On a Property Analysis of Representations for Spanning Tree Problems

  • Sang-Moon Soak
  • David Corne
  • Byung-Ha Ahn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3871)


This paper investigates on some properties of encodings of evolutionary algorithms for spanning tree based problems. Although debate continues on how and why evolutionary algorithms work, many researchers have observed that an EA is likely to perform well when its encoding and operators exhibit locality, heritability and diversity. To analyze these properties of various encodings, we use two kinds of analytical methods; static analysis and dynamic analysis and use the Optimum Communication Spanning Tree (OCST) problem as a test problem. We show it through these analysis that the encoding with extremely high locality and heritability may lose the diversity in population. And we show that EA using Edge Window Decoder (EWD) has high locality and high heritability but nevertheless it preserves high diversity for generations.


Crossover Operator High Heritability High Locality Span Tree Problem Star Tree 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Eckert, C., Gottlieb, J.: Direct Representation and Variation Operators for the Fixed Charge Transportation 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. 77–87. Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Gaube, T., Rothlauf, F.: The Link and Node Biased Encoding Revisited: Bias and Adjustment of Parameters. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) EvoIASP 2001, EvoWorkshops 2001, EvoFlight 2001, EvoSTIM 2001, EvoCOP 2001, and EvoLearn 2001. LNCS, vol. 2037, pp. 1–10. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Gen, M., Chen, R.: Genetic Algorithms and Engineering Design. Wiley, Chichester (1997); also see (for Prüfer encoding) Google Scholar
  4. 4.
    Gottlieb, J., Eckert, C.: A Comparision of Two Representations for the Fixed Charge Transportation Problem. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 345–354. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Julstrom, B.A.: The Blob Code: A Better String Coding of Spanning Trees for Evolutionary Search. In: Genetic and Evolutionary Computation Conference Workshop Program, pp. 256–261. Morgan Kaufmann, San Francisco (2001)Google Scholar
  6. 6.
    Manderick, B., de Weger, M., Spiessens, P.: The genetic algorithm and the structure of the fitness landscape. In: Proceedings of the 4th International Conference on Genetic Algorithms, pp. 143–150 (1991)Google Scholar
  7. 7.
    Merz, P., Freisleben, B.: Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning. Evolutionary Computation 8(1), 61–91 (2000)CrossRefGoogle Scholar
  8. 8.
    Palmer, C.C., Kershenbaum, A.: An Approach to a Problem in Network Design Using Genetic Algorithms. Networks 26, 151–163 (1995)CrossRefMATHGoogle Scholar
  9. 9.
    Raidl, G.R.: Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem, Evolutionary Computation Journal, MIT Press 13(4), (to appear, 2005)Google Scholar
  10. 10.
    Raidl, G.R., Julstrom, B.A.: Edge-Sets: An Effective Evolutionary Coding of Spanning Trees. IEEE Transactions on Evolutionary Computation 7(3), 225–239 (2003)CrossRefGoogle Scholar
  11. 11.
    Reeves, C.R., Yamada, T.: Genetic algorithms, path relinking, and the flowshop sequencing problem. Evolutionary Computation 6, 45–60Google Scholar
  12. 12.
    Rothlauf, F.: Locality, Distance Distortion, and Binary Representations of Integers, Working Papers (July 2003)Google Scholar
  13. 13.
    Rothlauf, F., Goldberg, D.E., Heinzl, A.: Network Random Keys - A Tree Network Representation Scheme for Genetic and Evolutionary Algorithms. Evolutionary Computation 10(1), 75–97 (2002)CrossRefGoogle Scholar
  14. 14.
    Rothlauf, F., Gerstacker, J., Heinzl, A.: On the Optimal Communication Spanning Tree Problem, Working Papers in Information Systems, University of Mannheim (2003)Google Scholar
  15. 15.
    Rothlauf, F.: On the Locality of Representations, Working Paper in Information Systems, University of Mannheim (2003)Google Scholar
  16. 16.
    Schuter, P.: Artificial Life and Molecular Evolutionary Biology. In: Moran, F., et al. (eds.) Advances in Artificial Life, pp. 3–19. Springer, Heidelberg (1995)Google Scholar
  17. 17.
    Sendhoff, B., Kreutz, M., Seelen, W.V.: A condition for the genotype-phenotype mapping: Causalty. In: Proceedings of the Seventh International Conference on Genetic Algorithms, Morgan Kaufmann, San Francisco (1997)Google Scholar
  18. 18.
    Soak, S.M., Corne, D., Ahn, B.H.: The Edge-Window-Decoder Representation for Tree-Based Problems, IEEE Transaction on Evolutionary Computation (submitted,2004)Google Scholar
  19. 19.
    Watson, J.P., Barbulescu, L., Whitley, L.D., Howe, A.E.: Constrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sang-Moon Soak
    • 1
  • David Corne
    • 2
  • Byung-Ha Ahn
    • 1
  1. 1.Dept. of MechatronicsGwangju Institute of Science and TechnologySouth Korea
  2. 2.Dept. of Computer ScienceUniversity of ExeterExeterUK

Personalised recommendations