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Results for the close-enough traveling salesman problem with a branch-and-bound algorithm

Author

Listed:
  • Wenda Zhang

    (University of Illinois at Urbana-Champaign)

  • Jason J. Sauppe

    (University of Wisconsin-La Crosse)

  • Sheldon H. Jacobson

    (University of Illinois at Urbana-Champaign)

Abstract

The Close-Enough Traveling Salesman Problem is a generalization of the Traveling Salesman Problem that requires a salesman to just get close enough to each customer instead of visiting the exact location of each customer. In this paper, we propose improvements to an existing branch-and-bound (B &B) algorithm for this problem that finds and proves optimality of solutions by examining partial sequences. The proposed improvements include a new search strategy, a simplified branching vertex selection scheme, a method to avoid unnecessary computation, a method to improve the quality of feasible solutions, and a method to reduce the space requirement of the algorithm. Numerical experiments show that the improved B &B algorithm proves optimality faster on some instances, finds good feasible solutions faster than the best known existing algorithm on instances that cannot be solved to optimality, and uses less space during the solving process.

Suggested Citation

  • Wenda Zhang & Jason J. Sauppe & Sheldon H. Jacobson, 2023. "Results for the close-enough traveling salesman problem with a branch-and-bound algorithm," Computational Optimization and Applications, Springer, vol. 85(2), pages 369-407, June.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:2:d:10.1007_s10589-023-00474-3
    DOI: 10.1007/s10589-023-00474-3
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    References listed on IDEAS

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    1. E. C. Sewell & S. H. Jacobson, 2012. "A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 433-442, August.
    2. Behnam Behdani & J. Cole Smith, 2014. "An Integer-Programming-Based Approach to the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 415-432, August.
    3. Walton Pereira Coutinho & Roberto Quirino do Nascimento & Artur Alves Pessoa & Anand Subramanian, 2016. "A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 752-765, November.
    4. Yang, Zhao & Xiao, Ming-Qing & Ge, Ya-Wei & Feng, De-Long & Zhang, Lei & Song, Hai-Fang & Tang, Xi-Lang, 2018. "A double-loop hybrid algorithm for the traveling salesman problem with arbitrary neighbourhoods," European Journal of Operational Research, Elsevier, vol. 265(1), pages 65-80.
    5. Francesco Carrabs & Carmine Cerrone & Raffaele Cerulli & Bruce Golden, 2020. "An Adaptive Heuristic Approach to Compute Upper and Lower Bounds for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1030-1048, October.
    6. Morrison, David R. & Sewell, Edward C. & Jacobson, Sheldon H., 2014. "An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset," European Journal of Operational Research, Elsevier, vol. 236(2), pages 403-409.
    7. David R. Morrison & Jason J. Sauppe & Wenda Zhang & Sheldon H. Jacobson & Edward C. Sewell, 2017. "Cyclic best first search: Using contours to guide branch‐and‐bound algorithms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 64-82, February.
    8. Edward Sewell & Jason Sauppe & David Morrison & Sheldon Jacobson & Gio Kao, 2012. "A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times," Journal of Global Optimization, Springer, vol. 54(4), pages 791-812, December.
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