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Branch-and-Bound Strategies for Dynamic Programming

Author

Listed:
  • Thomas L. Morin

    (Purdue University, West Lafayette, Indiana)

  • Roy E. Marsten

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

This paper shows how branch-and-bound methods can be used to reduce storage and, possibly, computational requirements in discrete dynamic programs. Relaxations and fathoming criteria are used to identify and to eliminate states whose corresponding subpolicies could not lead to optimal policies. The general dynamic programming/branch-and-bound approach is applied to the traveling-salesman problem and the nonlinear knapsack problem. Our computational experience demonstrates that the hybrid approach yields dramatic savings in both computer storage and computational requirements.

Suggested Citation

  • Thomas L. Morin & Roy E. Marsten, 1976. "Branch-and-Bound Strategies for Dynamic Programming," Operations Research, INFORMS, vol. 24(4), pages 611-627, August.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:611-627
    DOI: 10.1287/opre.24.4.611
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    Cited by:

    1. Boysen, Nils & Bock, Stefan, 2011. "Scheduling just-in-time part supply for mixed-model assembly lines," European Journal of Operational Research, Elsevier, vol. 211(1), pages 15-25, May.
    2. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    3. Isada, Yuriko & James, Ross J. W. & Nakagawa, Yuji, 2005. "An approach for solving nonlinear multi-objective separable discrete optimization problem with one constraint," European Journal of Operational Research, Elsevier, vol. 162(2), pages 503-513, April.
    4. Yavuz, Mesut & Tufekci, Suleyman, 2006. "A bounded dynamic programming solution to the batching problem in mixed-model just-in-time manufacturing systems," International Journal of Production Economics, Elsevier, vol. 103(2), pages 841-862, October.
    5. Gio Kao & Edward Sewell & Sheldon Jacobson & Shane Hall, 2012. "New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1253-1274, April.
    6. 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.
    7. 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.
    8. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.
    9. Bautista, J. & Companys, R. & Corominas, A., 1996. "Heuristics and exact algorithms for solving the Monden problem," European Journal of Operational Research, Elsevier, vol. 88(1), pages 101-113, January.
    10. Lubbecke, Marco E., 2005. "Dual variable based fathoming in dynamic programs for column generation," European Journal of Operational Research, Elsevier, vol. 162(1), pages 122-125, April.
    11. Robert L. Carraway & Robert L. Schmidt & Lawrence R. Weatherford, 1993. "An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 161-173, March.
    12. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    13. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    14. Nagar, Amit & Haddock, Jorge & Heragu, Sunderesh, 1995. "Multiple and bicriteria scheduling: A literature survey," European Journal of Operational Research, Elsevier, vol. 81(1), pages 88-104, February.

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