PARSMI, a parallel revised simplex algorithm incorporating minor iterations and Devex pricing

  • J. A. J. Hall
  • K. I. M. McKinnon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1184)


When solving linear programming problems using the revised simplex method, two common variants are the incorporation of minor iterations of the standard simplex method applied to a small subset of the variables and the use of Devex pricing. Although the extra work per iteration which is required when updating Devex weights removes the advantage of using minor iterations in a serial computation, the extra work parallelises readily. An asynchronous parallel algorithm PARSMI is presented in which computational components of the revised simplex method with Devex pricing are either overlapped or parallelism is exploited within them. Minor iterations are used to achieve good load balance and tackle problems caused by limited candidate persistence. Initial computational results for an six-processor implementation on a Cray T3D indicate that the algorithm has a significantly higher iteration rate than an efficient sequential implementation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Barriuso and A. Knies. SEMEM User's guide for Fortran. Cray Research inc.Google Scholar
  2. 2.
    R. E. Bixby and A. Martin. Parallelizing the dual simplex method. Technical Report SC-95-45, Konrad-Zuse-Zentrum für Informationstechnik Berlin, 1995.Google Scholar
  3. 3.
    D. M. Gay. Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter, 13:10–12, 1985.Google Scholar
  4. 4.
    A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM: Parallel Virtual Machine — A User's Guide and Tutorial for Networked Parallel Computing. MIT Press.Google Scholar
  5. 5.
    J. A. J. Hall and K. I. M. McKinnon. An asynchronous parallel revised simplex method algorithm. Technical Report MS 95-50, Department of Mathematics and Statistics, University of Edinburgh, 1995.Google Scholar
  6. 6.
    P. M. J. Harris. Pivot selection methods of the Devex LP code. Math. Prog., 5:1–28, 1973.Google Scholar
  7. 7.
    W. Shu and M. Wu. Sparse implementation of revised simplex algorithms on parallel computers. In Proceedings of 6 th SIAM Conference on Parallel Processing for Scientific Computing, pages 501–509, 1993.Google Scholar
  8. 8.
    R. Wunderling. Parallelizing the simplex algorithm. ILAY Workshop on Linear Algebra in Optimzation, Albi, April 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • J. A. J. Hall
    • 1
  • K. I. M. McKinnon
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of EdinburghUK

Personalised recommendations