IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v41y1993i2p319-337.html
   My bibliography  Save this article

A Massively Parallel Algorithm for Nonlinear Stochastic Network Problems

Author

Listed:
  • Soren S. Nielsen

    (The University of Texas, Austin, Texas)

  • Stavros A. Zenios

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

We develop an algorithm for solving nonlinear, two-stage stochastic problems with network recourse. The algorithm is based on the framework of row-action methods. The problem is formulated by replicating the first-stage variables and then adding nonanticipativity side constraints. A series of (independent) deterministic network problems are solved at each step of the algorithm, followed by an iterative step over the nonanticipativity constraints. The solution point of the iterates over the nonanticipativity constraints is obtained analytically. The row-action nature of the algorithm makes it suitable for parallel implementations. A data representation of the problem is developed that permits the massively parallel solution of all the scenario subproblems concurrently. The algorithm is implemented on a Connection Machine CM-2 with up to 32K processing elements and achieves computing rates of 276 MFLOPS. Very large problems—8,192 scenarios with a deterministic equivalent nonlinear program with 868,367 constraints and 2,474,017 variables—are solved within a few minutes. We report extensive numerical results regarding the effects of stochasticity on the efficiency of the algorithm.

Suggested Citation

  • Soren S. Nielsen & Stavros A. Zenios, 1993. "A Massively Parallel Algorithm for Nonlinear Stochastic Network Problems," Operations Research, INFORMS, vol. 41(2), pages 319-337, April.
  • Handle: RePEc:inm:oropre:v:41:y:1993:i:2:p:319-337
    DOI: 10.1287/opre.41.2.319
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.41.2.319
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Siva Sankaran & Tung Bui, 2008. "An organizational model for transitional negotiations: concepts, design and applications," Group Decision and Negotiation, Springer, vol. 17(2), pages 157-173, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:41:y:1993:i:2:p:319-337. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.