Document Open Access Logo

Exact Methods for the Travelling Salesperson Problem with Self-Deleting Graphs

Authors Daniel Pekar , J. Christopher Beck

PDF HTML 5

Files

Thumbnail PDF
PDF
LIPIcs.CP.2025.30.pdf
  • Filesize: 0.9 MB
  • 19 pages
HTML5 Logo HTML (experimental)
LIPIcs.CP.2025.30.html

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Decision Diagrams & Dynamic Programming
  • Operations Research & Mathematical Optimization
  • Modelling & Modelling Languages

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Finding the minimal-cost closed loop on a weighted graph where every vertex is visited exactly once is known as the Travelling Salesperson Problem (TSP). In a recently proposed variant, TSP with Self-Deleting graphs (TSP-SD), visiting a vertex i deletes a set of edges in the graph, preventing their subsequent traversal. Due to the dependency between vertex visits and edge deletion, in TSP-SD the feasibility of a cycle depends on the start node. The best performing solution approaches in the literature rely on a simple problem reformulation to find a backward tour where vertex visits add edges rather than delete them. This paper investigates exact model-based approaches, specifically Constraint Programming (CP), Domain-Independent Dynamic Programming (DIDP), and Mixed Integer Linear Programming (MIP) to solve TSP-SD. We show that simple preprocessing can substantially reduce the options for start/end vertex pairs but typically has a limited positive impact on search performance. Our numerical results demonstrate that the difference between the deletion and addition variants is small for CP and MIP but that the reformulation is critical for DIDP performance. Overall, the DIDP addition model is the best of the exact methods on all test instances and outperforms existing heuristic solvers for small and medium-sized instances while trailing in terms of solution quality on larger instances.

Cite As Get BibTex

Daniel Pekar and J. Christopher Beck. Exact Methods for the Travelling Salesperson Problem with Self-Deleting Graphs. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CP.2025.30

Author Details

Daniel Pekar
  • Department of Mechanical and Industrial Engineering, University of Toronto, Canada
J. Christopher Beck
  • Department of Mechanical and Industrial Engineering, University of Toronto, Canada

Funding

This work was supported the Natural Sciences and Engineering Research Council of Canada.

Acknowledgements

Computations were performed on the Niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by ISED Canada; the Digital Research Alliance of Canada; Ontario Research Fund:RE; and the University of Toronto.

Supplementary Materials

References

  1. Matan Atsmony, Baruch Mor, and Gur Mosheiov. Single machine scheduling with step-learning. Journal of Scheduling, 27(3):227-237, June 2024. URL: https://doi.org/10.1007/s10951-022-00763-5.
  2. S. Carmesin, D. Woller, D. Parker, M. Kulich, and M. Mansouri. The Hamiltonian Cycle and Travelling Salesperson problems with traversal-dependent edge deletion. Journal of Computational Science, 74:102156, 2023. URL: https://doi.org/10.1016/j.jocs.2023.102156.
  3. Erik Diessel and Heiner Ackermann. Domino sequencing: Scheduling with state-based sequence-dependent setup times. Operations Research Letters, 47(4):274-280, July 2019. URL: https://doi.org/10.1016/j.orl.2019.04.004.
  4. Y. Dumas, J. Desrosiers, E. Gelinas, and M.M. Solomon. An optimal algorithm for the traveling salesman problem with time windows. Operations Research, 43(2):367-371, 1995. URL: https://doi.org/10.1287/OPRE.43.2.367.
  5. T.A. Feo and M.G.C. Resende. A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8(2):67-71, 1989. URL: https://doi.org/10.1016/0167-6377(89)90002-3.
  6. F. Focacci, A. Lodi, and M. Milano. A hybrid exact algorithm for the tsptw. INFORMS Journal on Computing, 14(4):403, fall 2002. Google Scholar
  7. A.R. Güner, A. Murat, and R.B. Chinnam. Dynamic routing for milk-run tours with time windows in stochastic time-dependent networks. Transportation Research Part E: Logistics and Transportation Review, 97:251-267, 2017. URL: https://doi.org/10.1016/j.tre.2016.10.014.
  8. Christoph Hansknecht, Imke Joormann, and Sebastian Stiller. Dynamic Shortest Paths Methods for the Time-Dependent TSP. Algorithms, 14(1):21, January 2021. URL: https://doi.org/10.3390/a14010021.
  9. Jahangirnagar University, E. Islam, M. Sultana, and F. Ahmed. A Tale of Revolution: Discovery and Development of TSP. International Journal of Mathematics Trends and Technology, 57(2):136-139, May 2018. URL: https://doi.org/10.14445/22315373/IJMTT-V57P520.
  10. W.-K. Ku and J. C. Beck. Revisiting off-the-shelf mixed integer programming and constraint programming models for job shop scheduling. Computers & Operations Research, 73:165-173, 2016. Google Scholar
  11. M. Kulich, D. Woller, S. Carmesin, M. Mansouri, and L. Přeučil. Where to place a pile? In 2023 European Conference on Mobile Robots (ECMR), pages 1-7, 2023. URL: https://doi.org/10.1109/ECMR59166.2023.10256330.
  12. R. Kuroiwa. Domain-Independent Dynamic Programming. PhD thesis, University of Toronto, 2024. Google Scholar
  13. R. Kuroiwa and J.C. Beck. Domain-independent dynamic programming: Generic state space search for combinatorial optimization. In Proceedings of the Thirty-Third International Conference on Automated Planning and Scheduling (ICAPS2023), pages 245-253, 2023. Google Scholar
  14. Raphael Kühn, Christian Weiß, Heiner Ackermann, and Sandy Heydrich. Scheduling a single machine with multiple due dates per job. Journal of Scheduling, 27(6):565-585, December 2024. URL: https://doi.org/10.1007/s10951-024-00825-w.
  15. N. Lipovetzky, C. Burt, A. Pearce, and P. Stuckey. Planning for mining operations with time and resource constraints. Proceedings of the International Conference on Automated Planning and Scheduling, 24(1):404-412, May 2014. URL: https://doi.org/10.1609/icaps.v24i1.13666.
  16. Yiqing L. Luo and J. C. Beck. Packing by scheduling: Using constraint programming to solve a complex 2d cutting stock problem. In Pierre Schaus, editor, Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pages 249-265, Cham, 2022. Springer International Publishing. Google Scholar
  17. J.J. Miranda-Bront, I. Méndez-Díaz, and P. Zabala. An integer programming approach for the time-dependent tsp. Electronic Notes in Discrete Mathematics, 36:351-358, 2010. ISCO 2010 - International Symposium on Combinatorial Optimization. URL: https://doi.org/10.1016/j.endm.2010.05.045.
  18. Daniel Pekar and J. Christopher Beck. Travelling Salesperson Problem with Self Deleting Graphs. Software, swhId: https://archive.softwareheritage.org/swh:1:dir:c287b1067c276693ca630e6e6f7a18daf1a90d38;origin=https://github.com/uoft-tidel/tsp-sd;visit=swh:1:snp:80da2bba26c2bc64c9fbc04ae205e4b98c1a9a3b;anchor=swh:1:rev:7b6bd841d633ecb2ccbb9b7e4022639fe258ae30 (visited on 2025-07-28). URL: https://github.com/uoft-tidel/tsp-sd, URL: https://doi.org/10.4230/artifacts.23555.
  19. J.-C. Picard and M. Queyranne. The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Research, 26(1):86-110, 1978. URL: https://doi.org/10.1287/OPRE.26.1.86.
  20. G. Reinelt. Tsplib—a traveling salesman problem library. ORSA Journal on Computing, 3(4):376-384, 1991. URL: https://doi.org/10.1287/ijoc.3.4.376.
  21. D. Woller. URL: https://imr.ciirc.cvut.cz/Research/TSPSD.
  22. D. Woller, M. Mansouri, and M. Kulich. Making a complete mess and getting away with it: Traveling salesperson problems with circle placement variants. IEEE Robotics and Automation Letters, 9(10):8555-8562, 2024. URL: https://doi.org/10.1109/LRA.2024.3445817.
  23. J. Zhang and J.C. Beck. Domain-independent dynamic programming and constraint programming approaches for assembly line balancing problems with setups. INFORMS Journal on Computing, 2024. in press, published onlinne October 2024. URL: https://doi.org/10.1287/ijoc.2024.0603.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact