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PEBBL: an object-oriented framework for scalable parallel branch and bound

Abstract

Parallel Enumeration and Branch-and-Bound Library (PEBBL) is a C++ class library implementing the underlying operations needed to support a wide variety of branch-and-bound algorithms on MPI-based message-passing distributed-memory parallel computing environments. PEBBL can be customized to support application-specific operations, while managing the generic aspects of branch and bound, such as maintaining the active subproblem pool across multiple processors, load balancing, and termination detection. PEBBL is designed to provide highly scalable performance on large numbers of processor cores. We describe the basics of PEBBL’s architecture, with emphasis on the features most critical to is high scalability, including its flexible two-level load balancing architecture and its support for a synchronously parallel ramp-up phase. We also present an example application: the maximum monomial agreement problem arising from certain machine learning applications. For sufficiently difficult problem instances, we show essentially linear speedup on over 6000 processor cores, demonstrating a new state of the art in scalability for branch-and-bound implementations. We also show how processor cache effects can lead to reproducibly superlinear speedups.

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Acknowledgments

We thank Noam Goldberg for contributing the code to solve the MMA problem in serial using PEBBL. We also thank John Siirola for his stewardship of PEBBL within the ACRO framework. Jonathan Eckstein’s work on PEBBL was supported in part by NSF grant CCR-9902092. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Correspondence to Jonathan Eckstein.

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This work was performed in part at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94-AL85000. This work was also supported in part by National Science Foundation Grant CCR-9902092.

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Eckstein, J., Hart, W.E. & Phillips, C.A. PEBBL: an object-oriented framework for scalable parallel branch and bound. Math. Prog. Comp. 7, 429–469 (2015). https://doi.org/10.1007/s12532-015-0087-1

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  • DOI: https://doi.org/10.1007/s12532-015-0087-1

Keywords

  • Branch and bound
  • Parallel computation

Mathematics Subject Classification

  • 90C57
  • 65Y05