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Finding Knees in Multi-objective Optimization

  • Jürgen Branke
  • Kalyanmoy Deb
  • Henning Dierolf
  • Matthias Osswald
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)

Abstract

Many real-world optimization problems have several, usually conflicting objectives. Evolutionary multi-objective optimization usually solves this predicament by searching for the whole Pareto-optimal front of solutions, and relies on a decision maker to finally select a single solution. However, in particular if the number of objectives is large, the number of Pareto-optimal solutions may be huge, and it may be very difficult to pick one “best” solution out of this large set of alternatives. As we argue in this paper, the most interesting solutions of the Pareto-optimal front are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. These solutions are sometimes also called “knees”. We then introduce a new modified multi-objective evolutionary algorithm which is able to focus search on these knee regions, resulting in a smaller set of solutions which are likely to be more relevant to the decision maker.

Keywords

Multiobjective Optimization Marginal Utility Multiobjective Evolutionary Algorithm Knee Region Find Knee 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Branke, J., Deb, K.: Integrating user preferences into evolutionary multi-objective optimization. In: Jin, Y. (ed.) Knowledge Incorporation in Evolutionary Computation, Springer, Heidelberg (to appear)Google Scholar
  2. 2.
    Branke, J., Kaußler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 499–507 (2001)zbMATHCrossRefGoogle Scholar
  3. 3.
    Branke, J., Kaußler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32(6), 499–508 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  5. 5.
    Cvetković, D., Parmee, I.C.: Preferences and their Application in Evolutionary Multiobjective Optimisation. IEEE Transactions on Evolutionary Computation 6(1), 42–57 (2002)CrossRefGoogle Scholar
  6. 6.
    Das, I.: On characterizing the ’knee’ of the pareto curve based on normal-boundary intersection. Structural Optimization 18(2/3), 107–115 (1999)Google Scholar
  7. 7.
    Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary Computation Journal 7(3), 205–230 (1999)CrossRefGoogle Scholar
  8. 8.
    Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)zbMATHGoogle Scholar
  9. 9.
    Deb, K.: Multi-objective evolutionary algorithms: Introducing bias among Pareto-optimal solutions. In: Ghosh, A., Tsutsui, S. (eds.) Advances in Evolutionary Computing: Theory and Applications, pp. 263–292. Springer, Heidelberg (2003)Google Scholar
  10. 10.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  11. 11.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the Congress on Evolutionary Computation (CEC 2002), pp. 825–830 (2002)Google Scholar
  12. 12.
    Greenwood, G.W., Hu, X.S., D’Ambrosio, J.G.: Fitness Functions forMultiple Objective Optimization Problems: Combining Preferences with Pareto Rankings. In: Belew, R.K., Vose, M.D. (eds.) Foundations of Genetic Algorithms, vol. 4, pp. 437–455. Morgan Kaufmann, San Mateo (1997)Google Scholar
  13. 13.
    Ls11. The Kea-Project (v. 1.0). University of Dortmund, Informatics Department (2003), online http://ls11-www.cs.uni-dortmund.de
  14. 14.
    Mattson, C.A., Mullur, A.A., Messac, A.: Minimal representation of multiobjective design space using a smart pareto filter. In: AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization (2002)Google Scholar
  15. 15.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)zbMATHGoogle Scholar
  16. 16.
    Van Veldhuizen, D., Lamont, G.B.: Multiobjective evolutionary algorithms: Analyzing the state-of-the-art. Evolutionary Computation Journal 8(2), 125–148 (2000)CrossRefGoogle Scholar
  17. 17.
    Yu, P.L.: A class of solutions for group decision problems. Management Science 19(8), 936–946 (1973)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jürgen Branke
    • 1
  • Kalyanmoy Deb
    • 2
  • Henning Dierolf
    • 1
  • Matthias Osswald
    • 1
  1. 1.Institute AIFBUniversity of KarlsruheGermany
  2. 2.Department of Mechanical EngineeringIIT KanpurIndia

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