IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v38y1991i1p71-85.html
   My bibliography  Save this article

Vector processing approach to constrained network problems

Author

Listed:
  • M. A. Venkataramana
  • John J. Dinkel
  • John Mote

Abstract

Modification of algorithms designed for scalar computing, to take advantage of vector processing, raises several challenges. This article presents the vectorization of the primal simplex based network algorithm and results in a 50% improvement in computational time. One of the major contributors to this improvement is the matching of the size of the pricing candidate list to the vector register size. The side constraints are relaxed into a single surrogate constraint. The single constraint network algorithm is vectorized and used as the basis for solving large‐scale constrained network problems. Computational experiments are presented which illustrate the vectorization of the network code as well as the ability of the surrogate constraint approach to deal with large constrained network problems.

Suggested Citation

  • M. A. Venkataramana & John J. Dinkel & John Mote, 1991. "Vector processing approach to constrained network problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 71-85, February.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:1:p:71-85
    DOI: 10.1002/1520-6750(199102)38:13.0.CO;2-6
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199102)38:13.0.CO;2-6
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199102)38:13.0.CO;2-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Stavros A. Zenios & John M. Mulvey, 1986. "Nonlinear Network Programming on Vector Supercomputers: A Study on the CRAY X-MP," Operations Research, INFORMS, vol. 34(5), pages 667-682, October.
    2. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    3. Ellis L. Johnson, 1966. "Networks and Basic Solutions," Operations Research, INFORMS, vol. 14(4), pages 619-623, August.
    4. McBride, Richard D., 1985. "Solving embedded generalized network problems," European Journal of Operational Research, Elsevier, vol. 21(1), pages 82-92, July.
    5. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    6. Mark H. Karwan & Ronald L. Rardin, 1984. "Surrogate Dual Multiplier Search Procedures in Integer Programming," Operations Research, INFORMS, vol. 32(1), pages 52-69, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marco Antonio Boschetti & Vittorio Maniezzo, 2022. "Matheuristics: using mathematics for heuristic design," 4OR, Springer, vol. 20(2), pages 173-208, June.
    2. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    3. Saïd Hanafi & Christophe Wilbaut, 2011. "Improved convergent heuristics for the 0-1 multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 183(1), pages 125-142, March.
    4. Sanjiv Sarin & Mark H. Karwan & Ronald L. Rardin, 1987. "A new surrogate dual multiplier search procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 431-450, June.
    5. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    6. S.-L. Kim & S. Kim, 1998. "Exact Algorithm for the Surrogate Dual of an Integer Programming Problem: Subgradient Method Approach," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 363-375, February.
    7. A. Ruszczynski, 1993. "Regularized Decomposition of Stochastic Programs: Algorithmic Techniques and Numerical Results," Working Papers wp93021, International Institute for Applied Systems Analysis.
    8. Ethem Çanakoğlu & İbrahim Muter & Tevfik Aytekin, 2021. "Integrating Individual and Aggregate Diversity in Top- N Recommendation," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 300-318, January.
    9. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    10. Sankaran, Jayaram K., 1995. "Column generation applied to linear programs in course registration," European Journal of Operational Research, Elsevier, vol. 87(2), pages 328-342, December.
    11. Metrane, Abdelmoutalib & Soumis, François & Elhallaoui, Issmail, 2010. "Column generation decomposition with the degenerate constraints in the subproblem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 37-44, November.
    12. Belanger, Nicolas & Desaulniers, Guy & Soumis, Francois & Desrosiers, Jacques, 2006. "Periodic airline fleet assignment with time windows, spacing constraints, and time dependent revenues," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1754-1766, December.
    13. Williams, R. Lynn & Dillion, Carl R. & McCarl, Bruce A., 1992. "An Economic Investigation of Edwards Aquifer Water Use Tradeoffs," WAEA/ WFEA Conference Archive (1929-1995) 321395, Western Agricultural Economics Association.
    14. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    15. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    16. Melanie Erhard, 2021. "Flexible staffing of physicians with column generation," Flexible Services and Manufacturing Journal, Springer, vol. 33(1), pages 212-252, March.
    17. Thomas W. M. Vossen & Dan Zhang, 2015. "Reductions of Approximate Linear Programs for Network Revenue Management," Operations Research, INFORMS, vol. 63(6), pages 1352-1371, December.
    18. Ternoy, Jacques Emmanuel, 1969. "Cooperation and economic efficiency," ISU General Staff Papers 196901010800004786, Iowa State University, Department of Economics.
    19. John N. Hooker, 2002. "Logic, Optimization, and Constraint Programming," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 295-321, November.
    20. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:38:y:1991:i:1:p:71-85. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.