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Branch-and-Bound Methods: General Formulation and Properties

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  • L. G. Mitten

    (University of British Columbia, Vancouver, Canada)

Abstract

The branch-and-bound procedure is formulated in rather general terms and necessary conditions for the branching and bounding functions are precisely specified. Results include the standard properties for finite procedures, plus several convergence conditions for infinite procedures. Discrete programming which includes integer programming and combinatorial optimization problems, is discussed and Fibonacci search is presented as an example of a nonfinite branch-and-bound procedure employing an optimal convergence rule.

Suggested Citation

  • L. G. Mitten, 1970. "Branch-and-Bound Methods: General Formulation and Properties," Operations Research, INFORMS, vol. 18(1), pages 24-34, February.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:1:p:24-34
    DOI: 10.1287/opre.18.1.24
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    Cited by:

    1. Jiancheng Long & Wai Yuen Szeto, 2019. "Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks," Operations Research, INFORMS, vol. 67(1), pages 167-182, January.
    2. Thomas L. Morin & Roy E. Marsten, 1974. "Brand-and-Bound Strategies for Dynamic Programming," Discussion Papers 106, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Serdar Kadıoğlu, 2019. "Core group placement: allocation and provisioning of heterogeneous resources," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 243-264, September.
    4. Liberto, Giovanni Di & Kadioglu, Serdar & Leo, Kevin & Malitsky, Yuri, 2016. "DASH: Dynamic Approach for Switching Heuristics," European Journal of Operational Research, Elsevier, vol. 248(3), pages 943-953.
    5. M. A. Venkataramanan & Kathryn A. Wilson, 1991. "A branch‐and‐bound algorithm for flow‐path design of automated guided vehicle systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 431-445, June.
    6. Hendrix, Eligius M.T. & Casado, Leocadio G. & Garcí­a, Inmaculada, 2008. "The semi-continuous quadratic mixture design problem: Description and branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 191(3), pages 803-815, December.
    7. S S Chauhan & J-M Proth & A M Sarmiento & R Nagi, 2006. "Opportunistic supply chain formation from qualified partners for a new market demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(9), pages 1089-1099, September.
    8. Juan Herrera & Leocadio Casado & Eligius Hendrix & Inmaculada García, 2014. "Pareto optimality and robustness in bi-blending problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 254-273, April.
    9. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    10. Y. Xu & T. K. Ralphs & L. Ladányi & M. J. Saltzman, 2009. "Computational Experience with a Software Framework for Parallel Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 383-397, August.
    11. Jouglet, Antoine & Carlier, Jacques, 2011. "Dominance rules in combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 212(3), pages 433-444, August.
    12. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "A Recursive Approach To The Implementation Of Enumerative Methods," Econometric Institute Archives 272202, Erasmus University Rotterdam.
    13. Rafael Blanquero & Emilio Carrizosa, 2013. "Solving the median problem with continuous demand on a network," Computational Optimization and Applications, Springer, vol. 56(3), pages 723-734, December.
    14. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    15. Makowski, David & Hendrix, Eligius M. T. & van Ittersum, Martin K. & Rossing, Walter A. H., 2001. "Generation and presentation of nearly optimal solutions for mixed-integer linear programming, applied to a case in farming system design," European Journal of Operational Research, Elsevier, vol. 132(2), pages 425-438, July.
    16. Chauhan, Satyaveer S. & Frayret, Jean-Marc & LeBel, Luc, 2009. "Multi-commodity supply network planning in the forest supply chain," European Journal of Operational Research, Elsevier, vol. 196(2), pages 688-696, July.

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