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On parallel Branch and Bound frameworks for Global Optimization

Author

Listed:
  • Juan F. R. Herrera

    (The University of Edinburgh)

  • José M. G. Salmerón

    (University of Almeria (ceiA3))

  • Eligius M. T. Hendrix

    (Universidad de Málaga
    Wageningen University)

  • Rafael Asenjo

    (Universidad de Málaga)

  • Leocadio G. Casado

    (University of Almeria (ceiA3))

Abstract

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:3:d:10.1007_s10898-017-0508-y
    DOI: 10.1007/s10898-017-0508-y
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    References listed on IDEAS

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    1. Bernard Gendron & Teodor Gabriel Crainic, 1994. "Parallel Branch-and-Branch Algorithms: Survey and Synthesis," Operations Research, INFORMS, vol. 42(6), pages 1042-1066, December.
    2. Eligius M.T. Hendrix & Boglárka G.-Tóth, 2010. "Introduction to Nonlinear and Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-88670-1, June.
    3. A. Brüngger & A. Marzetta & K. Fukuda & J. Nievergelt, 1999. "The parallel search bench ZRAM and its applications," Annals of Operations Research, Springer, vol. 90(0), pages 45-63, January.
    4. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, 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.
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    Cited by:

    1. 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).
    2. 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.

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