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A Powerful New Encoding for Tree-Based Combinatorial Optimisation Problems

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Parallel Problem Solving from Nature - PPSN VIII (PPSN 2004)

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

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Abstract

We describe a new encoding scheme and associated operators for tree structures on graphs and test it in the context of an evolutionary algorithm applied to the degree-constrained minimum spanning tree problem (DC-MST). The new encoding is relatively simple and easily copes with degree constraints. We compare with three existing encoding schemes, including edge-set, which represents the current state of the art on the DC-MST. The new encoding demonstrates superior performance on the larger instances of the well-used ‘Structured Hard’ DC-MST problems, and similar performance on the smaller instances. We conclude that the new encoding is a recommended method for the DC-MST.

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References

  1. Abuali, F.N., Wainwright, R.L., Schoenefeld, D.A.: Determinant Factorization: A New Encoding Scheme for Spanning Trees Applied to the Probabilistic Minimum Spanning Tree Problem. In: Eshelman, L.J. (ed.) Proc. of the Sixth International Conference on Genetic Algorithms, pp. 470–477 (1995)

    Google Scholar 

  2. Dengiz, B., Altiparmak, F., Smith, A.E.: Local Search Genetic Algorithm for Optimal Design of Reliable Networks. IEEE Transactions on Evolutionary Computation 1(3), 179–188 (1997)

    Article  Google Scholar 

  3. Edgington, E.: Randomization Tests. Marcel Dekker Inc., New York (1980)

    MATH  Google Scholar 

  4. Freisleben, B., Merz, P.: A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesmen Problems. IEEE Int. CEC, 616–621 (1996)

    Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness, San Francisco, Freeman (1979)

    Google Scholar 

  6. Gen, M., Chen, R.: Genetic Algorithms and Engineering Design. Wiley, Chichester (1997), Also see (for Prüfer encoding) http://www.ads.tuwien.ac.at/publications/bib/pdf/gottlieb-01.pdf

    Google Scholar 

  7. Julstrom, B., Raidl, G.: Initialization is Robust in Evolutionary Algorithms that Encode Spanning Trees as Sets of Edges. In: ACM Symp. on Applied Computing (2002)

    Google Scholar 

  8. Palmer, C., Kershenbaum, A.: An Approach to a Problem in Network Design Using Genetic Algorithms. Networks 26, 151–163 (1995)

    Article  MATH  Google Scholar 

  9. Knowles, J., Corne, D.: A new evolutionary approach to the degree-constrained minimum spanning tree problem. IEEE Trans. on Evolutionary Computation 4(2), 125–134 (2000)

    Article  Google Scholar 

  10. Krishnamoorthy, M., Ernst, A., Sharaiha, Y.: Comparison of Algorithms for the DC-MST. Journal of Heuristics 7, 587–611 (2001)

    Article  MATH  Google Scholar 

  11. Kruskal, J.B.: On the shortest spanning tree of a graph and the travelling salesman problem. Proc. of the American Mathematical Society 7(1), 48–50 (1956)

    Article  MathSciNet  Google Scholar 

  12. Michalewicz, Z.: Genetic Algorithms+Data Structures=Evolution Programs. Springer, Heidelberg (1992)

    MATH  Google Scholar 

  13. Narula, S.C., Ho, C.A.: Degree-constrained minimum spanning tree. Computer and Operations Research 7, 239–249 (1980)

    Article  Google Scholar 

  14. Piggott, P., Suraweera, F.: Encoding graphs for genetic algorithms: An investigation using the minimum spanning tree problem. In: Yao, X. (ed.) AI-WS 1993 and 1994. LNCS, vol. 956, Springer, Heidelberg (1995)

    Google Scholar 

  15. Prim, R.: Shortest connection networks and some generalisations. Bell Systems Technical Journal 36, 1389–1401 (1957)

    Google Scholar 

  16. Raidl, G.R.: An Effecient Evolutionary Algorithm for the Degree-Constrained Minimum Spanning Tree Problem. In: Proc.IEEE CEC, pp. 104–111 (2000)

    Google Scholar 

  17. Raidl, G.R., Julstrom, B.: Edge-Sets: An Effective Evolutionary Coding of Spanning Trees. IEEE Trans. on Evolutionary Computation 7(3), 225–239 (2003), Also see http://citeseer.ist.psu.edu/547892.html

    Article  Google Scholar 

  18. Rothlauf, F., Goldberg, D., Heinzl, A.: Network Random Keys - A Tree Network Representation Scheme for Genetic and Evolutionary Algorithms. Evolutionary Computation 10(1), 75–97 (2002), Also see sss http://www.uni-mannheim.de/i3v/00068900/18198591.htm

    Article  Google Scholar 

  19. Schindler, B., Rothlauf, F., Pesch, H.: Evolution Strategies, Network Random Keys, and the One-Max Tree Problem. In: Evoworkshops, pp. 52–143. Springer, Heidelberg (2002)

    Google Scholar 

  20. Zhou, G., Gen, M.: An Effective GA Approach to The Quadratic Minimum Spanning Tree Problem. Computers in Operations Research 25(3), 229–237 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Mechatronics, Gwang-ju Institute of Sci. and Tech, Republic of Korea

    Sang-Moon Soak & Byung-Ha Ahn

  2. Department of Computer Science, University of Exeter, UK

    David Corne

Authors
  1. Sang-Moon Soak
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  2. David Corne
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  3. Byung-Ha Ahn
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Editor information

Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Xin Yao

  2. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund K. Burke

  3. Intelligent Systems Group Department of Computer Science and Artificial Intelligence, University of the Basque Country, Paseo Manuel de Lardizábal 1, 20018, San Sebastian, Donostia, Spain

    José A. Lozano

  4. University of the West of England, Bristol, United Kingdom

    Jim Smith

  5. GeNeura Team, Depto. Arquitectura y Tecnología de Computadores, Universidad de Granada, Spain

    Juan Julián Merelo-Guervós

  6. School of Computer Science, The University of Birmingham, B15 1TT, Edgbaston, Birmingham, UK

    John A. Bullinaria

  7. School of Computer Science, University of Birmingham, B15 2TT, Birmingham, Great Britain

    Jonathan E. Rowe

  8. School of Computer Science, University of Birmingham, United Kingdom

    Peter Tiňo

  9. School of Computer Science, The University of Birmingham, B15 2TT, Birmingham, UK

    Ata Kabán

  10. Faculty of Computer Science, Dortmund University of Technology, 44221, Dortmund, Germany

    Hans-Paul Schwefel

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© 2004 Springer-Verlag Berlin Heidelberg

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Soak, SM., Corne, D., Ahn, BH. (2004). A Powerful New Encoding for Tree-Based Combinatorial Optimisation Problems. In: Yao, X., et al. Parallel Problem Solving from Nature - PPSN VIII. PPSN 2004. Lecture Notes in Computer Science, vol 3242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30217-9_44

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  • DOI: https://doi.org/10.1007/978-3-540-30217-9_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23092-2

  • Online ISBN: 978-3-540-30217-9

  • eBook Packages: Springer Book Archive

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