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Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem

Author

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  • Giorgio Carpaneto

    (University of Bologna, Italy)

  • Paolo Toth

    (University of Bologna, Italy)

Abstract

Many algorithms have been developed for the optimal solution of the asymmetric travelling salesman problem: the most efficient ones are based on the subtour elimination approach. This paper presents a breadth-first branch and bound algorithm which differs from the method of Smith, Srinivasan and Thompson in the selection of the subtour to be split, in the ordering of the arcs in the selected subtour, in the computation of different partial lower bounds and in different data structures to facilitate the updating of the cost matrix. Extensive computational results considering random problems with up to 240 vertices are presented for various ranges of the coefficients of the cost matrix.

Suggested Citation

  • Giorgio Carpaneto & Paolo Toth, 1980. "Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem," Management Science, INFORMS, vol. 26(7), pages 736-743, July.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:7:p:736-743
    DOI: 10.1287/mnsc.26.7.736
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    Cited by:

    1. Moon, Chiung & Kim, Jongsoo & Choi, Gyunghyun & Seo, Yoonho, 2002. "An efficient genetic algorithm for the traveling salesman problem with precedence constraints," European Journal of Operational Research, Elsevier, vol. 140(3), pages 606-617, August.
    2. Bagchi, Tapan P. & Gupta, Jatinder N.D. & Sriskandarajah, Chelliah, 2006. "A review of TSP based approaches for flowshop scheduling," European Journal of Operational Research, Elsevier, vol. 169(3), pages 816-854, March.
    3. Gharehgozli, Amir Hossein & Yu, Yugang & de Koster, René & Udding, Jan Tijmen, 2014. "An exact method for scheduling a yard crane," European Journal of Operational Research, Elsevier, vol. 235(2), pages 431-447.
    4. Sakakibara, Katsuaki, 1998. "New edges not used in shortest tours of TSP," European Journal of Operational Research, Elsevier, vol. 104(1), pages 129-138, January.
    5. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    6. Rosemary T. Berger & Collette R. Coullard & Mark S. Daskin, 2007. "Location-Routing Problems with Distance Constraints," Transportation Science, INFORMS, vol. 41(1), pages 29-43, February.
    7. Lysgaard, Jens, 1999. "Cluster based branching for the asymmetric traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 119(2), pages 314-325, December.
    8. Gharehgozli, Amir & Zaerpour, Nima, 2020. "Robot scheduling for pod retrieval in a robotic mobile fulfillment system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    9. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    10. Belhoul, Lyes, 2014. "Résolution de problèmes d'optimisation combinatoire mono et multi-objectifs par énumération ordonnée," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14672 edited by Vanderpooten, Daniel.
    11. Turkensteen, Marcel & Ghosh, Diptesh & Goldengorin, Boris & Sierksma, Gerard, 2008. "Tolerance-based Branch and Bound algorithms for the ATSP," European Journal of Operational Research, Elsevier, vol. 189(3), pages 775-788, September.
    12. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    13. Sundararajan Arunapuram & Kamlesh Mathur & Daniel Solow, 2003. "Vehicle Routing and Scheduling with Full Truckloads," Transportation Science, INFORMS, vol. 37(2), pages 170-182, May.
    14. G Laporte, 2010. "A concise guide to the Traveling Salesman Problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 35-40, January.
    15. Nicholas G. Hall & Gilbert Laporte & Esaignani Selvarajah & Chelliah Sriskandarajah, 2005. "Scheduling and lot streaming in two‐machine open shops with no‐wait in process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 261-275, April.
    16. Jamal Ouenniche & Prasanna K. Ramaswamy & Michel Gendreau, 2017. "A dual local search framework for combinatorial optimization problems with TSP application," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1377-1398, November.

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