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Subproblem Separation in Logic-Based Benders' Decomposition for the Vehicle Routing Problem with Local Congestion

Authors Aigerim Saken , Stephen J. Maher



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Author Details

Aigerim Saken
  • Department of Mathematics, University of Exeter, United Kingdom
Stephen J. Maher
  • Quantagonia GmbH, Bad Homburg, Germany

Acknowledgements

Computational experiments were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) and National Academic Infrastructure for Supercomputing in Sweden (NAISS).

Cite AsGet BibTex

Aigerim Saken and Stephen J. Maher. Subproblem Separation in Logic-Based Benders' Decomposition for the Vehicle Routing Problem with Local Congestion. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 16:1-16:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/OASIcs.ATMOS.2023.16

Abstract

Subproblem separation is a common strategy for the acceleration of the logic-based Benders' decomposition (LBBD). However, it has only been applied to problems with an inherently separable subproblem structure. This paper proposes a new method to separate the subproblem using the connected components algorithm. The subproblem separation is applied to the vehicle routing problem with local congestion (VRPLC). Accordingly, new Benders' cuts are derived for the new subproblem formulation. The computational experiments evaluate the effectiveness of subproblem separation for different methods applying new cuts. It is shown that subproblem separation significantly benefits the LBBD scheme.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
  • Applied computing → Transportation
Keywords
  • logic-based Benders' decomposition
  • vehicle routing
  • subproblem separation
  • connected components

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References

  1. Florian Arnold, Michel Gendreau, and Kenneth Sörensen. Efficiently solving very large-scale routing problems. Computers & Operations Research, 107:32-42, 2019. Google Scholar
  2. Elvin Coban and John N Hooker. Single-facility scheduling by logic-based benders decomposition. Annals of Operations Research, 210:245-272, 2013. Google Scholar
  3. Simon Emde, Lukas Polten, and Michel Gendreau. Logic-based benders decomposition for scheduling a batching machine. Computers & Operations Research, 113:104777, 2020. Google Scholar
  4. John N Hooker. Logic-Based Benders Decomposition, chapter 19, pages 389-422. John Wiley & Sons, Ltd, 2000. Google Scholar
  5. John N Hooker. Planning and scheduling by logic-based benders decomposition. Operations research, 55(3):588-602, 2007. Google Scholar
  6. John N Hooker. Logic-Based Benders Decomposition for Large-Scale Optimization. Large Scale Optimization in Supply Chains and Smart Manufacturing: Theory and Applications, pages 1-26, 2019. Google Scholar
  7. John N Hooker and Greger Ottosson. Logic-based Benders decomposition. Mathematical Programming, 96(1):33-60, 2003. Google Scholar
  8. Emil Karlsson and Elina Rönnberg. Strengthening of Feasibility Cuts in Logic-Based Benders Decomposition. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 18th International Conference, CPAIOR 2021, Vienna, Austria, July 5-8, 2021, Proceedings 18, pages 45-61. Springer, 2021. Google Scholar
  9. Emil Karlsson and Elina Rönnberg. Logic-based Benders decomposition with a partial assignment acceleration technique for avionics scheduling. Computers & Operations Research, 146:105916, 2022. Google Scholar
  10. Edward Lam, Graeme Gange, Peter J Stuckey, Pascal Van Hentenryck, and Jip J Dekker. Nutmeg: a MIP and CP Hybrid Solver Using Branch-and-Check. SN Operations Research Forum, 1:1-27, 2020. Google Scholar
  11. Edward Lam, Panos M. Pardalos, and Pascal Van Hentenryck. A branch-and-price-and-check model for the vehicle routing problem with location congestion. Constraints, 21:394-412, 2016. Google Scholar
  12. Michele Lombardi and Michela Milano. Optimal methods for resource allocation and scheduling: a cross-disciplinary survey. Constraints, 17:51-85, 2012. Google Scholar
  13. Diego Pecin, Artur Pessoa, Marcus Poggi, and Eduardo Uchoa. Improved branch-cut-and-price for capacitated vehicle routing. Mathematical Programming Computation, 9:61-100, 2017. Google Scholar
  14. Günther R Raidl, Thomas Baumhauer, and Bin Hu. Speeding up Logic-Based Benders’ Decomposition by a Metaheuristic for a Bi-Level Capacitated Vehicle Routing Problem. In International Workshop on Hybrid Metaheuristics, pages 183-197. Springer, 2014. Google Scholar
  15. Günther R Raidl, Thomas Baumhauer, and Bin Hu. Boosting an Exact Logic-Based Benders Decomposition Approach by Variable Neighborhood Search. Electronic Notes in Discrete Mathematics, 47:149-156, 2015. Google Scholar
  16. Ted K. Ralphs, Leonid Kopman, William R. Pulleyblank, and Leslie E. Trotter. On the capacitated vehicle routing problem. Mathematical Programming, 94:343-359, 2003. Google Scholar
  17. Sarmad Riazi, Carla Seatzu, Oskar Wigström, and Bengt Lennartson. Benders/gossip methods for heterogeneous multi-vehicle routing problems. In 2013 IEEE 18th Conference on Emerging Technologies & Factory Automation (ETFA), pages 1-6. IEEE, 2013. Google Scholar
  18. Aigerim Saken, Emil Karlsson, Stephen J. Maher, and Elina Rönnberg. Computational Evaluation of Cut-Strengthening Techniques in Logic-Based Benders’ Decomposition. SN Operations Research Forum, 4:62, 2023. Google Scholar
  19. Defeng Sun, Lixin Tang, and Roberto Baldacci. A Benders decomposition-based framework for solving quay crane scheduling problems. European Journal of Operational Research, 273(2):504-515, 2019. Google Scholar
  20. Eduardo Uchoa, Diego Pecin, Artur Pessoa, Marcus Poggi, Thibaut Vidal, and Anand Subramanian. New benchmark instances for the Capacitated Vehicle Routing Problem. European Journal of Operational Research, 257(3):845-858, 2017. Google Scholar
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