Skip to main content
Book cover

International Conference on Hybrid Intelligent Systems

HIS 2016: Proceedings of the 16th International Conference on Hybrid Intelligent Systems (HIS 2016) pp 278–287Cite as

An Empirical Study of the Multi-fragment Tour Construction Algorithm for the Travelling Salesman Problem

  • 1186 Accesses

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 552)

Abstract

This paper proposes a detailed study of the Multi-Fragment (MF) tour construction (TC) algorithm for the Travelling Salesman Problem (TSP). This TC heuristic is based on an edge selection strategy which favors edges with the smallest cost under the constraint to have a feasible tour. Extensive computational experiments have been performed on benchmark instances from the literature. The results show that the studied algorithm generally outperforms other constructive heuristics for the TSP.

Keywords

  • Travelling Salesman Problem
  • Edge selection strategy
  • Tour construction
  • Heuristic

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-52941-7_28
  • Chapter length: 10 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   269.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-52941-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   349.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

References

  1. Applegate, D., Bixby, R., Chvátal, V., Cook, W.: Concorde: a code for solving traveling salesman problems (1999). http://www.math.uwaterloo.ca/tsp/concorde.html

  2. Bentley, J.J.: Fast algorithms for geometric traveling salesman problems. ORSA J. Comput. 4(4), 387–411 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Bentley, J.L.: Experiments on traveling salesman heuristics. In: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990, pp. 91–99. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1990). http://dl.acm.org/citation.cfm?id=320176.320186

  4. Borůvka, O.: O jistém problému minimálním (about a certain minimal problem) (in Czech, German summary) (1926)

    Google Scholar 

  5. Bull, J.M., Smith, L.A., Pottage, L., Freeman, R.: Benchmarking java against c and fortran for scientific applications. In: Proceedings of the 2001 Joint ACM-ISCOPE Conference on Java Grande, pp. 97–105. ACM (2001)

    Google Scholar 

  6. Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958). http://dx.doi.org/10.1287/opre.6.6.791

    CrossRef  MathSciNet  Google Scholar 

  7. Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified np-complete problems. In: Proceedings of the Sixth Annual ACM Symposium on Theory of Computing, STOC 1974, pp. 47–63, NY, USA (1974). http://doi.acm.org/10.1145/800119.803884

  8. Grefenstette, J., Gopal, R., Rosmaita, B., Van Gucht, D.: Genetic algorithms for the traveling salesman problem. In: Proceedings of the First International Conference on Genetic Algorithms and their Applications, pp. 160–168. Lawrence Erlbaum, New Jersey (1985)

    Google Scholar 

  9. Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees. Oper. Res. 18(6), 1138–1162 (1970)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Helsgaun, K.: An effective implementation of the lin-kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126(1), 106–130 (2000)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Johnson, D.S., McGeoch, L.A.: The Traveling Salesman Problem: a case study in local optimization. Local Search Comb. Optim. 1, 215–310 (1997)

    MATH  Google Scholar 

  12. Johnson, D.S., McGeoch, L.A.: Experimental analysis of heuristics for the STSP. In: Gutin, G., Punnen, A.P. (eds.) The Traveling Salesman Problem and its Variations, pp. 369–443. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  13. Knox, J.: Tabu search performance on the symmetric traveling salesman problem. Comput. Oper. Res. 21(8), 867–876 (1994)

    CrossRef  MATH  Google Scholar 

  14. Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7(1), 48–50 (1956)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Lawler, E.L., Lenstra, J.K., Kan, A.R., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, vol. 3. Wiley, New York (1985)

    MATH  Google Scholar 

  16. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Techn. J. 36(6), 1389–1401 (1957)

    CrossRef  Google Scholar 

  18. Reinelt, G.: TSPLIB–a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991). http://dx.doi.org/10.1287/ijoc.3.4.376

    CrossRef  MATH  Google Scholar 

  19. Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  20. Reinhelt, G.: \(\{\)TSPLIB\(\}\): a library of sample instances for the TSP (and related problems) from various sources and of various types (2014). http://comopt.ifi.uniheidelberg.de/software/TSPLIB95

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Mohammed V University in Rabat, Rabat, Morocco

    Mehdi El Krari, Belaïd Ahiod & Bouazza El Benani

  2. Computer Science Laboratory, Mohammed V University in Rabat, Rabat, Morocco

    Mehdi El Krari & Bouazza El Benani

  3. LRIT, Associated Unit to CNRST (URAC 29), Mohammed V University in Rabat, Rabat, Morocco

    Belaïd Ahiod

Authors
  1. Mehdi El Krari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Belaïd Ahiod
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bouazza El Benani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehdi El Krari .

Editor information

Editors and Affiliations

  1. (MIR Labs), Machine Intelligence Research Labs, Auburn, Washington, USA

    Ajith Abraham

  2. Hassan 1st University, Settat, Morocco

    Abdelkrim Haqiq

  3. ENIS, University of Sfax, Sfax, Tunisia

    Adel M. Alimi

  4. Technopolis Rabat-Shore Rocade, International University of Rabat, Sala el Jadida, Morocco

    Ghita Mezzour

  5. Inst Applied Dept of Electronics, Taffala, University of Sousse, Sousse, Tunisia

    Nizar Rokbani

  6. Fakulti Teknologi Maklumat dan Komunikas, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Malaysia

    Azah Kamilah Muda

Rights and permissions

Reprints and Permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

El Krari, M., Ahiod, B., El Benani, B. (2017). An Empirical Study of the Multi-fragment Tour Construction Algorithm for the Travelling Salesman Problem. In: Abraham, A., Haqiq, A., Alimi, A., Mezzour, G., Rokbani, N., Muda, A. (eds) Proceedings of the 16th International Conference on Hybrid Intelligent Systems (HIS 2016). HIS 2016. Advances in Intelligent Systems and Computing, vol 552. Springer, Cham. https://doi.org/10.1007/978-3-319-52941-7_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-52941-7_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52940-0

  • Online ISBN: 978-3-319-52941-7

  • eBook Packages: EngineeringEngineering (R0)