Skip to main content
SpringerLink
Log in

Improved Upper and Lower Bounds for the Close Enough Traveling Salesman Problem

  • Conference paper
  • First Online:
Green, Pervasive, and Cloud Computing (GPC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10232))

Included in the following conference series:

Abstract

This paper studies the close-enough traveling salesman problem, a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood of that node. We introduce an improved version of the adaptive internal discretization scheme, recently proposed in the literature, and a heuristic that combines this scheme with to a second-order cone programming algorithm. Our heuristic is able to compute tight bounds for the problem. The computational results, carried out on benchmark instances, confirm the improvements of the bounds computed with respect to the other algorithms proposed in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Andersen, E.D., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Program. 95(2), 249–277 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Behdani, B., Smith, J.C.: An integer-programming-based approach to the close-enough traveling salesman problem. INFORMS J. Comput. 26(3), 415–432 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carrabs, F., Cerrone, C., Cerulli, R.: A memetic algorithm for the weighted feedback vertex set problem. Networks 64(4), 339–356 (2014)

    Article  MathSciNet  Google Scholar 

  4. Carrabs, F., Cerrone, C., Cerulli, R.: A tabu search approach for the circle packing problem. In: 2014 17th International Conference on Network-Based Information Systems, pp. 165–171. IEEE (2014)

    Google Scholar 

  5. Carrabs, F., Cerrone, C., Cerulli, R., Gaudioso, M.: A novel discretization scheme for the close enough traveling salesman problem. Comput. Oper. Res. 78, 163–171 (2017)

    Article  MathSciNet  Google Scholar 

  6. Carrabs, F., Cerulli, R., D’Ambrosio, C., Raiconi, A.: Extending lifetime through partial coverage and roles allocation in connectivity-constrained sensor networks. IFAC-PapersOnLine 49(12), 973–978 (2016)

    Article  MATH  Google Scholar 

  7. Carrabs, F., Cerulli, R., D’Ambrosio, C., Raiconi, A.: An exact algorithm to extend lifetime through roles allocation in sensor networks with connectivity constraints. Optimi. Lett., 1–16 (2016)

    Google Scholar 

  8. Cerrone, C., Cerulli, R., Gaudioso, M.: Omega one multi ethnic genetic approach. Optim. Lett. 10(2), 309–324 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cerrone, C., Cerulli, R., Gentili, M.: Vehicle-id sensor location for route flow recognition: models and algorithms. Eur. J. Oper. Res. 247(2), 618–629 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cerrone, C., Cerulli, R., Golden, B.: Carousel greedy: a generalized greedy algorithm with applications in optimization. University of Maryland (submitted for publication)

    Google Scholar 

  11. Coutinho, W.P., Do Nascimento, R.Q., Pessoa, A.A., Subramanian, A.: A branch-and-bound algorithm for the close-enough traveling salesman problem. INFORMS J. Comput. 28(4), 752–765 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dong, J., Yang, N., Chen, M.: Heuristic approaches for a TSP variant: the automatic meter reading shortest tour problem. Oper. Res./Comput. Sci. Interf. Ser. 37, 145–163 (2007)

    MATH  Google Scholar 

  13. Fischetti, M., Salazar-Gonzalez, J., Toth, P.: The generalized traveling salesman and orienteering problems. In: Gutin, G., Punnen, A.P. (eds.) The Traveling Salesman Problem and Its Variations. Combinatorial Optimization, vol. 12, pp. 609–662. Springer, New York (2007)

    Google Scholar 

  14. Gulczynski, D., Heath, J., Price, C.: Close enough traveling salesman problem: a discussion of several heuristics. In: Alt, F.B., Fu, M.C., Golden, B.L. (eds.) Perspectives in Operations Research. Operations Research/Computer Science Interfaces Series, vol. 36, pp. 271–283. Springer, New York (2006)

    Google Scholar 

  15. Mennell, W.K.: Heuristics for solving three routing problems: close-enough traveling salesman problem, close-enough vehicle routing problem, sequence-dependent team orienteering problem. PhD thesis, The Robert H. Smith School of Business, University of Maryland, College Park (2009)

    Google Scholar 

  16. Mennell, W.K., Golden, B., Wasil, E.: A steiner-zone heuristic for solving the close-enough traveling salesman problem. In: 2nd INFORMS Computing Society Conference: Operations Research, Computing, and Homeland Defense (2011)

    Google Scholar 

  17. Yuan, B., Orlowska, M., Sadiq, S.: On the optimal robot routing problem in wireless sensor networks. IEEE Trans. Knowl. Data Eng. 19(9), 1252–1261 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Italy

    Francesco Carrabs, Raffaele Cerulli & Ciriaco D’Ambrosio

  2. Department of Biosciences and Territory, University of Molise, Campobasso, Italy

    Carmine Cerrone

Authors
  1. Francesco Carrabs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carmine Cerrone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raffaele Cerulli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ciriaco D’Ambrosio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carmine Cerrone .

Editor information

Editors and Affiliations

  1. Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Man Ho Allen Au

  2. University of Salerno, Fisciano, Italy

    Arcangelo Castiglione

  3. University of Texas at San Antonio, San Antonio, Texas, USA

    Kim-Kwang Raymond Choo

  4. University of Salerno, Fisciano, Italy

    Francesco Palmieri

  5. Providence University, Taichung City, Taiwan

    Kuan-Ching Li

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Carrabs, F., Cerrone, C., Cerulli, R., D’Ambrosio, C. (2017). Improved Upper and Lower Bounds for the Close Enough Traveling Salesman Problem. In: Au, M., Castiglione, A., Choo, KK., Palmieri, F., Li, KC. (eds) Green, Pervasive, and Cloud Computing. GPC 2017. Lecture Notes in Computer Science(), vol 10232. Springer, Cham. https://doi.org/10.1007/978-3-319-57186-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57186-7_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57185-0

  • Online ISBN: 978-3-319-57186-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation