Expected Runtimes of a Simple Evolutionary Algorithm for the Multi-objective Minimum Spanning Tree Problem

  • Frank Neumann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3242)


Evolutionary algorithms are applied to problems that are not well understood as well as to problems in combinatorial optimization. The analysis of these search heuristics has been started for some well-known polynomial solvable problems. Such analyses are starting points for the analysis of evolutionary algorithms of difficult problems. We consider the NP-hard multi-objective minimum spanning tree problem and give upper bounds on the expected time until a simple evolutionary algorithm has produced a population including for each extremal point of the Pareto Front a corresponding spanning tree.


Span Tree Pareto Front Minimum Span Tree Search Point Minimum Span Tree Problem 
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  1. 1.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51–81 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Scharnow, J., Tinnefeld, K., Wegener, I.: Fitness landscapes based on sorting and shortest paths problems. In: IWDW 2003, vol. 2939, pp. 54–63 (2002)Google Scholar
  3. 3.
    Giel, O.: Evolutionary algorithms and the maximum matching problem. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 415–426. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Neumann, F.: Expected Runtimes of evolutionary algorithms for the Eulerian cycle problem. Accepted for CEC 2004 (2004)Google Scholar
  5. 5.
    Neumann, F., Wegener, I.: Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 713–724. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., Deb, K.: Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 44–53. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Giel, O.: Expected Runtimes of a Simple Multi-objective Evolutionary Algorithm. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), pp. 1918–1925 (2003)Google Scholar
  8. 8.
    Zhou, G., Gen, M.: Genetic algorithm approach on multi-criteria minimum spanning tree problem. European Journal of Operational Research 114, 141–152 (1999)MATHCrossRefGoogle Scholar
  9. 9.
    Knowles, J.D., Corne, D.W.: A comparison of encodings and algorithms for multiobjective minimum spanning tree problems. CEC 2001 (2001)Google Scholar
  10. 10.
    Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2000)MATHGoogle Scholar
  11. 11.
    Raidl, G.R., Julstrom, B.A.: Edge sets: an effective evolutionary coding of spanning trees. IEEE Trans. on Evolutionary Computation 7, 225–239 (2003)CrossRefGoogle Scholar
  12. 12.
    Kano, M.: Maximum and kth maximal spanning trees of a weighted graph. Combinatorica 7, 205–214 (1987)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Mayr, E.W., Plaxton, C.G.: On the spanning trees of weighted graphs. Combinatorica 12, 433–447 (1992)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Frank Neumann
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Univ. zu KielKielGermany

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