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Parallel Branch-and-Branch Algorithms: Survey and Synthesis

Author

Listed:
  • Bernard Gendron

    (University of Montreal, Montreal, Quebec, Canada)

  • Teodor Gabriel Crainic

    (DSA, University of Quebec at Montreal and CRT, University of Montreal, Montreal, Quebec, Canada)

Abstract

We present a detailed and up-to-date survey of the literature on parallel branch-and-bound algorithms. We synthesize previous work in this area and propose a new classification of parallel branch-and-bound algorithms. This classification is used to analyze the methods proposed in the literature. To facilitate our analysis, we give a new characterization of branch-and-bound algorithms, which consists of isolating the performed operations without specifying any particular order for their execution.

Suggested Citation

  • Bernard Gendron & Teodor Gabriel Crainic, 1994. "Parallel Branch-and-Branch Algorithms: Survey and Synthesis," Operations Research, INFORMS, vol. 42(6), pages 1042-1066, December.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:6:p:1042-1066
    DOI: 10.1287/opre.42.6.1042
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    Citations

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    Cited by:

    1. Juan F. R. Herrera & José M. G. Salmerón & Eligius M. T. Hendrix & Rafael Asenjo & Leocadio G. Casado, 2017. "On parallel Branch and Bound frameworks for Global Optimization," Journal of Global Optimization, Springer, vol. 69(3), pages 547-560, November.
    2. Le‐Yu Chen & Sokbae Lee, 2018. "Exact computation of GMM estimators for instrumental variable quantile regression models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 553-567, June.
    3. Guido Schryen & Natalia Kliewer & Andreas Fink, 2018. "Call for Papers Issue 1/2020," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 60(5), pages 439-440, October.
    4. 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.
    5. Julius Žilinskas, 2012. "Parallel branch and bound for multidimensional scaling with city-block distances," Journal of Global Optimization, Springer, vol. 54(2), pages 261-274, October.
    6. Guido Schryen & Natalia Kliewer & Andreas Fink, 2020. "High Performance Business Computing," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 62(1), pages 1-3, February.
    7. D. Espinoza & R. Garcia & M. Goycoolea & G. L. Nemhauser & M. W. P. Savelsbergh, 2008. "Per-Seat, On-Demand Air Transportation Part II: Parallel Local Search," Transportation Science, INFORMS, vol. 42(3), pages 279-291, August.
    8. Crainic, Teodor Gabriel, 2000. "Service network design in freight transportation," European Journal of Operational Research, Elsevier, vol. 122(2), pages 272-288, April.
    9. Eva K. Lee, 2004. "Generating Cutting Planes for Mixed Integer Programming Problems in a Parallel Computing Environment," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 3-26, February.
    10. Mhand Hifi & Toufik Saadi, 2012. "A parallel algorithm for two-staged two-dimensional fixed-orientation cutting problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 783-807, March.
    11. Lahrichi, Nadia & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter & Crişan, Gloria Cerasela & Vidal, Thibaut, 2015. "An integrative cooperative search framework for multi-decision-attribute combinatorial optimization: Application to the MDPVRP," European Journal of Operational Research, Elsevier, vol. 246(2), pages 400-412.
    12. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    13. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    14. Jan Gmys, 2022. "Exactly Solving Hard Permutation Flowshop Scheduling Problems on Peta-Scale GPU-Accelerated Supercomputers," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2502-2522, September.
    15. Michael R. Bussieck & Michael C. Ferris & Alexander Meeraus, 2009. "Grid-Enabled Optimization with GAMS," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 349-362, August.
    16. Schryen, Guido, 2020. "Parallel computational optimization in operations research: A new integrative framework, literature review and research directions," European Journal of Operational Research, Elsevier, vol. 287(1), pages 1-18.
    17. Charlotte Truchet & Alejandro Arbelaez & Florian Richoux & Philippe Codognet, 2016. "Estimating parallel runtimes for randomized algorithms in constraint solving," Journal of Heuristics, Springer, vol. 22(4), pages 613-648, August.
    18. Stripinis, Linas & Žilinskas, Julius & Casado, Leocadio G. & Paulavičius, Remigijus, 2021. "On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization," Applied Mathematics and Computation, Elsevier, vol. 390(C).

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