D., Lee, G.M.: On robust multiobjective optimization. Vietnam Journal of Mathematics 40(2&3), 305–317 (2012)

    MATH  MathSciNet  Google Scholar 

  13. Avigad, G., Branke, J.: Embedded evolutionary multi-objective optimization for worst case robustness. In: Proc. GECCO 2008, pp. 617–624 (2008)

    Google Scholar 

  14. 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

  15. 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

  16. Wackerly, D.D., Mendenhall, W., Scheaffer, R.L.: Mathematical Statistics with Applications, 7th edn. Thomson Learning, Inc. (2008)

    Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. 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)

    Chapter  Google Scholar 

  22. 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)

    Google Scholar 

  23. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. TIK-Technical Report, 112, 1–27 (2001)

    Google Scholar 

  24. Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13749-0_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13748-3

  • Online ISBN: 978-3-319-13749-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics