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An Additive Bounding Procedure for Combinatorial Optimization Problems

Author

Listed:
  • Matteo Fischetti

    (University of Bologna, Bologna, Italy)

  • Paolo Toth

    (University of Bologna, Bologna, Italy)

Abstract

We know that the effectiveness of the branch-and-bound algorithms proposed for the solution of combinatorial optimization problems greatly depends on the tightness of the available bounds. In this paper, we consider optimization problems with a linear objective function. We propose an additive approach for computing lower bounds that yields an increasing sequence of values. An application to the traveling salesman problem with precedence constraints is presented to exemplify the technique.

Suggested Citation

  • Matteo Fischetti & Paolo Toth, 1989. "An Additive Bounding Procedure for Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 37(2), pages 319-328, April.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:2:p:319-328
    DOI: 10.1287/opre.37.2.319
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    Cited by:

    1. 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.
    2. Quadrifoglio, Luca & Dessouky, Maged M. & Ordonez, Fernando, 2008. "Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints," European Journal of Operational Research, Elsevier, vol. 185(2), pages 481-494, March.
    3. You, Jintao & Wang, Yuan & Xue, Zhaojie, 2023. "An exact algorithm for the multi-trip container drayage problem with truck platooning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    4. Koorush Ziarati & François Soumis & Jacques Desrosiers & Marius M. Solomon, 1999. "A Branch-First, Cut-Second Approach for Locomotive Assignment," Management Science, INFORMS, vol. 45(8), pages 1156-1168, August.
    5. Francesco Carrabs & Jean-François Cordeau & Gilbert Laporte, 2007. "Variable Neighborhood Search for the Pickup and Delivery Traveling Salesman Problem with LIFO Loading," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 618-632, November.
    6. Vigo, Daniele, 1996. "A heuristic algorithm for the asymmetric capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 89(1), pages 108-126, February.
    7. 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.
    8. Quan Lu & Maged Dessouky, 2004. "An Exact Algorithm for the Multiple Vehicle Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 38(4), pages 503-514, November.
    9. Cowling, Peter & Maffioli, Francesco, 1995. "A bound for the symmetric travelling salesman problem through matroid formulation," European Journal of Operational Research, Elsevier, vol. 83(2), pages 301-309, June.
    10. Klein, Robert & Scholl, Armin, 1999. "Computing lower bounds by destructive improvement: An application to resource-constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 112(2), pages 322-346, January.
    11. Roberto Baldacci & Paolo Toth & Daniele Vigo, 2010. "Exact algorithms for routing problems under vehicle capacity constraints," Annals of Operations Research, Springer, vol. 175(1), pages 213-245, March.
    12. Andrea Lodi & Michela Milano & Louis-Martin Rousseau, 2006. "Discrepancy-Based Additive Bounding Procedures," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 480-493, November.
    13. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    14. Yanik, Seda & Bozkaya, Burcin & deKervenoael, Ronan, 2014. "A new VRPPD model and a hybrid heuristic solution approach for e-tailing," European Journal of Operational Research, Elsevier, vol. 236(3), pages 879-890.
    15. Li, Yongquan & Lim, Andrew & Oon, Wee-Chong & Qin, Hu & Tu, Dejian, 2011. "The tree representation for the pickup and delivery traveling salesman problem with LIFO loading," European Journal of Operational Research, Elsevier, vol. 212(3), pages 482-496, August.
    16. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    17. A. Mingozzi & M. A. Boschetti & S. Ricciardelli & L. Bianco, 1999. "A Set Partitioning Approach to the Crew Scheduling Problem," Operations Research, INFORMS, vol. 47(6), pages 873-888, December.
    18. Roberto Baldacci & Vittorio Maniezzo & Aristide Mingozzi, 2004. "An Exact Method for the Car Pooling Problem Based on Lagrangean Column Generation," Operations Research, INFORMS, vol. 52(3), pages 422-439, June.
    19. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2020. "An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 263-278, April.
    20. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    21. Amin Hosseininasab & Willem-Jan van Hoeve, 2021. "Exact Multiple Sequence Alignment by Synchronized Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 721-738, May.

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