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Efficient GPU-based implementations of simplex type algorithms

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  • Ploskas, Nikolaos
  • Samaras, Nikolaos

Abstract

Recent hardware advances have made it possible to solve large scale Linear Programming problems in a short amount of time. Graphical Processing Units (GPUs) have gained a lot of popularity and have been applied to linear programming algorithms. In this paper, we propose two efficient GPU-based implementations of the Revised Simplex Algorithm and a Primal–Dual Exterior Point Simplex Algorithm. Both parallel algorithms have been implemented in MATLAB using MATLAB’s Parallel Computing Toolbox. Computational results on randomly generated optimal sparse and dense linear programming problems and on a set of benchmark problems (netlib, kennington, Mészáros) are also presented. The results show that the proposed GPU implementations outperform MATLAB’s interior point method.

Suggested Citation

  • Ploskas, Nikolaos & Samaras, Nikolaos, 2015. "Efficient GPU-based implementations of simplex type algorithms," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 552-570.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:552-570
    DOI: 10.1016/j.amc.2014.10.096
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    References listed on IDEAS

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    1. J. Hall, 2010. "Towards a practical parallelisation of the simplex method," Computational Management Science, Springer, vol. 7(2), pages 139-170, April.
    2. Paparrizos, Konstantinos & Samaras, Nikolaos & Stephanides, George, 2003. "An efficient simplex type algorithm for sparse and dense linear programs," European Journal of Operational Research, Elsevier, vol. 148(2), pages 323-334, July.
    3. Jonathan Eckstein & İ. İlkay Boduroğlu & Lazaros C. Polymenakos & Donald Goldfarb, 1995. "Data-Parallel Implementations of Dense Simplex Methods on the Connection Machine CM-2," INFORMS Journal on Computing, INFORMS, vol. 7(4), pages 402-416, November.
    4. Robert E. Bixby & Alexander Martin, 2000. "Parallelizing the Dual Simplex Method," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 45-56, February.
    5. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    6. J. Hall & K. McKinnon, 1998. "ASYNPLEX, an asynchronous parallelrevised simplex algorithm," Annals of Operations Research, Springer, vol. 81(0), pages 27-50, June.
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    Cited by:

    1. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    2. Hua, Hao & Hovestadt, Ludger & Tang, Peng & Li, Biao, 2019. "Integer programming for urban design," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1125-1137.

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