New Approaches to Coevolutionary Worst-Case Optimization

  • Jürgen Branke
  • Johanna Rosenbusch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


Many real-world optimization problems involve uncertainty. In this paper, we consider the case of worst-case optimization, i.e., the user is interested in a solution’s performance in the worst case only. If the number of possible scenarios is large, it is an optimization problem by itself to determine a solution’s worst case performance. In this paper, we apply coevolutionary algorithms to co-evolve the worst case test cases along with the solution candidates. We propose a number of new variants of coevolutionary algorithms, and show that these techniques outperform previously proposed coevolutionary worst-case optimizers on some simple test problems.


Solution Candidate Greedy Method Coevolutionary Algorithm Local Ranking Selected Test Case 
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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  1. 1.
    Avigad, G., Branke, J.: Worst-case robustness and related decision support. In: Genetic and Evolutionary Computation Conference, ACM Press, New York (to appear)Google Scholar
  2. 2.
    Barbosa, H.J.C.: A coevolutionary genetic algorithm for constrained optimization. In: Congress on Evolutionary Computation, vol. 3, pp. 1605–1611 (1999)Google Scholar
  3. 3.
    Branke, J.: Evolutionary Optimization in Dynamic Environments. Kluwer Academic Publishers, Norwell (2001)Google Scholar
  4. 4.
    Daum, D.A., Deb, K., Branke, J.: Reliability-based optimization for multiple constraints with evolutionary algorithms. In: Congress on Evolutionary Computation, pp. 911–918. IEEE Computer Society Press, Los Alamitos (2007)Google Scholar
  5. 5.
    de Jong, E.: The maxsolve algorithm for coevolution. In: Conference on Genetic and Evolutionary Computation, pp. 483–489. ACM Press, New York (2005)Google Scholar
  6. 6.
    Herrmann, J.W.: A genetic algorithm for minimax optimization problems. In: Congress on Evolutionary Computation, vol. 2, pp. 1099–1103. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  7. 7.
    Hillis, D.W.: Co-evolving parasites improve simulated evolution in an optimization procedure. Physica D 42, 228–234 (1990)CrossRefGoogle Scholar
  8. 8.
    Jensen, M.T.: Finding worst-case flexible schedules using coevolution. In: Spector, L., et al. (eds.) Genetic and Evolutionary Computation Conference, pp. 1144–1151. Morgan Kaufmann, San Francisco (2001)Google Scholar
  9. 9.
    Jensen, M.T.: A new look at solving minimax problems with coevolutionary genetic algorithms. Applied Optimization 86, 369–384 (2004)CrossRefGoogle Scholar
  10. 10.
    Korn, R., Steffensen, M.: On worst-case portfolio optimization. SIAM Journal on Control and Optimization 46(6), 2013–2030 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Luke, S., Wiegand, R.P.: When coevolutionary algorithms exhibit evolutionary dynamics. In: Barry, A.M. (ed.) GECCO 2002: Proceedings of the Bird of a Feather Workshops, Genetic and Evolutionary Computation Conference, pp. 236–241. AAAI Press, Menlo Park (2002)Google Scholar
  12. 12.
    Ong, Y.-S., Nair, P.B., Lum, K.Y.: Max-min surrogate-assisted evolutionary algorithm for robust design. IEEE Transactions on Evolutionary Computation 10(4), 392–404 (2006)CrossRefGoogle Scholar
  13. 13.
    Pagie, L., Hogeweg, P.: Information integration and red queen dynamics in coevolutionary optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 2, pp. 1260–1267 (2000)Google Scholar
  14. 14.
    Paredis, J.: Coevolutionary computation. Artificial Life 2(4), 355–375 (1995)CrossRefGoogle Scholar
  15. 15.
    Sebald, A.V., Schlenzig, J.: Minimax design of neural net controllers for highly uncertain plants. IEEE Transactions on Neural Networks 5(1), 73–82 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jürgen Branke
    • 1
  • Johanna Rosenbusch
    • 1
  1. 1.Institute AIFBUniversity of KarlsruheGermany

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