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A Memetic Algorithm and a Solution Archive for the Rooted Delay-Constrained Minimum Spanning Tree Problem

  • Mario Ruthmair
  • Günther R. Raidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6927)

Abstract

We present a memetic algorithm for a combinatorial optimization problem called rooted delay-constrained minimum spanning tree problem arising for example in centralized broadcasting networks where quality of service constraints are of concern. The memetic algorithm is based on a specialized solution representation and a simple and effective decoding mechanism. Solutions are locally improved by a variable neighborhood descent in two neighborhood structures. Furthermore, to tackle the problem of repeated examination of already visited solutions we investigate a simple hash-based method to only detect duplicates or, alternatively, a trie-based complete solution archive to additionally derive new unvisited solutions. Experimental results show that our memetic algorithm outperforms existing heuristic approaches for this problem in most cases. Including the hash-based duplicate detection mostly further improves solution quality whereas the solution archive can only rarely obtain better results due to its operational overhead.

Keywords

network design memetic algorithm solution archive delay constraints 

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References

  1. 1.
    Gouveia, L., Paias, A., Sharma, D.: Modeling and Solving the Rooted Distance-Constrained Minimum Spanning Tree Problem. Computers and Operations Research 35(2), 600–613 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Gruber, M., van Hemert, J., Raidl, G.R.: Neighborhood Searches for the Bounded Diameter Minimum Spanning Tree Problem Embedded in a VNS, EA, and ACO. In: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1187–1194. ACM, New York (2006)Google Scholar
  3. 3.
    Kratica, J.: Improving Performances of the Genetic Algorithm by Caching. Computers and Artificial Intelligence 18(3), 271–283 (1999)MATHGoogle Scholar
  4. 4.
    Leggieri, V., Haouari, M., Triki, C.: An Exact Algorithm for the Steiner Tree Problem with Delays. Electronic Notes in Discrete Mathematics, vol. 36, pp. 223–230. Elsevier, Amsterdam (2010)Google Scholar
  5. 5.
    Leitner, M., Ruthmair, M., Raidl, G.R.: Stabilized Branch-and-Price for the Rooted Delay-Constrained Steiner Tree Problem. In: Pahl, J. (ed.) INOC 2011. LNCS, vol. 6701, pp. 124–138. Springer, Heidelberg (2011)Google Scholar
  6. 6.
    Manyem, P., Stallmann, M.: Some approximation results in multicasting. Tech. Rep. TR-96-03, North Carolina State University (1996)Google Scholar
  7. 7.
    Prüfer, H.: Neuer beweis eines satzes über permutationen. Archiv für Mathematik und Physik 27, 142–144 (1918)MATHGoogle Scholar
  8. 8.
    Raidl, G.R., Hu, B.: Enhancing Genetic Algorithms by a Trie-Based Complete Solution Archive. In: Cowling, P., Merz, P. (eds.) EvoCOP 2010. LNCS, vol. 6022, pp. 239–251. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Ruthmair, M., Raidl, G.R.: A Kruskal-Based Heuristic for the Rooted Delay-Constrained Minimum Spanning Tree Problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2009. LNCS, vol. 5717, pp. 713–720. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Ruthmair, M., Raidl, G.R.: Variable Neighborhood Search and Ant Colony Optimization for the Rooted Delay-Constrained Minimum Spanning Tree Problem. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol. 6239, pp. 391–400. Springer, Heidelberg (2010)Google Scholar
  11. 11.
    Ruthmair, M., Raidl, G.R.: A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems. In: Günlük, O., Woeginger, G. (eds.) IPCO 2011 Part XV. LNCS, vol. 6655, pp. 376–388. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Salama, H.F., Reeves, D.S., Viniotis, Y.: An Efficient Delay-Constrained Minimum Spanning Tree Heuristic. In: Proceedings of the 5th International Conference on Computer Communications and Networks. IEEE Press, Los Alamitos (1996)Google Scholar
  13. 13.
    Whitley, D.: A genetic algorithm tutorial. Statistics and computing 4(2), 65–85 (1994)CrossRefGoogle Scholar
  14. 14.
    Xu, Y., Qu, R.: A GRASP approach for the Delay-constrained Multicast routing problem. In: Proceedings of the 4th Multidisplinary International Scheduling Conference (MISTA4), Dublin, Ireland, pp. 93–104 (2009)Google Scholar
  15. 15.
    Xu, Y., Qu, R.: A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems. Applied Intelligence 1–13 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mario Ruthmair
    • 1
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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