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A Multiobjective Evolutionary Algorithm Guided by Averaged Hausdorff Distance to Aspiration Sets

  • Günter RudolphEmail author
  • Oliver Schütze
  • Christian Grimme
  • Heike Trautmann
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 288)

Abstract

The incorporation of expert knowledge into multiobjective optimization is an important issue which in this paper is reflected in terms of an aspiration set consisting of multiple reference points. The behaviour of the recently introduced evolutionary multiobjective algorithm AS-EMOA is analysed in detail and comparatively studied for bi-objective optimization problems w.r.t. R-NSGA2 and a respective variant. It will be shown that the averaged Hausdorff distance, integrated into AS-EMOA, is an efficient means to accurately approximate the desired aspiration set.

Keywords

multi-objective optimization aspiration set preferences 

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References

  1. 1.
    Wierzbicki, A.: The use of reference objectives in multiobjective optimization. In: Fandel, G., Gal, T. (eds.) Multiple Objective Decision Making, Theory and Application, pp. 468–486. Springer (1980)Google Scholar
  2. 2.
    Schütze, O., Esquivel, X., Lara, A., Coello Coello, C.A.: Using the averaged Hausdorff distance as a performance measure in evolutionary multi-objective optimization. IEEE Transactions on Evolutionary Computation 16(4), 504–522 (2012)CrossRefGoogle Scholar
  3. 3.
    Rudolph, G., Schütze, O., Grimme, C., Trautmann, H.: An aspiration set EMOA based on averaged Hausdorff distances. In: Proceedings of the 8th Int’l. Conference on Learning and Intelligent Optimization (LION 8). Springer (to appear, 2014)Google Scholar
  4. 4.
    Gerstl, K., Rudolph, G., Schütze, O., Trautmann, H.: Finding evenly spaced fronts for multiobjective control via averaging Hausdorff-measure. In: Proceedings of 8th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1–6. IEEE Press (2011)Google Scholar
  5. 5.
    Trautmann, H., Rudolph, G., Dominguez-Medina, C., Schütze, O.: Finding evenly spaced pareto fronts for three-objective optimization problems. In: Schütze, O., et al. (eds.) EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. AISC, vol. 175, pp. 89–105. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Rudolph, G., Trautmann, H., Sengupta, S., Schütze, O.: Evenly spaced pareto front approximations for tricriteria problems based on triangulation. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds.) EMO 2013. LNCS, vol. 7811, pp. 443–458. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Dominguez-Medina, C., Rudolph, G., Schütze, O., Trautmann, H.: Evenly spaced pareto fronts of quad-objective problems using PSA partitioning technique. In: Proceedings of 2013 IEEE Congress on Evolutionary Computation (CEC 2013), Piscataway (NJ), pp. 3190–3197. IEEE Press (2013)Google Scholar
  8. 8.
    Ignizio, J.: Goal programming and extensions. Lexington books. Lexington Books (1976)Google Scholar
  9. 9.
    Branke, J.: Consideration of partial user preferences in evolutionary multiobjective optimization. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 157–178. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Trautmann, H., Wagner, T., Biermann, D., Weihs, C.: Indicator-based selection in evolutionary multiobjective optimization algorithms based on the desirability index. Journal of Multi-Criteria Decision Analysis, 319–337 (2013)Google Scholar
  11. 11.
    Deb, K., Sundar, J.: Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the Conference on Genetic and Evolutionary Computation (GECCO 2006), pp. 635–642. ACM Press (2006)Google Scholar
  12. 12.
    Figueira, J., Liefooghe, A., Talbi, E.G., Wierzbicki, A.: A parallel multiple reference point approach for multi-objective optimization. European Journal of Operational Research 205(2), 390–400 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Heinonen, J.: Lectures on Analysis on Metric Spaces. Springer New York (2001)Google Scholar
  14. 14.
    Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007) ISBN 978-0-387-33254-3Google Scholar
  15. 15.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  16. 16.
    Schütze, O., Laumanns, M., Tantar, E., Coello Coello, C.A., Talbi, E.: Computing gap free pareto front approximations with stochastic search algorithms. Evol. Comput. 18(1), 65–96 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Günter Rudolph
    • 1
    Email author
  • Oliver Schütze
    • 2
  • Christian Grimme
    • 3
  • Heike Trautmann
    • 3
  1. 1.Department of Computer ScienceTU Dortmund UniversityDortmundGermany
  2. 2.Department of Computer ScienceCINVESTAVMexico CityMexico
  3. 3.Department of Information SystemsUniversity of MünsterMünsterGermany

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