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Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges

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Algorithmic Aspects in Information and Management (AAIM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5564))

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Abstract

We introduce a reduction technique for the well-known TSP. The basic idea of the approach consists of transforming a TSP instance to another one with smaller size by contracting pseudo backbone edges computed in a preprocessing step, where pseudo backbone edges are edges which are likely to be in an optimal tour. A tour of the small instance can be re-transformed to a tour of the original instance. We experimentally investigated TSP benchmark instances by our reduction technique combined with the currently leading TSP heuristic of Helsgaun. The results strongly demonstrate the effectivity of this reduction technique: for the six VLSI instances xvb13584, pjh17845, fnc19402, ido21215, boa28924, and fht47608 we could set world records, i.e., find better tours than the best tours known so far. The success of this approach is mainly due to the effective reduction of the problem size so that we can search the more important tour subspace more intensively.

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References

  1. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem. A Computational Study. Princeton University Press, Princeton (2006)

    MATH  Google Scholar 

  2. Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J., Espinoza, D., Goycoolea, M., Helsgaun, K.: Certification of an optimal Tour through 85,900 cities. Oper. Res. Lett. 37(1), 11–15 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cook, W., Seymour, P.: Tour Merging via Branch-Decomposition. INFORMS J. Comput. 15(3), 233–248 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)

    Book  MATH  Google Scholar 

  5. Ernst, C., Dong, C., Jäger, G., Molitor, P., Richter, D.: Finding Good Tours for Huge Euclidean TSP Instances by Iterative Backbone Contraction (submitted for Publication, 2009)

    Google Scholar 

  6. Fischer, T., Merz, P.: Reducing the Size of Traveling Salesman Problem Instances by Fixing Edges. In: Cotta, C., van Hemert, J. (eds.) EvoCOP 2007. LNCS, vol. 4446, pp. 72–83. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006)

    MATH  Google Scholar 

  8. Goldengorin, B., Jäger, G., Molitor, P.: Some Basics on Tolerances. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 194–206. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Goldengorin, B., Jäger, G., Molitor, P.: Tolerances Applied in Combinatorial Optimization. J. Comput. Sci. 2(9), 716–734 (2006)

    Article  Google Scholar 

  10. Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. SIGACT News 38(1), 31–45 (2007)

    Article  Google Scholar 

  11. Gutin, G., Punnen, A.P. (eds.): The Traveling Salesman Problem and Its Variations. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  12. Helsgaun, K.: An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. European Journal Oper. Res. 126(1), 106–130 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Helsgaun, K.: An Effective Implementation of K-opt Moves for the Lin-Kernighan TSP Heuristic. Writings on Computer Science 109 (2007)

    Google Scholar 

  14. Hüffner, F.: Algorithms and Experiments for Parameterized Approaches to Hard Graph Problems. PhD Thesis, Friedrich-Schiller-University Jena, Germany (2007)

    Google Scholar 

  15. Kilby, P., Slaney, J.K., Walsh, T.: The Backbone of the Travelling Salesperson. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 175–180 (2005)

    Google Scholar 

  16. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.): The Traveling Salesman Problem - A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chicester (1985)

    MATH  Google Scholar 

  17. Lin, S., Kernighan, B.W.: An Effective Heuristic Algorithm for the Traveling Salesman Problem. Oper. Res. 21, 498–516 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  18. Möbius, A., Freisleben, B., Merz, P., Schreiber, M.: Combinatorial Optimization by Iterative Partial Transcription. Phys. Rev. E 59(4), 4667–4674 (1999)

    Article  Google Scholar 

  19. Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B., Troyanski, L.: Determining Computational Complexity for Characteristic Phase Transitions. Nature 400, 133–137 (1998)

    MathSciNet  Google Scholar 

  20. Niedermeier, R.: Invitation to Fixed-Parameter Tractability. Oxford University Press, Oxford (2006)

    Book  MATH  Google Scholar 

  21. Reinelt, G.: TSPLIB – a Traveling Salesman Problem Library. ORSA J. Comput. 3, 376–384 (1991)

    Article  MATH  Google Scholar 

  22. Ribeiro, C.C., Toso, R.F.: Experimental Analysis of Algorithms for Updating Minimum Spanning Trees on Graphs Subject to Changes on Edge Weights. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 393–405. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. Richter, D.: Toleranzen in Helsgauns Lin-Kernighan-Heuristik für das TSP. Diploma Thesis, Martin-Luther-University Halle-Wittenberg, Germany (2006)

    Google Scholar 

  24. Richter, D., Goldengorin, B., Jäger, G., Molitor, P.: Improving the Efficiency of Helsgaun’s Lin-Kernighan Heuristic for the Symmetric TSP. In: Janssen, J., Prałat, P. (eds.) CAAN 2007. LNCS, vol. 4852, pp. 99–111. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. Slaney, J.K., Walsh, T.: The Backbones in Optimization and Approximation. In: Nebel, B. (ed.) Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI 2001), pp. 254–259 (2001)

    Google Scholar 

  26. Zhang, W., Looks, M.: A Novel Local Search Algorithm for the Traveling Salesman Problem that Exploits Backbones. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 343–350 (2005)

    Google Scholar 

  27. DIMACS Implementation Challenge: http://www.research.att.com/~dsj/chtsp/

  28. TSPLIB: http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsplib.html

  29. TSP Homepage, http://www.tsp.gatech.edu/

  30. National Instances from the TSP Homepage, http://www.tsp.gatech.edu/world/summary.html

  31. VLSI Instances from the TSP Homepage, http://www.tsp.gatech.edu/vlsi/summary.html

  32. World TSP from the TSP Homepage, http://www.tsp.gatech.edu/world/

  33. Source Code of [1] (Concorde), http://www.tsp.gatech.edu/concorde/index.html

  34. Source Code of [12] (LKH), http://www.akira.ruc.dk/~keld/research/LKH/

  35. Additional Information about Experiments of this Paper, http://www.informatik.uni-halle.de/ti/forschung/toleranzen/kantenkontraktion

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Dong, C., Jäger, G., Richter, D., Molitor, P. (2009). Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-02158-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02157-2

  • Online ISBN: 978-3-642-02158-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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