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Runtime Analyses for Using Fairness in Evolutionary Multi-Objective Optimization

  • Tobias Friedrich
  • Christian Horoba
  • Frank Neumann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness introduced by Laumanns et al.[7]. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present showcase examples to point out situations where the right mechanism can speed up the optimization process significantly.

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References

  1. 1.
    Deb, K., Agrawal, S., Pratap, 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 VI 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51–81 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Friedrich, T., He, J., Hebbinghaus, N., Neumann, F., Witt, C.: Approximating covering problems by randomized search heuristics using multi-objective models. In: Proceedings of Conference on Genetic and Evolutionary Computation (GECCO), vol. 1, pp. 797–804. ACM Press, New York (2007)CrossRefGoogle Scholar
  4. 4.
    Friedrich, T., Hebbinghaus, N., Neumann, F.: Plateaus can be harder in multi-objective optimization. In: Proceedings of Congress on Evolutionary Computation (CEC), pp. 2622–2629. IEEE Press, Los Alamitos (2007)Google Scholar
  5. 5.
    Giel, O.: Expected runtimes of a simple multi-objective evolutionary algorithm. In: Proceedings of Congress on Evolutionary Computation (CEC), pp. 1918–1925. IEEE Press, Los Alamitos (2003)Google Scholar
  6. 6.
    Jansen, T., Wegener, I.: Evolutionary algorithms - how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Transactions on Evolutionary Computation 5(6), 589–599 (2001)CrossRefGoogle Scholar
  7. 7.
    Laumanns, M., Thiele, L., Zitzler, E.: Running time analysis of multiobjective evolutionary algorithms on pseudo-boolean functions. IEEE Transactions on Evolutionary Computation 8(2), 170–182 (2004)CrossRefGoogle Scholar
  8. 8.
    Neumann, F.: Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem. European Journal of Operational Research 181(3), 1620–1629 (2007)CrossRefzbMATHGoogle Scholar
  9. 9.
    Neumann, F., Wegener, I.: Minimum spanning trees made easier via multi-objective optimization. Natural Computing 5(3), 305–319 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Proc. of EUROGEN 2001, pp. 95–100. International Center for Numerical Methods in Engineering (CIMNE) (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tobias Friedrich
    • 1
  • Christian Horoba
    • 2
  • Frank Neumann
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Fakultät für Informatik, LS 2TU DortmundDortmundGermany

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