Hybrid Evolutionary Algorithms for the Rectilinear Steiner Tree Problem Using Fitness Estimation

  • Byounghak Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3982)


The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the minimum spanning tree without Steiner points. We introduced four evolutionary algorithm based upon fitness estimation and hybrid operator. Experimental results show that the quality of solution is improved by the hybrid operator and the calculation time is reduced by the fitness estimation. The best evolutionary algorithm is better than the previously proposed other heuristics. The solution of evolutionary algorithm is 99.4% of the optimal solution.


Evolutionary Algorithm Minimum Span Tree Steiner Tree Steiner Point Hybrid Operator 
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.
    Bäck, T.: Evolutionary Algorithm in Theory and Practice. Oxford University Press, Oxford (1996)Google Scholar
  2. 2.
    Barreiros, J.: An Hierarchic Genetic Algorithm for Computing (near) Optimal Euclidean Stein Steiner Trees. In: Workshop on Application of hybrid Evolutionary Algorithms to NP-Complete Problems, Chicago (2003)Google Scholar
  3. 3.
    Beasley, J.E.: OR-Library: distributing test problems by electronic mail. Journal of the Operational Research Society 41, 1069–1072 (1990)Google Scholar
  4. 4.
    Beasley, J.E.: A heuristic for Euclidean and rectilinear Steiner problems. European Journal of Operational Research 58, 284–292 (1992)MATHCrossRefGoogle Scholar
  5. 5.
    Borah, M., Owens, R.M.: An Edge-Based Heuristic for Steiner Routing. IEEE Trans. on Computer Aided Design 13, 1563–1568 (1994)CrossRefGoogle Scholar
  6. 6.
    France, R.L.: A note on the optimum location of new machines in existing plant layouts. J. Industrial Engineering 14, 57–59 (1963)Google Scholar
  7. 7.
    Ganley, J.L.: Computing optimal rectilinear Steiner trees: A survey and experimental evaluation. Discrete Applied Mathematics 90, 161–171 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics 32, 826–834 (1977)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hanan, M.: On Steiner’s problem with rectilinear distance. SLAM Journal on Applied Mathematics 14, 255–265 (1966)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hesser, J., Manner, R., Stucky, O.: Optimization of Steiner Trees using Genetic Algorithms. In: Proceedings of the Third International Conference on Genetic Algorithm, pp. 231–236 (1989)Google Scholar
  11. 11.
    Jin, Y.: A Survey on fitness Approximation in Evolutionary Computation. Journal of Soft Computing 9, 3–12 (2005)CrossRefGoogle Scholar
  12. 12.
    Julstrom, B.A.: Encoding Rectilinear Trees as Lists of Edges. In: Proceedings of the 16th ACM Symposium on Applied Computing, pp. 356–360 (2001)Google Scholar
  13. 13.
    Kahng, A.B., Robins, B.: A New Class of Iterative Steiner Tree Heuristics with Good Performance. IEEE Trans. on Computer Aided Design 11, 893–902 (1992)CrossRefGoogle Scholar
  14. 14.
    Lee, J.L., Bose, N.K., Hwang, F.K.: Use of Steiner’s problem in suboptimal routing in rectilinear metric. IEEE Transaction son Circuits and Systems 23, 470–476 (1976)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sock, S.M., Ahn, B.H.: A New Tree Representation for Evolutionary Algorithms. Journal of the Korean Institute of Industrial Engineers 31, 10–19 (2005)Google Scholar
  16. 16.
    Soukup, J., Chow, W.F.: Set of test problems for the minimum length connection networks. ACM/SIGMAP Newsletter 15, 48–51 (1973)Google Scholar
  17. 17.
    Warme, D.M., Winter, P., Zachariasen, M.: Exact Algorithms for Plane Steiner Tree Problems: A Computational Study. In: Du, D.Z., Smith, J.M., Rubinstein, J.H. (eds.) Advances in Steiner Tree. Kluser Academic Publishers, Dordrecht (1998)Google Scholar
  18. 18.
  19. 19.
    Yang, B.H.: An Evolution Algorithm for the Rectilinear Steiner Tree Problem. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganá, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005. LNCS, vol. 3483, pp. 241–249. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Byounghak Yang
    • 1
  1. 1.Department of Industrial EngineeringKyungwon UniversityKyunggi-doKorea

Personalised recommendations